From 819258121d322fae360d0adfcdcfe42c57fa6fb9 Mon Sep 17 00:00:00 2001
From: jadep <jade.philipoom@gmail.com>
Date: Wed, 28 Jun 2017 19:29:53 -0400
Subject: Add wrappers for subborrow and add_with_get_carry so they work when
 it is not known that they split on a power of 2

---
 src/Util/ZUtil/AddGetCarry.v | 49 +++++++++++++++++++++++++++++++++-----------
 src/Util/ZUtil/Definitions.v | 12 +++++++++++
 2 files changed, 49 insertions(+), 12 deletions(-)

(limited to 'src')

diff --git a/src/Util/ZUtil/AddGetCarry.v b/src/Util/ZUtil/AddGetCarry.v
index 34f5f2ea8..18822cbe3 100644
--- a/src/Util/ZUtil/AddGetCarry.v
+++ b/src/Util/ZUtil/AddGetCarry.v
@@ -52,26 +52,51 @@ Module Z.
     Qed.
   End with_bitwidth.
 
-  Local Hint Unfold Z.add_get_carry_full Z.add_get_carry
-        Z.add_with_get_carry Z.get_carry Z.add_with_carry.
+  Local Ltac easypeasy :=
+    repeat progress autounfold;
+    break_match; autorewrite with cancel_pair zsimplify;
+    solve [repeat (f_equal; try ring)].
+
+  Local Hint Unfold Z.get_carry Z.get_borrow
+        Z.add_get_carry_full Z.add_with_get_carry_full
+        Z.add_get_carry Z.add_with_get_carry Z.add_with_carry
+        Z.sub_get_borrow_full Z.sub_with_get_borrow_full
+        Z.sub_get_borrow Z.sub_with_get_borrow Z.sub_with_borrow.
+  
   Lemma add_get_carry_full_mod s x y :
     fst (Z.add_get_carry_full s x y)  = (x + y) mod s.
-  Proof.
-    repeat progress autounfold.
-    break_match; autorewrite with cancel_pair zsimplify;
-      reflexivity.
-  Qed.
+  Proof. easypeasy. Qed.
 
   Lemma add_get_carry_full_div s x y :
     snd (Z.add_get_carry_full s x y)  = (x + y) / s.
-  Proof.
-    repeat progress autounfold.
-    break_match; autorewrite with cancel_pair zsimplify;
-      reflexivity.
-  Qed.
+  Proof. easypeasy. Qed.
+
+  Lemma add_with_get_carry_full_mod s c x y :
+    fst (Z.add_with_get_carry_full s c x y)  = (c + x + y) mod s.
+  Proof. easypeasy. Qed.
+
+  Lemma add_with_get_carry_full_div s c x y :
+    snd (Z.add_with_get_carry_full s c x y)  = (c + x + y) / s.
+  Proof. easypeasy. Qed.
 
   Lemma sub_with_borrow_to_add_get_carry c x y
     : Z.sub_with_borrow c x y = Z.add_with_carry (-c) x (-y).
   Proof. reflexivity. Qed.
 
+  Lemma sub_get_borrow_full_mod s x y :
+    fst (Z.sub_get_borrow_full s x y)  = (x - y) mod s.
+  Proof. easypeasy. Qed.
+
+  Lemma sub_get_borrow_full_div s x y :
+    snd (Z.sub_get_borrow_full s x y)  = - ((x - y) / s).
+  Proof. easypeasy. Qed.
+
+  Lemma sub_with_get_borrow_full_mod s c x y :
+    fst (Z.sub_with_get_borrow_full s c x y)  = (x - y - c) mod s.
+  Proof. easypeasy. Qed.
+
+  Lemma sub_with_get_borrow_full_div s c x y :
+    snd (Z.sub_with_get_borrow_full s c x y)  = - ((x - y - c) / s).
+  Proof. easypeasy. Qed.
+
 End Z.
diff --git a/src/Util/ZUtil/Definitions.v b/src/Util/ZUtil/Definitions.v
index f6892be13..d80b2bde5 100644
--- a/src/Util/ZUtil/Definitions.v
+++ b/src/Util/ZUtil/Definitions.v
@@ -35,6 +35,18 @@ Module Z.
     := if dec (2 ^ (Z.log2 bound) = bound)
        then add_get_carry (Z.log2 bound) x y
        else ((x + y) mod bound, (x + y) / bound).
+  Definition add_with_get_carry_full (bound : Z) (c x y : Z) : Z * Z
+    := if dec (2 ^ (Z.log2 bound) = bound)
+       then add_with_get_carry (Z.log2 bound) c x y
+       else ((c + x + y) mod bound, (c + x + y) / bound).
+  Definition sub_get_borrow_full (bound : Z) (x y : Z) : Z * Z
+    := if dec (2 ^ (Z.log2 bound) = bound)
+       then sub_get_borrow (Z.log2 bound) x y
+       else ((x - y) mod bound, -((x - y) / bound)).
+  Definition sub_with_get_borrow_full (bound : Z) (c x y : Z) : Z * Z
+    := if dec (2 ^ (Z.log2 bound) = bound)
+       then sub_with_get_borrow (Z.log2 bound) c x y
+       else ((x - y - c) mod bound, -((x - y - c) / bound)).
 
   Definition mul_split_at_bitwidth (bitwidth : Z) (x y : Z) : Z * Z
     := dlet xy := x * y in
-- 
cgit v1.2.3


From 23849ac14d910792b98f58c665bed85dd9c5088e Mon Sep 17 00:00:00 2001
From: jadep <jade.philipoom@gmail.com>
Date: Wed, 28 Jun 2017 19:40:18 -0400
Subject: Skeleton for add/subtract chains (see #222)

---
 src/Arithmetic/Saturated.v | 88 ++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 88 insertions(+)

(limited to 'src')

diff --git a/src/Arithmetic/Saturated.v b/src/Arithmetic/Saturated.v
index 619d97c4a..a63208e9e 100644
--- a/src/Arithmetic/Saturated.v
+++ b/src/Arithmetic/Saturated.v
@@ -171,6 +171,94 @@ Hint Opaque Associational.mul Associational.multerm : uncps.
 Hint Rewrite @Associational.mul_id @Associational.multerm_id : uncps.
 Hint Rewrite @Associational.eval_mul @Associational.eval_map_multerm using (omega || assumption) : push_basesystem_eval.
 
+Module Positional.
+  Section Positional.
+    Context (weight : nat->Z) {s:Z}. (* s is number at which to split *)
+    Section GenericOp.
+      Context {op : Z -> Z -> Z}
+              {op_get_carry : Z -> Z -> Z * Z} (* no carry in, carry out *)
+              {op_with_carry : Z -> Z -> Z -> Z * Z}. (* carry in, carry out  *)
+
+      Fixpoint chain_op'_cps {n}:
+        option Z->Z^n->Z^n->forall T, (Z*Z^n->T)->T :=
+        match n with
+        | O => fun c p _ _ f =>
+                 let carry := match c with | None => 0 | Some x => x end in
+                 f (carry,p)
+        | S n' =>
+          fun c p q _ f =>
+            (* for the first call, use op_get_carry, then op_with_carry *)
+            let op' := match c with
+                       | None => op_get_carry
+                       | Some x => op_with_carry x end in
+            dlet carry_result := op' (hd p) (hd q) in
+              chain_op'_cps (Some (fst carry_result)) (tl p) (tl q) _
+                            (fun carry_pq =>
+                               f (fst carry_pq,
+                                  append (snd carry_result) (snd carry_pq)))
+        end.
+      Definition chain_op' {n} c p q := @chain_op'_cps n c p q _ id.
+      Definition chain_op_cps {n} p q {T} f := @chain_op'_cps n None p q T f.
+      Definition chain_op {n} p q : Z * Z^n := chain_op_cps p q id.
+
+      Lemma chain_op'_id {n} : forall c p q T f,
+        @chain_op'_cps n c p q T f = f (chain_op' c p q).
+      Proof.
+        cbv [chain_op']; induction n; intros; destruct c;
+          simpl chain_op'_cps; cbv [Let_In]; try reflexivity.
+        { etransitivity; rewrite IHn; reflexivity. }
+        { etransitivity; rewrite IHn; reflexivity. }
+      Qed.
+
+      Lemma chain_op_id {n} p q T f :
+        @chain_op_cps n p q T f = f (chain_op p q).
+      Proof. apply chain_op'_id. Qed.
+    End GenericOp.
+
+    Section AddSub.
+      Local Definition eval {n} := B.Positional.eval (n:=n) weight.
+      
+      Definition sat_add_cps {n} p q T (f:Z*Z^n->T) :=
+        chain_op_cps (op_get_carry := Z.add_get_carry_full s)
+                     (op_with_carry := Z.add_with_get_carry_full s)
+                     p q f.
+      Definition sat_add {n} p q := @sat_add_cps n p q _ id.
+
+      Lemma sat_add_id n p q T f :
+        @sat_add_cps n p q T f = f (sat_add p q).
+      Proof. cbv [sat_add sat_add_cps]. rewrite !chain_op_id. reflexivity. Qed.
+
+      Lemma sat_add_mod n p q :
+        eval (snd (@sat_add n p q)) = (eval p + eval q) mod s.
+      Admitted.
+
+      Lemma sat_add_div n p q :
+        fst (@sat_add n p q) = (eval p + eval q) / s.
+      Admitted.
+      
+      Definition sat_sub_cps {n} p q T (f:Z*Z^n->T) :=
+        chain_op_cps (op_get_carry := Z.sub_get_borrow_full s)
+                     (op_with_carry := Z.sub_with_get_borrow_full s)
+                     p q f.
+      Definition sat_sub {n} p q := @sat_sub_cps n p q _ id.
+
+      Lemma sat_sub_id n p q T f :
+        @sat_sub_cps n p q T f = f (sat_sub p q).
+      Proof. cbv [sat_sub sat_sub_cps]. rewrite !chain_op_id. reflexivity. Qed.
+
+      Lemma sat_sub_mod n p q :
+        eval (snd (@sat_sub n p q)) = (eval p - eval q) mod s.
+      Admitted.
+
+      Lemma sat_sub_div n p q :
+        fst (@sat_sub n p q) = - ((eval p - eval q) / s).
+      Admitted.
+                 
+    End Add.
+  End Positional.
+End Positional.
+
+
 Module Columns.
   Section Columns.
     Context (weight : nat->Z)
-- 
cgit v1.2.3


From 878b1b98ffa72f4d1f356fa5722153f89a0d9ee6 Mon Sep 17 00:00:00 2001
From: jadep <jade.philipoom@gmail.com>
Date: Thu, 29 Jun 2017 09:43:09 -0400
Subject: new add/carry chain logic with admitted proofs

---
 src/Arithmetic/Saturated.v | 363 +++++++++++++++++++++++----------------------
 1 file changed, 183 insertions(+), 180 deletions(-)

(limited to 'src')

diff --git a/src/Arithmetic/Saturated.v b/src/Arithmetic/Saturated.v
index a63208e9e..a7b9e6484 100644
--- a/src/Arithmetic/Saturated.v
+++ b/src/Arithmetic/Saturated.v
@@ -171,93 +171,6 @@ Hint Opaque Associational.mul Associational.multerm : uncps.
 Hint Rewrite @Associational.mul_id @Associational.multerm_id : uncps.
 Hint Rewrite @Associational.eval_mul @Associational.eval_map_multerm using (omega || assumption) : push_basesystem_eval.
 
-Module Positional.
-  Section Positional.
-    Context (weight : nat->Z) {s:Z}. (* s is number at which to split *)
-    Section GenericOp.
-      Context {op : Z -> Z -> Z}
-              {op_get_carry : Z -> Z -> Z * Z} (* no carry in, carry out *)
-              {op_with_carry : Z -> Z -> Z -> Z * Z}. (* carry in, carry out  *)
-
-      Fixpoint chain_op'_cps {n}:
-        option Z->Z^n->Z^n->forall T, (Z*Z^n->T)->T :=
-        match n with
-        | O => fun c p _ _ f =>
-                 let carry := match c with | None => 0 | Some x => x end in
-                 f (carry,p)
-        | S n' =>
-          fun c p q _ f =>
-            (* for the first call, use op_get_carry, then op_with_carry *)
-            let op' := match c with
-                       | None => op_get_carry
-                       | Some x => op_with_carry x end in
-            dlet carry_result := op' (hd p) (hd q) in
-              chain_op'_cps (Some (fst carry_result)) (tl p) (tl q) _
-                            (fun carry_pq =>
-                               f (fst carry_pq,
-                                  append (snd carry_result) (snd carry_pq)))
-        end.
-      Definition chain_op' {n} c p q := @chain_op'_cps n c p q _ id.
-      Definition chain_op_cps {n} p q {T} f := @chain_op'_cps n None p q T f.
-      Definition chain_op {n} p q : Z * Z^n := chain_op_cps p q id.
-
-      Lemma chain_op'_id {n} : forall c p q T f,
-        @chain_op'_cps n c p q T f = f (chain_op' c p q).
-      Proof.
-        cbv [chain_op']; induction n; intros; destruct c;
-          simpl chain_op'_cps; cbv [Let_In]; try reflexivity.
-        { etransitivity; rewrite IHn; reflexivity. }
-        { etransitivity; rewrite IHn; reflexivity. }
-      Qed.
-
-      Lemma chain_op_id {n} p q T f :
-        @chain_op_cps n p q T f = f (chain_op p q).
-      Proof. apply chain_op'_id. Qed.
-    End GenericOp.
-
-    Section AddSub.
-      Local Definition eval {n} := B.Positional.eval (n:=n) weight.
-      
-      Definition sat_add_cps {n} p q T (f:Z*Z^n->T) :=
-        chain_op_cps (op_get_carry := Z.add_get_carry_full s)
-                     (op_with_carry := Z.add_with_get_carry_full s)
-                     p q f.
-      Definition sat_add {n} p q := @sat_add_cps n p q _ id.
-
-      Lemma sat_add_id n p q T f :
-        @sat_add_cps n p q T f = f (sat_add p q).
-      Proof. cbv [sat_add sat_add_cps]. rewrite !chain_op_id. reflexivity. Qed.
-
-      Lemma sat_add_mod n p q :
-        eval (snd (@sat_add n p q)) = (eval p + eval q) mod s.
-      Admitted.
-
-      Lemma sat_add_div n p q :
-        fst (@sat_add n p q) = (eval p + eval q) / s.
-      Admitted.
-      
-      Definition sat_sub_cps {n} p q T (f:Z*Z^n->T) :=
-        chain_op_cps (op_get_carry := Z.sub_get_borrow_full s)
-                     (op_with_carry := Z.sub_with_get_borrow_full s)
-                     p q f.
-      Definition sat_sub {n} p q := @sat_sub_cps n p q _ id.
-
-      Lemma sat_sub_id n p q T f :
-        @sat_sub_cps n p q T f = f (sat_sub p q).
-      Proof. cbv [sat_sub sat_sub_cps]. rewrite !chain_op_id. reflexivity. Qed.
-
-      Lemma sat_sub_mod n p q :
-        eval (snd (@sat_sub n p q)) = (eval p - eval q) mod s.
-      Admitted.
-
-      Lemma sat_sub_div n p q :
-        fst (@sat_sub n p q) = - ((eval p - eval q) / s).
-      Admitted.
-                 
-    End Add.
-  End Positional.
-End Positional.
-
 
 Module Columns.
   Section Columns.
@@ -795,8 +708,108 @@ Section UniformWeight.
     ring.
   Qed.
 
+  Definition small {n} (p : Z^n) : Prop :=
+    forall x, In x (to_list _ p) -> 0 <= x < bound.
+
 End UniformWeight.
 
+Module Positional.
+  Section Positional.
+    Context {s:Z}. (* s is bitwidth *)
+    Let small {n} := @small s n.
+    Section GenericOp.
+      Context {op : Z -> Z -> Z}
+              {op_get_carry : Z -> Z -> Z * Z} (* no carry in, carry out *)
+              {op_with_carry : Z -> Z -> Z -> Z * Z}. (* carry in, carry out  *)
+
+      Fixpoint chain_op'_cps {n}:
+        option Z->Z^n->Z^n->forall T, (Z*Z^n->T)->T :=
+        match n with
+        | O => fun c p _ _ f =>
+                 let carry := match c with | None => 0 | Some x => x end in
+                 f (carry,p)
+        | S n' =>
+          fun c p q _ f =>
+            (* for the first call, use op_get_carry, then op_with_carry *)
+            let op' := match c with
+                       | None => op_get_carry
+                       | Some x => op_with_carry x end in
+            dlet carry_result := op' (hd p) (hd q) in
+              chain_op'_cps (Some (fst carry_result)) (tl p) (tl q) _
+                            (fun carry_pq =>
+                               f (fst carry_pq,
+                                  append (snd carry_result) (snd carry_pq)))
+        end.
+      Definition chain_op' {n} c p q := @chain_op'_cps n c p q _ id.
+      Definition chain_op_cps {n} p q {T} f := @chain_op'_cps n None p q T f.
+      Definition chain_op {n} p q : Z * Z^n := chain_op_cps p q id.
+
+      Lemma chain_op'_id {n} : forall c p q T f,
+        @chain_op'_cps n c p q T f = f (chain_op' c p q).
+      Proof.
+        cbv [chain_op']; induction n; intros; destruct c;
+          simpl chain_op'_cps; cbv [Let_In]; try reflexivity.
+        { etransitivity; rewrite IHn; reflexivity. }
+        { etransitivity; rewrite IHn; reflexivity. }
+      Qed.
+
+      Lemma chain_op_id {n} p q T f :
+        @chain_op_cps n p q T f = f (chain_op p q).
+      Proof. apply chain_op'_id. Qed.
+    End GenericOp.
+
+    Section AddSub.
+      Let eval {n} := B.Positional.eval (n:=n) (uweight s).
+      
+      Definition sat_add_cps {n} p q T (f:Z*Z^n->T) :=
+        chain_op_cps (op_get_carry := Z.add_get_carry_full s)
+                     (op_with_carry := Z.add_with_get_carry_full s)
+                     p q f.
+      Definition sat_add {n} p q := @sat_add_cps n p q _ id.
+
+      Lemma sat_add_id n p q T f :
+        @sat_add_cps n p q T f = f (sat_add p q).
+      Proof. cbv [sat_add sat_add_cps]. rewrite !chain_op_id. reflexivity. Qed.
+
+      Lemma sat_add_mod n p q :
+        eval (snd (@sat_add n p q)) = (eval p + eval q) mod (uweight s n).
+      Admitted.
+
+      Lemma sat_add_div n p q :
+        fst (@sat_add n p q) = (eval p + eval q) / (uweight s n).
+      Admitted.
+
+      Lemma small_sat_add n p q : small (snd (@sat_add n p q)).
+      Admitted.
+      
+      Definition sat_sub_cps {n} p q T (f:Z*Z^n->T) :=
+        chain_op_cps (op_get_carry := Z.sub_get_borrow_full s)
+                     (op_with_carry := Z.sub_with_get_borrow_full s)
+                     p q f.
+      Definition sat_sub {n} p q := @sat_sub_cps n p q _ id.
+
+      Lemma sat_sub_id n p q T f :
+        @sat_sub_cps n p q T f = f (sat_sub p q).
+      Proof. cbv [sat_sub sat_sub_cps]. rewrite !chain_op_id. reflexivity. Qed.
+
+      Lemma sat_sub_mod n p q :
+        eval (snd (@sat_sub n p q)) = (eval p - eval q) mod (uweight s n).
+      Admitted.
+
+      Lemma sat_sub_div n p q :
+        fst (@sat_sub n p q) = - ((eval p - eval q) / uweight s n).
+      Admitted.
+
+      Lemma small_sat_sub n p q : small (snd (@sat_sub n p q)).
+      Admitted.
+                 
+    End AddSub.
+  End Positional.
+End Positional.
+Hint Opaque Positional.sat_sub Positional.sat_add Positional.chain_op Positional.chain_op' : uncps.
+Hint Rewrite @Positional.sat_sub_id @Positional.sat_add_id @Positional.chain_op_id @Positional.chain_op' : uncps.
+Hint Rewrite @Positional.sat_sub_mod @Positional.sat_sub_div @Positional.sat_add_mod @Positional.sat_add_div using (omega || assumption) : push_basesystem_eval.
+
 Section API.
   Context (bound : Z) {bound_pos : bound > 0}.
   Definition T : nat -> Type := tuple Z.
@@ -804,8 +817,7 @@ Section API.
   (* lowest limb is less than its bound; this is required for [divmod]
   to simply separate the lowest limb from the rest and be equivalent
   to normal div/mod with [bound]. *)
-  Definition small {n} (p : T n) : Prop :=
-    forall x, In x (to_list _ p) -> 0 <= x < bound.
+  Local Notation small := (@small bound).
 
   Definition zero {n:nat} : T n := B.Positional.zeros n.
 
@@ -835,21 +847,33 @@ Section API.
       (fun carry_result =>f (snd carry_result)).
   Definition scmul {n} c p : T (S n) := @scmul_cps n c p _ id.
 
-  Definition add_cps {n m pred_nm} (p : T n) (q : T m) {R} (f:T (S pred_nm)->R) :=
-    Columns.add_cps (uweight bound) p q
-      (fun carry_result => Tuple.left_append_cps (fst carry_result) (snd carry_result)
-      f).
-  Definition add {n m pred_nm} p q : T (S pred_nm) := @add_cps n m pred_nm p q _ id.
-
-  Definition sub_then_maybe_add_cps {n} mask (p q r : T n) {R} (f:T n -> R) :=
-    Columns.unbalanced_sub_cps (n3:=n) (uweight bound) p q
+  Definition add_cps {n} (p q: T n) {R} (f:T n->R) :=
+    Positional.sat_add_cps (s:=bound) p q _
+      (* drops last carry, this relies on bounds *)
+      (fun carry_result => f (snd carry_result)).
+  Definition add {n} p q : T n := @add_cps n p q _ id.
+
+  (* Wrappers for additions with slightly uneven limb counts *)
+  Definition add_S1_cps {n} (p: T (S n)) (q: T n) {R} (f:T (S n)->R) :=
+    join0_cps q (fun Q => add_cps p Q f).
+  Definition add_S1 {n} p q := @add_S1_cps n p q _ id. 
+  Definition add_S2_cps {n} (p: T n) (q: T (S n)) {R} (f:T (S n)->R) :=
+    join0_cps p (fun P => add_cps P q f).
+  Definition add_S2 {n} p q := @add_S2_cps n p q _ id. 
+
+  Definition sub_then_maybe_add_cps {n} mask (p q r : T n)
+             {R} (f:T n -> R) :=
+    Positional.sat_sub_cps (s:=bound) p q _
       (* the carry will be 0 unless we underflow--we do the addition only
          in the underflow case *)
       (fun carry_result =>
-         Columns.conditional_add_cps (uweight bound) mask (fst carry_result) (left_append (fst carry_result) (snd carry_result)) r
-      (* We can now safely discard the carry. This relies on the
-         precondition that p - q + r < bound^n. *)
-      (fun carry_result' => f (snd carry_result'))).
+         B.Positional.select_cps mask (fst carry_result) r
+      (fun selected => join0_cps selected
+      (fun selected' =>
+         Positional.sat_sub_cps (s:=bound) (left_append (fst carry_result) (snd carry_result)) selected' _
+      (* We can now safely discard the carry and the highest digit.
+         This relies on the precondition that p - q + r < bound^n. *)
+      (fun carry_result' => drop_high_cps (snd carry_result') f)))).
   Definition sub_then_maybe_add {n} mask (p q r : T n) :=
     sub_then_maybe_add_cps mask p q r id.
 
@@ -857,14 +881,15 @@ Section API.
     that 0 <= p < 2*q and q < bound^n (this ensures the output is less
     than bound^n). *)
   Definition conditional_sub_cps {n} (p:Z^S n) (q:Z^n) R (f:Z^n->R) :=
-    Columns.unbalanced_sub_cps (n3:=S n) (uweight bound) p q
+    join0_cps q
+    (fun qq => Positional.sat_sub_cps (s:=bound) p qq _
       (* if carry is zero, we select the result of the subtraction,
       otherwise the first input *)
       (fun carry_result =>
         Tuple.map2_cps (Z.zselect (fst carry_result)) (snd carry_result) p
       (* in either case, since our result must be < q and therefore <
       bound^n, we can drop the high digit *)
-      (fun r => drop_high_cps r f)).
+      (fun r => drop_high_cps r f))).
   Definition conditional_sub {n} p q := @conditional_sub_cps n p q _ id.
 
   Hint Opaque join0 divmod drop_high scmul add sub_then_maybe_add conditional_sub : uncps.
@@ -894,17 +919,26 @@ Section API.
       @scmul_cps n c p R f = f (scmul c p).
     Proof. cbv [scmul_cps scmul]. prove_id. Qed.
 
-    Lemma add_id n m pred_nm p q R f :
-      @add_cps n m pred_nm p q R f = f (add p q).
+    Lemma add_id n p q R f :
+      @add_cps n p q R f = f (add p q).
     Proof. cbv [add_cps add Let_In]. prove_id. Qed.
+    Hint Rewrite add_id : uncps.
+    
+    Lemma add_S1_id n p q R f :
+      @add_S1_cps n p q R f = f (add_S1 p q).
+    Proof. cbv [add_S1_cps add_S1 join0_cps]. prove_id. Qed.
+    
+    Lemma add_S2_id n p q R f :
+      @add_S2_cps n p q R f = f (add_S2 p q).
+    Proof. cbv [add_S2_cps add_S2 join0_cps]. prove_id. Qed.
 
     Lemma sub_then_maybe_add_id n mask p q r R f :
       @sub_then_maybe_add_cps n mask p q r R f = f (sub_then_maybe_add mask p q r).
-    Proof. cbv [sub_then_maybe_add_cps sub_then_maybe_add Let_In]. prove_id. Qed.
+    Proof. cbv [sub_then_maybe_add_cps sub_then_maybe_add join0_cps Let_In]. prove_id. Qed.
 
     Lemma conditional_sub_id n p q R f :
       @conditional_sub_cps n p q R f = f (conditional_sub p q).
-    Proof. cbv [conditional_sub_cps conditional_sub Let_In]. prove_id. Qed.
+    Proof. cbv [conditional_sub_cps conditional_sub join0_cps Let_In]. prove_id. Qed.
 
   End CPSProofs.
   Hint Rewrite nonzero_id join0_id divmod_id drop_high_id scmul_id add_id sub_then_maybe_add_id conditional_sub_id : uncps.
@@ -1005,13 +1039,13 @@ Section API.
       pose proof Z.mul_split_div; pose proof Z.mul_split_mod;
       pose proof div_correct; pose proof modulo_correct.
 
-    Lemma eval_add_nz n m pred_nm p q :
-      pred_nm <> 0%nat ->
-      eval (@add n m pred_nm p q) = eval p + eval q.
+    Lemma eval_add_nz n p q :
+      n <> 0%nat -> (0 <= eval p + eval q < uweight bound n) ->
+      eval (@add n p q) = eval p + eval q.
     Proof.
       intros. pose_all.
       repeat match goal with
-             | _ => progress (cbv [add_cps add eval Let_In]; repeat autounfold)
+             | _ => progress (cbv [add_cps add eval Let_In] in *; repeat autounfold)
              | _ => progress autorewrite with uncps push_id cancel_pair push_basesystem_eval
              | _ => rewrite B.Positional.eval_left_append
 
@@ -1019,33 +1053,36 @@ Section API.
                       (rewrite <-!from_list_default_eq with (d:=0);
                        erewrite !length_to_list, !from_list_default_eq,
                        from_list_to_list)
-             | _ => rewrite Z.mul_div_eq by auto;
-                      omega
+             | _ => apply Z.mod_small; omega 
              end.
     Qed.
 
-    Lemma eval_add_z n m pred_nm p q :
-      pred_nm = 0%nat ->
+    Lemma eval_add_z n p q :
       n = 0%nat ->
-      m = 0%nat ->
-      eval (@add n m pred_nm p q) = eval p + eval q.
+      eval (@add n p q) = eval p + eval q.
     Proof. intros; subst; reflexivity. Qed.
 
-    Lemma eval_add n m pred_nm p q (Hpred_nm : pred_nm = 0%nat -> n = 0%nat /\ m = 0%nat)
-      :  eval (@add n m pred_nm p q) = eval p + eval q.
+    Lemma eval_add n p q (H:0 <= eval p + eval q < uweight bound n)
+      :  eval (@add n p q) = eval p + eval q.
     Proof.
-      destruct (Nat.eq_dec pred_nm 0%nat); intuition auto using eval_add_z, eval_add_nz.
+      destruct (Nat.eq_dec n 0%nat); intuition auto using eval_add_z, eval_add_nz.
     Qed.
-    Lemma eval_add_same n p q
-      :  eval (@add n n n p q) = eval p + eval q.
-    Proof. apply eval_add; omega. Qed.
-    Lemma eval_add_S1 n p q
-      :  eval (@add (S n) n (S n) p q) = eval p + eval q.
+    Lemma eval_add_same n p q (H:0 <= eval p + eval q < uweight bound n)
+      :  eval (@add n p q) = eval p + eval q.
     Proof. apply eval_add; omega. Qed.
-    Lemma eval_add_S2 n p q
-      :  eval (@add n (S n) (S n) p q) = eval p + eval q.
-    Proof. apply eval_add; omega. Qed.
-    Hint Rewrite eval_add_same eval_add_S1 eval_add_S2 : push_basesystem_eval.
+    Lemma eval_add_S1 n p q (H:0 <= eval p + eval q < uweight bound (S n))
+      :  eval (@add_S1 n p q) = eval p + eval q.
+    Proof.
+      cbv [add_S1 add_S1_cps]. autorewrite with uncps push_id.
+      rewrite eval_add; rewrite eval_join0; [reflexivity|assumption].
+    Qed.
+    Lemma eval_add_S2 n p q (H:0 <= eval p + eval q < uweight bound (S n))
+      :  eval (@add_S2 n p q) = eval p + eval q.
+    Proof.
+      cbv [add_S2 add_S2_cps]. autorewrite with uncps push_id.
+      rewrite eval_add; rewrite eval_join0; [reflexivity|assumption].
+    Qed.
+    Hint Rewrite eval_add_same eval_add_S1 eval_add_S2 using (omega || assumption): push_basesystem_eval.
 
     Lemma uweight_le_mono n m : (n <= m)%nat ->
       uweight bound n <= uweight bound m.
@@ -1104,43 +1141,15 @@ Section API.
         apply Z.mod_pos_bound, Z.gt_lt, bound_pos. }
     Qed.
 
-    Lemma small_add n m pred_nm a b :
-      (2 <= bound) -> (max n m <= pred_nm)%nat ->
-      small a -> small b -> small (@add n m pred_nm a b).
+    Lemma small_add n a b :
+      (2 <= bound) -> 
+      small a -> small b -> small (@add n a b).
     Proof.
       intros. pose_all.
-      cbv [small add_cps add Let_In]. repeat autounfold.
+      cbv [add_cps add Let_In].
       autorewrite with uncps push_id.
-      rewrite Tuple.to_list_left_append.
-      let H := fresh "H" in intros x H; apply in_app_or in H;
-                              destruct H as [H | H];
-                              [apply (small_compact _ _ H)
-                              |destruct H; [|exfalso; assumption] ].
-      subst x.
-      rewrite Columns.compact_div by assumption.
-      repeat match goal with
-               H : small ?x |- _ => apply eval_small in H; cbv [eval] in H
-             end.
-      destruct pred_nm as [|pred_pred_nm]; autorewrite with push_basesystem_eval;
-        repeat match goal with
-               | [ H : (max ?x ?y <= 0)%nat |- _ ]
-                 => assert (x = 0%nat) by omega *;
-                      assert (y = 0%nat) by omega *;
-                      clear H
-               | _ => progress subst
-               end.
-      { destruct bound; cbv -[Z.le Z.lt]; lia. }
-      split; [ solve [ unfold uweight in *; Z.zero_bounds ] | ].
-      apply Zdiv_lt_upper_bound; [ solve [ unfold uweight in *; Z.zero_bounds ] | ].
-      apply Z.lt_le_trans with (m:=uweight bound n + uweight bound m);
-          [omega|].
-      apply Z.le_trans with (m:=uweight bound (max n m) + uweight bound (max n m)); auto using Z.add_le_mono, uweight_le_mono, Max.le_max_l, Max.le_max_r.
-      rewrite Z.add_diag.
-      pose proof (uweight_le_mono (max n m) (S pred_pred_nm)).
-      specialize_by_assumption.
-      apply Z.mul_le_mono_nonneg; try omega.
-      apply Max.max_case_strong; omega.
-    Qed.
+      apply Positional.small_sat_add.
+    Admitted.
 
     Lemma small_left_tl n (v:T (S n)) : small v -> small (left_tl v).
     Proof. cbv [small]. auto using Tuple.In_to_list_left_tl. Qed.
@@ -1190,29 +1199,22 @@ Section API.
              | _ => progress (cbv [sub_then_maybe_add sub_then_maybe_add_cps eval] in *; intros)
              | _ => progress autounfold
              | _ => progress autorewrite with uncps push_id push_basesystem_eval
+             | _ => rewrite eval_drop_high
+             | _ => rewrite eval_join0
              | H : small _ |- _ => apply eval_small in H
              | _ => progress break_match
              | _ => (rewrite Z.add_opp_r in * )
-             | _ => progress autorewrite with zsimplify; [ ]
              | H : _ |- _ => rewrite Z.ltb_lt in H;
                                rewrite <-div_nonzero_neg_iff with
                                (y:=uweight bound n) in H by (auto; omega)
              | H : _ |- _ => rewrite Z.ltb_ge in H
              | _ => rewrite Z.mod_small by omega
              | _ => omega
-             end;
-      repeat match goal with
-             | H : _ |- _ => rewrite div_nonzero_neg_iff in H
-                 by (auto; omega)
-             | |- context [-?x + ?y mod ?x] =>
-               replace (-x + y mod x) with y
-                 by (rewrite Z.mod_eq, Z.div_small_neg; omega)
-             | _ => apply Z.mod_small; omega
-             | _ => omega
+             | _ => progress autorewrite with zsimplify; [ ]
              end.
-    Qed.
+    Admitted.
 
-    Lemma eval_sub_then_maybe_add n mask p q r:
+    Lemma eval_sub_then_maybe_add n mask p q r :
       small p -> small q -> small r ->
       (map (Z.land mask) r = r) ->
       (0 <= eval p < eval r) -> (0 <= eval q < eval r) ->
@@ -1227,7 +1229,7 @@ Section API.
    Proof.
      cbv [sub_then_maybe_add_cps sub_then_maybe_add]; intros.
      repeat progress autounfold. autorewrite with uncps push_id.
-     apply small_compact.
+     apply small_drop_high, Positional.small_sat_sub.
    Qed.
 
    (* TODO : remove if unneeded when all admits are proven
@@ -1277,12 +1279,13 @@ Section API.
                | _ => progress cbv [eval]
                | H : (_ <=? _) = true |- _ => apply Z.leb_le in H
                | H : (_ <=? _) = false |- _ => apply Z.leb_gt in H
-               | _ => rewrite eval_drop_high by auto using small_compact
+               | _ => rewrite eval_drop_high by auto using Positional.small_sat_sub
+               | _ => (rewrite eval_join0 in * )
                | _ => progress autorewrite with uncps push_id push_basesystem_eval
-               | _ => rewrite Z.mod_small by (rewrite ?Z.mod_small; omega)
+               | _ => repeat rewrite Z.mod_small; omega
                | _ => omega
                end.
-   Qed.
+    Admitted.
 
     Lemma eval_conditional_sub n (p:T (S n)) (q:T n)
            (psmall : small p) (qsmall : small q) :
@@ -1391,4 +1394,4 @@ Definition base2pow25p5 i := Eval compute in 2^(25*Z.of_nat i + ((Z.of_nat i + 1
 Time Eval cbv -[runtime_add runtime_mul Let_In] in
     (fun adc a0 a1 a2 a3 a4 a5 a6 a7 a8 a9 b0 b1 b2 b3 b4 b5 b6 b7 b8 b9 =>
        Columns.mul_cps (weight := base2pow25p5) (n:=10) (a9,a8,a7,a6,a5,a4,a3,a2,a1,a0) (b9,b8,b7,b6,b5,b4,b3,b2,b1,b0) (fun ab => Columns.compact (n:=19) (add_get_carry:=adc) (weight:=base2pow25p5) ab)). (* Finished transaction in 97.341 secs *)
-*)
+*)
\ No newline at end of file
-- 
cgit v1.2.3


From 0ff642cd6a6901c3fb0805092df40f5432280ef1 Mon Sep 17 00:00:00 2001
From: Jason Gross <jgross@mit.edu>
Date: Thu, 29 Jun 2017 13:04:32 -0400
Subject: Fix type signatures of saturated things for WBW

This required admitting some proofs.  @jadephilipoom, please
sanity-check this.
---
 src/Arithmetic/Saturated.v | 80 +++++++++++++++++++++++++++++-----------------
 1 file changed, 50 insertions(+), 30 deletions(-)

(limited to 'src')

diff --git a/src/Arithmetic/Saturated.v b/src/Arithmetic/Saturated.v
index a7b9e6484..5ecb5eebd 100644
--- a/src/Arithmetic/Saturated.v
+++ b/src/Arithmetic/Saturated.v
@@ -674,7 +674,7 @@ Section UniformWeight.
     B.Positional.eval wt p = B.Positional.eval_from uweight offset p.
   Proof. cbv [B.Positional.eval_from]. auto using B.Positional.eval_wt_equiv. Qed.
 
-  Lemma uweight_eval_from {n} (p:Z^n): forall offset, 
+  Lemma uweight_eval_from {n} (p:Z^n): forall offset,
     B.Positional.eval_from uweight offset p = uweight offset * B.Positional.eval uweight p.
   Proof.
     induction n; intros; cbv [B.Positional.eval_from];
@@ -683,7 +683,7 @@ Section UniformWeight.
            | _ => destruct p
            | _ => rewrite B.Positional.eval_unit; [ ]
            | _ => rewrite B.Positional.eval_step; [ ]
-           | _ => rewrite IHn; [ ] 
+           | _ => rewrite IHn; [ ]
            | _ => rewrite eval_from_eq with (offset0:=S offset)
                by (intros; f_equal; omega)
            | _ => rewrite eval_from_eq with
@@ -760,7 +760,7 @@ Module Positional.
 
     Section AddSub.
       Let eval {n} := B.Positional.eval (n:=n) (uweight s).
-      
+
       Definition sat_add_cps {n} p q T (f:Z*Z^n->T) :=
         chain_op_cps (op_get_carry := Z.add_get_carry_full s)
                      (op_with_carry := Z.add_with_get_carry_full s)
@@ -781,7 +781,7 @@ Module Positional.
 
       Lemma small_sat_add n p q : small (snd (@sat_add n p q)).
       Admitted.
-      
+
       Definition sat_sub_cps {n} p q T (f:Z*Z^n->T) :=
         chain_op_cps (op_get_carry := Z.sub_get_borrow_full s)
                      (op_with_carry := Z.sub_with_get_borrow_full s)
@@ -802,7 +802,7 @@ Module Positional.
 
       Lemma small_sat_sub n p q : small (snd (@sat_sub n p q)).
       Admitted.
-                 
+
     End AddSub.
   End Positional.
 End Positional.
@@ -847,19 +847,19 @@ Section API.
       (fun carry_result =>f (snd carry_result)).
   Definition scmul {n} c p : T (S n) := @scmul_cps n c p _ id.
 
-  Definition add_cps {n} (p q: T n) {R} (f:T n->R) :=
+  Definition add_cps {n} (p q: T n) {R} (f:T (S n)->R) :=
     Positional.sat_add_cps (s:=bound) p q _
-      (* drops last carry, this relies on bounds *)
-      (fun carry_result => f (snd carry_result)).
-  Definition add {n} p q : T n := @add_cps n p q _ id.
+      (* join the last carry *)
+      (fun carry_result => Tuple.left_append_cps (fst carry_result) (snd carry_result) f).
+  Definition add {n} p q : T (S n) := @add_cps n p q _ id.
 
   (* Wrappers for additions with slightly uneven limb counts *)
-  Definition add_S1_cps {n} (p: T (S n)) (q: T n) {R} (f:T (S n)->R) :=
+  Definition add_S1_cps {n} (p: T (S n)) (q: T n) {R} (f:T (S (S n))->R) :=
     join0_cps q (fun Q => add_cps p Q f).
-  Definition add_S1 {n} p q := @add_S1_cps n p q _ id. 
-  Definition add_S2_cps {n} (p: T n) (q: T (S n)) {R} (f:T (S n)->R) :=
+  Definition add_S1 {n} p q := @add_S1_cps n p q _ id.
+  Definition add_S2_cps {n} (p: T n) (q: T (S n)) {R} (f:T (S (S n))->R) :=
     join0_cps p (fun P => add_cps P q f).
-  Definition add_S2 {n} p q := @add_S2_cps n p q _ id. 
+  Definition add_S2 {n} p q := @add_S2_cps n p q _ id.
 
   Definition sub_then_maybe_add_cps {n} mask (p q r : T n)
              {R} (f:T n -> R) :=
@@ -923,11 +923,11 @@ Section API.
       @add_cps n p q R f = f (add p q).
     Proof. cbv [add_cps add Let_In]. prove_id. Qed.
     Hint Rewrite add_id : uncps.
-    
+
     Lemma add_S1_id n p q R f :
       @add_S1_cps n p q R f = f (add_S1 p q).
     Proof. cbv [add_S1_cps add_S1 join0_cps]. prove_id. Qed.
-    
+
     Lemma add_S2_id n p q R f :
       @add_S2_cps n p q R f = f (add_S2 p q).
     Proof. cbv [add_S2_cps add_S2 join0_cps]. prove_id. Qed.
@@ -1040,7 +1040,7 @@ Section API.
       pose proof div_correct; pose proof modulo_correct.
 
     Lemma eval_add_nz n p q :
-      n <> 0%nat -> (0 <= eval p + eval q < uweight bound n) ->
+      n <> 0%nat ->
       eval (@add n p q) = eval p + eval q.
     Proof.
       intros. pose_all.
@@ -1053,35 +1053,35 @@ Section API.
                       (rewrite <-!from_list_default_eq with (d:=0);
                        erewrite !length_to_list, !from_list_default_eq,
                        from_list_to_list)
-             | _ => apply Z.mod_small; omega 
+             | _ => apply Z.mod_small; omega
              end.
-    Qed.
+    Admitted.
 
     Lemma eval_add_z n p q :
       n = 0%nat ->
       eval (@add n p q) = eval p + eval q.
     Proof. intros; subst; reflexivity. Qed.
 
-    Lemma eval_add n p q (H:0 <= eval p + eval q < uweight bound n)
+    Lemma eval_add n p q
       :  eval (@add n p q) = eval p + eval q.
     Proof.
       destruct (Nat.eq_dec n 0%nat); intuition auto using eval_add_z, eval_add_nz.
     Qed.
-    Lemma eval_add_same n p q (H:0 <= eval p + eval q < uweight bound n)
+    Lemma eval_add_same n p q
       :  eval (@add n p q) = eval p + eval q.
     Proof. apply eval_add; omega. Qed.
-    Lemma eval_add_S1 n p q (H:0 <= eval p + eval q < uweight bound (S n))
+    Lemma eval_add_S1 n p q
       :  eval (@add_S1 n p q) = eval p + eval q.
     Proof.
       cbv [add_S1 add_S1_cps]. autorewrite with uncps push_id.
-      rewrite eval_add; rewrite eval_join0; [reflexivity|assumption].
-    Qed.
-    Lemma eval_add_S2 n p q (H:0 <= eval p + eval q < uweight bound (S n))
+      (*rewrite eval_add; rewrite eval_join0; [reflexivity|assumption].*)
+    Admitted.
+    Lemma eval_add_S2 n p q
       :  eval (@add_S2 n p q) = eval p + eval q.
     Proof.
       cbv [add_S2 add_S2_cps]. autorewrite with uncps push_id.
-      rewrite eval_add; rewrite eval_join0; [reflexivity|assumption].
-    Qed.
+      (*rewrite eval_add; rewrite eval_join0; [reflexivity|assumption].*)
+    Admitted.
     Hint Rewrite eval_add_same eval_add_S1 eval_add_S2 using (omega || assumption): push_basesystem_eval.
 
     Lemma uweight_le_mono n m : (n <= m)%nat ->
@@ -1142,13 +1142,33 @@ Section API.
     Qed.
 
     Lemma small_add n a b :
-      (2 <= bound) -> 
+      (2 <= bound) ->
       small a -> small b -> small (@add n a b).
     Proof.
       intros. pose_all.
       cbv [add_cps add Let_In].
       autorewrite with uncps push_id.
-      apply Positional.small_sat_add.
+      (*apply Positional.small_sat_add.*)
+    Admitted.
+
+    Lemma small_add_S1 n a b :
+      (2 <= bound) ->
+      small a -> small b -> small (@add_S1 n a b).
+    Proof.
+      intros. pose_all.
+      cbv [add_cps add add_S1 Let_In].
+      autorewrite with uncps push_id.
+      (*apply Positional.small_sat_add.*)
+    Admitted.
+
+    Lemma small_add_S2 n a b :
+      (2 <= bound) ->
+      small a -> small b -> small (@add_S2 n a b).
+    Proof.
+      intros. pose_all.
+      cbv [add_cps add add_S2 Let_In].
+      autorewrite with uncps push_id.
+      (*apply Positional.small_sat_add.*)
     Admitted.
 
     Lemma small_left_tl n (v:T (S n)) : small v -> small (left_tl v).
@@ -1370,7 +1390,7 @@ Section API.
 
   End Proofs.
 End API.
-Hint Rewrite nonzero_id join0_id divmod_id drop_high_id scmul_id add_id sub_then_maybe_add_id conditional_sub_id : uncps.
+Hint Rewrite nonzero_id join0_id divmod_id drop_high_id scmul_id add_id add_S1_id add_S2_id sub_then_maybe_add_id conditional_sub_id : uncps.
 
 (*
 (* Just some pretty-printing *)
@@ -1394,4 +1414,4 @@ Definition base2pow25p5 i := Eval compute in 2^(25*Z.of_nat i + ((Z.of_nat i + 1
 Time Eval cbv -[runtime_add runtime_mul Let_In] in
     (fun adc a0 a1 a2 a3 a4 a5 a6 a7 a8 a9 b0 b1 b2 b3 b4 b5 b6 b7 b8 b9 =>
        Columns.mul_cps (weight := base2pow25p5) (n:=10) (a9,a8,a7,a6,a5,a4,a3,a2,a1,a0) (b9,b8,b7,b6,b5,b4,b3,b2,b1,b0) (fun ab => Columns.compact (n:=19) (add_get_carry:=adc) (weight:=base2pow25p5) ab)). (* Finished transaction in 97.341 secs *)
-*)
\ No newline at end of file
+*)
-- 
cgit v1.2.3


From ff89c5cc3fb7240c1e87d4234ab8b84859fc23ea Mon Sep 17 00:00:00 2001
From: Jason Gross <jgross@mit.edu>
Date: Thu, 29 Jun 2017 13:05:21 -0400
Subject: Adapt to new arguments of saturated things

---
 .../MontgomeryReduction/WordByWord/Definition.v        | 18 +++++++++---------
 src/Arithmetic/MontgomeryReduction/WordByWord/Proofs.v |  8 ++++----
 2 files changed, 13 insertions(+), 13 deletions(-)

(limited to 'src')

diff --git a/src/Arithmetic/MontgomeryReduction/WordByWord/Definition.v b/src/Arithmetic/MontgomeryReduction/WordByWord/Definition.v
index d1221d006..f344cb7de 100644
--- a/src/Arithmetic/MontgomeryReduction/WordByWord/Definition.v
+++ b/src/Arithmetic/MontgomeryReduction/WordByWord/Definition.v
@@ -22,8 +22,8 @@ Section WordByWordMontgomery.
     (N : T R_numlimbs).
 
   Local Notation scmul := (@scmul (Z.pos r)).
-  Local Notation addT' := (fun n => @Saturated.add (Z.pos r) (S n) n (S n)).
-  Local Notation addT := (fun n => @Saturated.add (Z.pos r) n n n).
+  Local Notation addT' := (@Saturated.add_S1 (Z.pos r)).
+  Local Notation addT := (@Saturated.add (Z.pos r)).
   Local Notation conditional_sub_cps := (fun V => @conditional_sub_cps (Z.pos r) _ V N _).
   Local Notation conditional_sub := (fun V => @conditional_sub (Z.pos r) _ V N).
   Local Notation sub_then_maybe_add_cps :=
@@ -32,23 +32,23 @@ Section WordByWordMontgomery.
 
   Definition redc_body_no_cps (B : T R_numlimbs) (k : Z) {pred_A_numlimbs} (A_S : T (S pred_A_numlimbs) * T (S R_numlimbs))
     : T pred_A_numlimbs * T (S R_numlimbs)
-    := @redc_body T (@divmod) r R_numlimbs (@scmul) addT addT' (@drop_high (S R_numlimbs)) N B k _ A_S.
+    := @redc_body T (@divmod) r R_numlimbs (@scmul) (@addT) (@addT') (@drop_high (S R_numlimbs)) N B k _ A_S.
   Definition redc_loop_no_cps (B : T R_numlimbs) (k : Z) (count : nat) (A_S : T count * T (S R_numlimbs))
     : T 0 * T (S R_numlimbs)
-    := @redc_loop T (@divmod) r R_numlimbs (@scmul) addT addT' (@drop_high (S R_numlimbs)) N B k count A_S.
+    := @redc_loop T (@divmod) r R_numlimbs (@scmul) (@addT) (@addT') (@drop_high (S R_numlimbs)) N B k count A_S.
   Definition pre_redc_no_cps {A_numlimbs} (A : T A_numlimbs) (B : T R_numlimbs) (k : Z) : T (S R_numlimbs)
-    := @pre_redc T (@zero) (@divmod) r R_numlimbs (@scmul) addT addT' (@drop_high (S R_numlimbs)) N _ A B k.
+    := @pre_redc T (@zero) (@divmod) r R_numlimbs (@scmul) (@addT) (@addT') (@drop_high (S R_numlimbs)) N _ A B k.
   Definition redc_no_cps {A_numlimbs} (A : T A_numlimbs) (B : T R_numlimbs) (k : Z) : T R_numlimbs
-    := @redc T (@zero) (@divmod) r R_numlimbs (@scmul) addT addT' (@drop_high (S R_numlimbs)) conditional_sub N _ A B k.
+    := @redc T (@zero) (@divmod) r R_numlimbs (@scmul) (@addT) (@addT') (@drop_high (S R_numlimbs)) conditional_sub N _ A B k.
 
   Definition redc_body_cps {pred_A_numlimbs} (A : T (S pred_A_numlimbs)) (B : T R_numlimbs) (k : Z) (S' : T (S R_numlimbs))
              {cpsT} (rest : T pred_A_numlimbs * T (S R_numlimbs) -> cpsT)
     : cpsT
     := divmod_cps A (fun '(A, a) =>
-       @scmul_cps r _ a B _ (fun aB => @add_cps r _ _ (S R_numlimbs) S' aB _ (fun S1 =>
+       @scmul_cps r _ a B _ (fun aB => @add_cps r _ S' aB _ (fun S1 =>
        divmod_cps S1 (fun '(_, s) =>
        dlet q := fst (Z.mul_split r s k) in
-       @scmul_cps r _ q N _ (fun qN => @add_cps r _ _ _ S1 qN _ (fun S2 =>
+       @scmul_cps r _ q N _ (fun qN => @add_S1_cps r _ S1 qN _ (fun S2 =>
        divmod_cps S2 (fun '(S3, _) =>
        @drop_high_cps (S R_numlimbs) S3 _ (fun S4 => rest (A, S4))))))))).
 
@@ -85,7 +85,7 @@ Section WordByWordMontgomery.
     := @opp T (@zero) R_numlimbs (@sub_then_maybe_add) A.
 
   Definition add_cps (A B : T R_numlimbs) {cpsT} (rest : T R_numlimbs -> cpsT) : cpsT
-    := @add_cps r _ _ R_numlimbs A B
+    := @add_cps r _ A B
                 _ (fun v => conditional_sub_cps v rest).
   Definition add (A B : T R_numlimbs) : T R_numlimbs
     := add_cps A B id.
diff --git a/src/Arithmetic/MontgomeryReduction/WordByWord/Proofs.v b/src/Arithmetic/MontgomeryReduction/WordByWord/Proofs.v
index a55f9cffe..747280fe6 100644
--- a/src/Arithmetic/MontgomeryReduction/WordByWord/Proofs.v
+++ b/src/Arithmetic/MontgomeryReduction/WordByWord/Proofs.v
@@ -16,8 +16,8 @@ Section WordByWordMontgomery.
           (R_numlimbs : nat).
   Local Notation small := (@small (Z.pos r)).
   Local Notation eval := (@eval (Z.pos r)).
-  Local Notation addT' := (fun n => @Saturated.add (Z.pos r) (S n) n (S n)).
-  Local Notation addT := (fun n => @Saturated.add (Z.pos r) n n n).
+  Local Notation addT' := (@Saturated.add_S1 (Z.pos r)).
+  Local Notation addT := (@Saturated.add (Z.pos r)).
   Local Notation scmul := (@scmul (Z.pos r)).
   Local Notation eval_zero := (@eval_zero (Z.pos r)).
   Local Notation small_zero := (@small_zero r (Zorder.Zgt_pos_0 _)).
@@ -65,7 +65,7 @@ Section WordByWordMontgomery.
   Qed.
   Local Lemma small_addT' : forall n a b, small a -> small b -> small (@addT' n a b).
   Proof.
-    intros; apply Saturated.small_add; auto; lia.
+    intros; apply Saturated.small_add_S1; auto; lia.
   Qed.
 
   Local Notation conditional_sub_cps := (fun V : T (S R_numlimbs) => @conditional_sub_cps (Z.pos r) _ V N _).
@@ -225,7 +225,7 @@ Section WordByWordMontgomery.
     Local Notation eval_sub_then_maybe_add :=
       (fun p q smp smq => @eval_sub_then_maybe_add (Z.pos r) (Zorder.Zgt_pos_0 _) _ (Z.pos r - 1) p q N smp smq small_N N_mask).
     Local Notation small_sub_then_maybe_add :=
-      (fun p q => @small_sub_then_maybe_add (Z.pos r) (Zorder.Zgt_pos_0 _) _ (Z.pos r - 1) p q N).
+      (fun p q => @small_sub_then_maybe_add (Z.pos r) (*(Zorder.Zgt_pos_0 _)*) _ (Z.pos r - 1) p q N).
 
     Definition add_no_cps_bound : 0 <= eval add_no_cps < eval N
       := @add_bound T (@eval) r R R_numlimbs (@small) (@addT) (@eval_addT) (@small_addT) N N_lt_R (@conditional_sub) (@eval_conditional_sub) Av Bv small_Av small_Bv Av_bound Bv_bound.
-- 
cgit v1.2.3


From 8eec11bfb6d97a3cbb21e74f26c469157c58e2d8 Mon Sep 17 00:00:00 2001
From: Jason Gross <jgross@mit.edu>
Date: Thu, 29 Jun 2017 13:37:20 -0400
Subject: Fix unfolding to not unfold sub_with_get_borrow in P256

---
 src/Specific/MontgomeryP256_128.v            | 17 ++++++++++++-----
 src/Specific/NISTP256/AMD64/MontgomeryP256.v |  8 ++++----
 2 files changed, 16 insertions(+), 9 deletions(-)

(limited to 'src')

diff --git a/src/Specific/MontgomeryP256_128.v b/src/Specific/MontgomeryP256_128.v
index 086a454e8..323be5533 100644
--- a/src/Specific/MontgomeryP256_128.v
+++ b/src/Specific/MontgomeryP256_128.v
@@ -34,7 +34,7 @@ Definition mulmod_256' : { f:Tuple.tuple Z sz -> Tuple.tuple Z sz -> Tuple.tuple
                             }.
 Proof.
   eapply (lift2_sig (fun A B c => c = _)); eexists.
-  cbv -[Definitions.Z.add_get_carry Definitions.Z.mul_split_at_bitwidth Definitions.Z.zselect runtime_add runtime_mul runtime_and runtime_opp Let_In].
+  cbv -[Definitions.Z.add_with_get_carry Definitions.Z.add_with_carry Definitions.Z.sub_with_get_borrow Definitions.Z.sub_with_borrow Definitions.Z.mul_split_at_bitwidth Definitions.Z.zselect runtime_add runtime_mul runtime_and runtime_opp Let_In].
   (*
   cbv [
       r wt sz p256
@@ -42,9 +42,10 @@ Proof.
        CPSUtil.to_list_cps CPSUtil.to_list'_cps CPSUtil.to_list_cps' CPSUtil.flat_map_cps CPSUtil.fold_right_cps
        CPSUtil.map_cps CPSUtil.Tuple.left_append_cps CPSUtil.firstn_cps CPSUtil.combine_cps CPSUtil.on_tuple_cps CPSUtil.update_nth_cps CPSUtil.from_list_default_cps CPSUtil.from_list_default'_cps
        fst snd length List.seq List.hd List.app
-       redc redc_cps redc_loop_cps redc_body_cps
+       redc pre_redc_cps redc_cps redc_loop_cps redc_body_cps
        Positional.to_associational_cps
        Saturated.divmod_cps
+       Saturated.conditional_sub_cps
        Saturated.scmul_cps
        Saturated.uweight
        Saturated.Columns.mul_cps
@@ -52,13 +53,19 @@ Proof.
        (*Z.of_nat Pos.of_succ_nat  Nat.pred
        Z.pow Z.pow_pos Z.mul Pos.iter Pos.mul Pos.succ*)
        Tuple.hd Tuple.append Tuple.tl Tuple.hd' Tuple.tl' CPSUtil.Tuple.left_tl_cps CPSUtil.Tuple.left_hd_cps CPSUtil.Tuple.hd_cps CPSUtil.Tuple.tl_cps
+       CPSUtil.Tuple.map2_cps
        Saturated.Columns.from_associational_cps
        Saturated.Associational.multerm_cps
+       Saturated.Positional.sat_add_cps
+       Saturated.Positional.sat_sub_cps
+       Saturated.Positional.chain_op_cps
+       Saturated.Positional.chain_op'_cps
        Saturated.Columns.compact_cps
        Saturated.Columns.compact_step_cps
        Saturated.Columns.compact_digit_cps
        Saturated.drop_high_cps
        Saturated.add_cps
+       Saturated.add_S1_cps
        Saturated.Columns.add_cps
        Saturated.Columns.cons_to_nth_cps
        Nat.pred
@@ -138,7 +145,7 @@ Definition add' : { f:Tuple.tuple Z sz -> Tuple.tuple Z sz -> Tuple.tuple Z sz
                  }.
 Proof.
   eapply (lift2_sig (fun A B c => c = _)); eexists.
-  cbv -[Definitions.Z.add_get_carry Definitions.Z.mul_split_at_bitwidth Definitions.Z.zselect runtime_add runtime_mul runtime_and runtime_opp Let_In].
+  cbv -[Definitions.Z.add_with_get_carry Definitions.Z.add_with_carry Definitions.Z.sub_with_get_borrow Definitions.Z.sub_with_borrow Definitions.Z.mul_split_at_bitwidth Definitions.Z.zselect runtime_add runtime_mul runtime_and runtime_opp Let_In].
   reflexivity.
 Defined.
 
@@ -149,7 +156,7 @@ Definition sub' : { f:Tuple.tuple Z sz -> Tuple.tuple Z sz -> Tuple.tuple Z sz
                  }.
 Proof.
   eapply (lift2_sig (fun A B c => c = _)); eexists.
-  cbv -[Definitions.Z.add_get_carry Definitions.Z.mul_split_at_bitwidth Definitions.Z.zselect runtime_add runtime_mul runtime_and runtime_opp Let_In].
+  cbv -[Definitions.Z.add_with_get_carry Definitions.Z.add_with_carry Definitions.Z.sub_with_get_borrow Definitions.Z.sub_with_borrow Definitions.Z.mul_split_at_bitwidth Definitions.Z.zselect runtime_add runtime_mul runtime_and runtime_opp Let_In].
   reflexivity.
 Defined.
 
@@ -160,7 +167,7 @@ Definition opp' : { f:Tuple.tuple Z sz -> Tuple.tuple Z sz
                  }.
 Proof.
   eapply (lift1_sig (fun A c => c = _)); eexists.
-  cbv -[Definitions.Z.add_get_carry Definitions.Z.mul_split_at_bitwidth Definitions.Z.zselect runtime_add runtime_mul runtime_and runtime_opp Let_In].
+  cbv -[Definitions.Z.add_with_get_carry Definitions.Z.add_with_carry Definitions.Z.sub_with_get_borrow Definitions.Z.sub_with_borrow Definitions.Z.mul_split_at_bitwidth Definitions.Z.zselect runtime_add runtime_mul runtime_and runtime_opp Let_In].
   reflexivity.
 Defined.
 
diff --git a/src/Specific/NISTP256/AMD64/MontgomeryP256.v b/src/Specific/NISTP256/AMD64/MontgomeryP256.v
index d90a63bfb..ae5a3cb43 100644
--- a/src/Specific/NISTP256/AMD64/MontgomeryP256.v
+++ b/src/Specific/NISTP256/AMD64/MontgomeryP256.v
@@ -34,7 +34,7 @@ Definition mulmod_256' : { f:Tuple.tuple Z sz -> Tuple.tuple Z sz -> Tuple.tuple
                             }.
 Proof.
   eapply (lift2_sig (fun A B c => c = _)); eexists.
-  cbv -[Definitions.Z.add_get_carry Definitions.Z.mul_split_at_bitwidth Definitions.Z.zselect runtime_add runtime_mul runtime_and runtime_opp Let_In].
+  cbv -[Definitions.Z.add_with_get_carry Definitions.Z.add_with_carry Definitions.Z.sub_with_get_borrow Definitions.Z.sub_with_borrow Definitions.Z.mul_split_at_bitwidth Definitions.Z.zselect runtime_add runtime_mul runtime_and runtime_opp Let_In].
   (*
   cbv [
       r wt sz p256
@@ -139,7 +139,7 @@ Definition add' : { f:Tuple.tuple Z sz -> Tuple.tuple Z sz -> Tuple.tuple Z sz
                  }.
 Proof.
   eapply (lift2_sig (fun A B c => c = _)); eexists.
-  cbv -[Definitions.Z.add_get_carry Definitions.Z.mul_split_at_bitwidth Definitions.Z.zselect runtime_add runtime_mul runtime_and runtime_opp Let_In].
+  cbv -[Definitions.Z.add_with_get_carry Definitions.Z.add_with_carry Definitions.Z.sub_with_get_borrow Definitions.Z.sub_with_borrow Definitions.Z.mul_split_at_bitwidth Definitions.Z.zselect runtime_add runtime_mul runtime_and runtime_opp Let_In].
   reflexivity.
 Defined.
 
@@ -150,7 +150,7 @@ Definition sub' : { f:Tuple.tuple Z sz -> Tuple.tuple Z sz -> Tuple.tuple Z sz
                  }.
 Proof.
   eapply (lift2_sig (fun A B c => c = _)); eexists.
-  cbv -[Definitions.Z.add_get_carry Definitions.Z.mul_split_at_bitwidth Definitions.Z.zselect runtime_add runtime_mul runtime_and runtime_opp Let_In].
+  cbv -[Definitions.Z.add_with_get_carry Definitions.Z.add_with_carry Definitions.Z.sub_with_get_borrow Definitions.Z.sub_with_borrow Definitions.Z.mul_split_at_bitwidth Definitions.Z.zselect runtime_add runtime_mul runtime_and runtime_opp Let_In].
   reflexivity.
 Defined.
 
@@ -161,7 +161,7 @@ Definition opp' : { f:Tuple.tuple Z sz -> Tuple.tuple Z sz
                  }.
 Proof.
   eapply (lift1_sig (fun A c => c = _)); eexists.
-  cbv -[Definitions.Z.add_get_carry Definitions.Z.mul_split_at_bitwidth Definitions.Z.zselect runtime_add runtime_mul runtime_and runtime_opp Let_In].
+  cbv -[Definitions.Z.add_with_get_carry Definitions.Z.add_with_carry Definitions.Z.sub_with_get_borrow Definitions.Z.sub_with_borrow Definitions.Z.mul_split_at_bitwidth Definitions.Z.zselect runtime_add runtime_mul runtime_and runtime_opp Let_In].
   reflexivity.
 Defined.
 
-- 
cgit v1.2.3


From a6fe61b6001857907f40f54e45964d46b754a30d Mon Sep 17 00:00:00 2001
From: Jason Gross <jgross@mit.edu>
Date: Thu, 29 Jun 2017 13:43:03 -0400
Subject: Fix the sense of op_{get,with}_carry in Saturated

Now it lines up with the things in Z.Definitions
---
 src/Arithmetic/Saturated.v | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

(limited to 'src')

diff --git a/src/Arithmetic/Saturated.v b/src/Arithmetic/Saturated.v
index 5ecb5eebd..14f689322 100644
--- a/src/Arithmetic/Saturated.v
+++ b/src/Arithmetic/Saturated.v
@@ -735,10 +735,10 @@ Module Positional.
                        | None => op_get_carry
                        | Some x => op_with_carry x end in
             dlet carry_result := op' (hd p) (hd q) in
-              chain_op'_cps (Some (fst carry_result)) (tl p) (tl q) _
+              chain_op'_cps (Some (snd carry_result)) (tl p) (tl q) _
                             (fun carry_pq =>
                                f (fst carry_pq,
-                                  append (snd carry_result) (snd carry_pq)))
+                                  append (fst carry_result) (snd carry_pq)))
         end.
       Definition chain_op' {n} c p q := @chain_op'_cps n c p q _ id.
       Definition chain_op_cps {n} p q {T} f := @chain_op'_cps n None p q T f.
-- 
cgit v1.2.3


From 87f500134152809f182c7c85bf59cc3cc8a3d86f Mon Sep 17 00:00:00 2001
From: Jason Gross <jgross@mit.edu>
Date: Thu, 29 Jun 2017 14:14:51 -0400
Subject: More C Notations for uin8_t-valued addcarryx

---
 src/Compilers/Z/CNotations.v | 349 +++++++++++++++++++++++++++++++++++++++++--
 1 file changed, 337 insertions(+), 12 deletions(-)

(limited to 'src')

diff --git a/src/Compilers/Z/CNotations.v b/src/Compilers/Z/CNotations.v
index 8bc42a72d..335d4ad4b 100644
--- a/src/Compilers/Z/CNotations.v
+++ b/src/Compilers/Z/CNotations.v
@@ -68,6 +68,79 @@ Reserved Notation "'mulx_u128ℤ' ( a , b )" (format "'mulx_u128ℤ' ( a ,  b )"
 #!/usr/bin/env python
 # -*- coding: utf-8 -*-
 import math
+
+print(r"""Require Export Crypto.Compilers.Syntax.
+Require Import Crypto.Compilers.Z.Syntax.
+Require Export Crypto.Compilers.Z.HexNotationConstants.
+Require Export Crypto.Util.Notations.
+
+Reserved Notation "T x = A ; b" (at level 200, b at level 200, format "T  x  =  A ; '//' b").
+Reserved Notation "T x = A ; 'return' b" (at level 200, b at level 200, format "T  x  =  A ; '//' 'return'  b").
+Reserved Notation "T x = A ; 'return' ( b0 , b1 , .. , b2 )" (at level 200, format "T  x  =  A ; '//' 'return'  ( b0 ,  b1 ,  .. ,  b2 )").
+Reserved Notation "T0 x , T1 y = A ; b" (at level 200, b at level 200, format "T0  x ,  T1  y  =  A ; '//' b").
+Reserved Notation "T0 x , T1 y = A ; 'return' b" (at level 200, b at level 200, format "T0  x ,  T1  y  =  A ; '//' 'return'  b").
+Reserved Notation "T0 x , T1 y = A ; 'return' ( b0 , b1 , .. , b2 )" (at level 200, format "T0  x ,  T1  y  =  A ; '//' 'return'  ( b0 ,  b1 ,  .. ,  b2 )").
+Reserved Notation "v == 0 ? a : b" (at level 40, a at level 10, b at level 10).
+Reserved Notation "v == 0 ?ℤ a : b" (at level 40, a at level 10, b at level 10).
+Reserved Notation "x & y" (at level 40).
+Reserved Notation "x | y" (at level 45).
+
+Global Open Scope expr_scope.
+
+Notation "T x = A ; b" := (LetIn (tx:=T) A (fun x => b)) : expr_scope.
+Notation "T x = A ; 'return' b" := (LetIn (tx:=T) A (fun x => Var b)) : expr_scope.
+Notation "T x = A ; 'return' ( b0 , b1 , .. , b2 )" := (LetIn (tx:=T) A (fun x => Pair .. (Pair b0%expr b1%expr) .. b2%expr)) : expr_scope.
+Notation "T x = A ; 'return' ( b0 , b1 , .. , b2 )" := (LetIn (tx:=T) A (fun x => Pair .. (Pair (Var b0) (Var b1)) .. (Var b2))) : expr_scope.
+Notation "T0 x , T1 y = A ; b" := (LetIn (tx:=Prod T0 T1) A (fun '((x, y)%core) => b)) : expr_scope.
+Notation "T0 x , T1 y = A ; 'return' b" := (LetIn (tx:=Prod T0 T1) A (fun '((x, y)%core) => Var b)) : expr_scope.
+(*Notation "T0 x , T1 y = A ; 'return' ( b0 , b1 , .. , b2 )" := (LetIn (tx:=Prod T0 T1) A (fun '((x, y)%core) => (Pair .. (Pair b0%expr b1%expr) .. b2%expr))) : expr_scope.*) (* Error: Unsupported construction in recursive notations., https://coq.inria.fr/bugs/show_bug.cgi?id=5523 *)
+(*Notation "T0 x , T1 y = A ; 'return' ( b0 , b1 , .. , b2 )" := (LetIn (tx:=Prod T0 T1) A (fun '((x, y)%core) => (Pair .. (Pair (Var b0) (Var b1)) .. (Var b2)))) : expr_scope.*) (* Error: Unsupported construction in recursive notations., https://coq.inria.fr/bugs/show_bug.cgi?id=5523 *)
+
+(* for now, handle with
+<<
+sed s':^\([^,]*\) \([^, ]*\)\(\s*\),\(.*\)\(addcarryx.*\))\([; ]*\)$:\1 \2\3;\4_\5, \&\2)\6:'
+sed s':^\([^,]*\) \([^, ]*\)\(\s*\),\(.*\)\(subborrow.*\))\([; ]*\)$:\1 \2\3;\4_\5, \&\2)\6:'
+sed s':^\([^,]*\) \([^, ]*\)\(\s*\),\(.*\)\(mulx.*\))\([; ]*\)$:\1 \2\3;\4_\5, \&\2)\6:'
+>>
+
+   Once we get https://coq.inria.fr/bugs/show_bug.cgi?id=5526, we can print actual C notations:
+<<
+Reserved Notation "T0 out ; T1 c_out = '_addcarryx_u32' ( c_in , a , b , & out ) ; REST"
+ (at level 200, REST at level 200, only printing format "T0  out ; '//' T1  c_out  =  '_addcarryx_u64' ( c_in ,  a ,  b ,  & out ) ; '//' REST").
+Reserved Notation "T0 out ; T1 c_out = '_addcarryx_u64' ( c_in , a , b , & out ) ; REST"
+ (at level 200, REST at level 200, only printing format "T0  out ; '//' T1  c_out  =  '_addcarryx_u64' ( c_in ,  a ,  b ,  & out ) ; '//' REST").
+>> *)
+Reserved Notation "'addcarryx_u32' ( c , a , b )" (format "'addcarryx_u32' ( c ,  a ,  b )").
+Reserved Notation "'addcarryx_u64' ( c , a , b )" (format "'addcarryx_u64' ( c ,  a ,  b )").
+Reserved Notation "'addcarryx_u128' ( c , a , b )" (format "'addcarryx_u128' ( c ,  a ,  b )").
+Reserved Notation "'addcarryx_u51' ( c , a , b )" (format "'addcarryx_u51' ( c ,  a ,  b )"). (* temporary for testing *)
+Reserved Notation "'subborrow_u32' ( c , a , b )" (format "'subborrow_u32' ( c ,  a ,  b )").
+Reserved Notation "'subborrow_u64' ( c , a , b )" (format "'subborrow_u64' ( c ,  a ,  b )").
+Reserved Notation "'subborrow_u128' ( c , a , b )" (format "'subborrow_u128' ( c ,  a ,  b )").
+Reserved Notation "'subborrow_u51' ( c , a , b )" (format "'subborrow_u51' ( c ,  a ,  b )"). (* temporary for testing *)
+Reserved Notation "'mulx_u32' ( a , b )" (format "'mulx_u32' ( a ,  b )").
+Reserved Notation "'mulx_u64' ( a , b )" (format "'mulx_u64' ( a ,  b )").
+Reserved Notation "'mulx_u128' ( a , b )" (format "'mulx_u128' ( a ,  b )").
+
+Reserved Notation "'addcarryx_u32ℤ' ( c , a , b )" (format "'addcarryx_u32ℤ' ( c ,  a ,  b )").
+Reserved Notation "'addcarryx_u64ℤ' ( c , a , b )" (format "'addcarryx_u64ℤ' ( c ,  a ,  b )").
+Reserved Notation "'addcarryx_u128ℤ' ( c , a , b )" (format "'addcarryx_u128ℤ' ( c ,  a ,  b )").
+Reserved Notation "'addcarryx_u51ℤ' ( c , a , b )" (format "'addcarryx_u51ℤ' ( c ,  a ,  b )"). (* temporary for testing *)
+Reserved Notation "'subborrow_u32ℤ' ( c , a , b )" (format "'subborrow_u32ℤ' ( c ,  a ,  b )").
+Reserved Notation "'subborrow_u64ℤ' ( c , a , b )" (format "'subborrow_u64ℤ' ( c ,  a ,  b )").
+Reserved Notation "'subborrow_u128ℤ' ( c , a , b )" (format "'subborrow_u128ℤ' ( c ,  a ,  b )").
+Reserved Notation "'subborrow_u51ℤ' ( c , a , b )" (format "'subborrow_u51ℤ' ( c ,  a ,  b )"). (* temporary for testing *)
+Reserved Notation "'mulx_u32ℤ' ( a , b )" (format "'mulx_u32ℤ' ( a ,  b )").
+Reserved Notation "'mulx_u64ℤ' ( a , b )" (format "'mulx_u64ℤ' ( a ,  b )").
+Reserved Notation "'mulx_u128ℤ' ( a , b )" (format "'mulx_u128ℤ' ( a ,  b )").
+
+(* python:
+<<""")
+
+print(open(__file__).read())
+
+print(r">> *)")
+
 def log2_up(x):
     return int(math.ceil(math.log(x, 2)))
 types = ('bool', 'uint8_t', 'uint8_t', 'uint8_t', 'uint16_t', 'uint32_t', 'uint64_t', 'uint128_t', 'uint256_t')
@@ -210,18 +283,13 @@ for opn, op in (('addcarryx', 'AddWithGetCarry'), ('subborrow', 'SubWithGetBorro
                     c = ('c' if not v0 else '(Var c)')
                     a = ('a' if not v1 else '(Var a)')
                     b = ('b' if not v2 else '(Var b)')
-                    print(('Notation "\'%s_u%d\' ( c , a , b )" := (Op (%s %d (TWord 0) (TWord %d) (TWord %d) (TWord %d) (TWord 0)) (Pair (Pair %s %s) %s)).') % (opn, wordsz, op, wordsz, lgwordsz, lgwordsz, lgwordsz, c, a, b))
-                    print(('Notation "\'%s_u%d\' ( c , a , b )" := (Op (%s %d (TWord 0) (TWord 0) (TWord %d) (TWord %d) (TWord 0)) (Pair (Pair %s %s) %s)).') % (opn, wordsz, op, wordsz, lgwordsz, lgwordsz, c, a, b))
-                    print(('Notation "\'%s_u%d\' ( c , a , b )" := (Op (%s %d (TWord 0) (TWord %d) (TWord 0) (TWord %d) (TWord 0)) (Pair (Pair %s %s) %s)).') % (opn, wordsz, op, wordsz, lgwordsz, lgwordsz, c, a, b))
-                    print(('(' + '*Notation "T0 out ; T1 c_out = \'_%s_u%d\' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (%s %d (TWord 0) (TWord %d) (TWord %d) (TWord %d) (TWord 0)) (Pair (Pair %s %s) %s)) (fun \'((out, c_out)%%core) => REST)).*' + ')') % (opn, wordsz, op, wordsz, lgwordsz, lgwordsz, lgwordsz, c, a, b))
-                    print(('(' + '*Notation "T0 out ; T1 c_out = \'_%s_u%d\' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (%s %d (TWord 0) (TWord 0) (TWord %d) (TWord %d) (TWord 0)) (Pair (Pair %s %s) %s)) (fun \'((out, c_out)%%core) => REST)).*' + ')') % (opn, wordsz, op, wordsz, lgwordsz, lgwordsz, c, a, b))
-                    print(('(' + '*Notation "T0 out ; T1 c_out = \'_%s_u%d\' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (%s %d (TWord 0) (TWord %d) (TWord 0) (TWord %d) (TWord 0)) (Pair (Pair %s %s) %s)) (fun \'((out, c_out)%%core) => REST)).*' + ')') % (opn, wordsz, op, wordsz, lgwordsz, lgwordsz, c, a, b))
-                    print(('Notation "\'%s_u%d\' ( c , a , b )" := (Op (%s %d (TWord 3) (TWord %d) (TWord %d) (TWord %d) (TWord 3)) (Pair (Pair %s %s) %s)).') % (opn, wordsz, op, wordsz, lgwordsz, lgwordsz, lgwordsz, c, a, b))
-                    print(('Notation "\'%s_u%d\' ( c , a , b )" := (Op (%s %d (TWord 3) (TWord 3) (TWord %d) (TWord %d) (TWord 3)) (Pair (Pair %s %s) %s)).') % (opn, wordsz, op, wordsz, lgwordsz, lgwordsz, c, a, b))
-                    print(('Notation "\'%s_u%d\' ( c , a , b )" := (Op (%s %d (TWord 3) (TWord %d) (TWord 3) (TWord %d) (TWord 3)) (Pair (Pair %s %s) %s)).') % (opn, wordsz, op, wordsz, lgwordsz, lgwordsz, c, a, b))
-                    print(('(' + '*Notation "T0 out ; T1 c_out = \'_%s_u%d\' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (%s %d (TWord 3) (TWord %d) (TWord %d) (TWord %d) (TWord 3)) (Pair (Pair %s %s) %s)) (fun \'((out, c_out)%%core) => REST)).*' + ')') % (opn, wordsz, op, wordsz, lgwordsz, lgwordsz, lgwordsz, c, a, b))
-                    print(('(' + '*Notation "T0 out ; T1 c_out = \'_%s_u%d\' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (%s %d (TWord 3) (TWord 3) (TWord %d) (TWord %d) (TWord 3)) (Pair (Pair %s %s) %s)) (fun \'((out, c_out)%%core) => REST)).*' + ')') % (opn, wordsz, op, wordsz, lgwordsz, lgwordsz, c, a, b))
-                    print(('(' + '*Notation "T0 out ; T1 c_out = \'_%s_u%d\' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (%s %d (TWord 3) (TWord %d) (TWord 3) (TWord %d) (TWord 3)) (Pair (Pair %s %s) %s)) (fun \'((out, c_out)%%core) => REST)).*' + ')') % (opn, wordsz, op, wordsz, lgwordsz, lgwordsz, c, a, b))
+                    for lgwordsz_small in (0, 3):
+                        for notation_string in ('Notation "\'%s_u%d\' ( c , a , b )" := (Op (%s %d (TWord %d) (TWord %d) (TWord %d) (TWord %d) (TWord %d)) (Pair (Pair %s %s) %s)).',
+                                                '(*Notation "T0 out ; T1 c_out = \'_%s_u%d\' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (%s %d (TWord %d) (TWord %d) (TWord %d) (TWord %d) (TWord %d)) (Pair (Pair %s %s) %s)) (fun \'((out, c_out)%%core) => REST)).*)'):
+                            print(notation_string % (opn, wordsz, op, wordsz, lgwordsz_small, lgwordsz, lgwordsz, lgwordsz, lgwordsz_small, c, a, b))
+                            print(notation_string % (opn, wordsz, op, wordsz, lgwordsz_small, lgwordsz_small, lgwordsz, lgwordsz, lgwordsz_small, c, a, b))
+                            print(notation_string % (opn, wordsz, op, wordsz, lgwordsz_small, lgwordsz, lgwordsz_small, lgwordsz, lgwordsz_small, c, a, b))
+                            print(notation_string % (opn, wordsz, op, wordsz, lgwordsz_small, lgwordsz_small, lgwordsz_small, lgwordsz, lgwordsz_small, c, a, b))
 for opn, op in (('mulx', 'MulSplit'),):
     for wordsz in (32, 64, 128, 51):
         lgwordsz = log2_up(wordsz)
@@ -257,6 +325,7 @@ for opn, op in (('mulx', 'MulSplit'),):
                 print(('(' + '*Notation "T0 out ; T1 c_out = \'_%s_u%dℤ\' ( a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (%s %d _ _ TZ _) (Pair %s %s)) (fun \'((out, c_out)%%core) => REST)).*' + ')') % (opn, wordsz, op, wordsz, a, b))
 print('Notation Return x := (Var x).')
 print('Notation C_like := (Expr base_type op _).')
+
 >> *)
 Notation "'bool'" := (Tbase (TWord 0)).
 Notation "'uint8_t'" := (Tbase (TWord 1)).
@@ -1784,771 +1853,1027 @@ Notation "v == 0 ? x : y" := (Op (Zselect _ (TWord 8) (TWord 8) (TWord 8)) (Pair
 Notation "'addcarryx_u32' ( c , a , b )" := (Op (AddWithGetCarry 32 (TWord 0) (TWord 5) (TWord 5) (TWord 5) (TWord 0)) (Pair (Pair c a) b)).
 Notation "'addcarryx_u32' ( c , a , b )" := (Op (AddWithGetCarry 32 (TWord 0) (TWord 0) (TWord 5) (TWord 5) (TWord 0)) (Pair (Pair c a) b)).
 Notation "'addcarryx_u32' ( c , a , b )" := (Op (AddWithGetCarry 32 (TWord 0) (TWord 5) (TWord 0) (TWord 5) (TWord 0)) (Pair (Pair c a) b)).
+Notation "'addcarryx_u32' ( c , a , b )" := (Op (AddWithGetCarry 32 (TWord 0) (TWord 0) (TWord 0) (TWord 5) (TWord 0)) (Pair (Pair c a) b)).
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 32 (TWord 0) (TWord 5) (TWord 5) (TWord 5) (TWord 0)) (Pair (Pair c a) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 32 (TWord 0) (TWord 0) (TWord 5) (TWord 5) (TWord 0)) (Pair (Pair c a) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 32 (TWord 0) (TWord 5) (TWord 0) (TWord 5) (TWord 0)) (Pair (Pair c a) b)) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_addcarryx_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 32 (TWord 0) (TWord 0) (TWord 0) (TWord 5) (TWord 0)) (Pair (Pair c a) b)) (fun '((out, c_out)%core) => REST)).*)
 Notation "'addcarryx_u32' ( c , a , b )" := (Op (AddWithGetCarry 32 (TWord 3) (TWord 5) (TWord 5) (TWord 5) (TWord 3)) (Pair (Pair c a) b)).
 Notation "'addcarryx_u32' ( c , a , b )" := (Op (AddWithGetCarry 32 (TWord 3) (TWord 3) (TWord 5) (TWord 5) (TWord 3)) (Pair (Pair c a) b)).
 Notation "'addcarryx_u32' ( c , a , b )" := (Op (AddWithGetCarry 32 (TWord 3) (TWord 5) (TWord 3) (TWord 5) (TWord 3)) (Pair (Pair c a) b)).
+Notation "'addcarryx_u32' ( c , a , b )" := (Op (AddWithGetCarry 32 (TWord 3) (TWord 3) (TWord 3) (TWord 5) (TWord 3)) (Pair (Pair c a) b)).
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 32 (TWord 3) (TWord 5) (TWord 5) (TWord 5) (TWord 3)) (Pair (Pair c a) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 32 (TWord 3) (TWord 3) (TWord 5) (TWord 5) (TWord 3)) (Pair (Pair c a) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 32 (TWord 3) (TWord 5) (TWord 3) (TWord 5) (TWord 3)) (Pair (Pair c a) b)) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_addcarryx_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 32 (TWord 3) (TWord 3) (TWord 3) (TWord 5) (TWord 3)) (Pair (Pair c a) b)) (fun '((out, c_out)%core) => REST)).*)
 Notation "'addcarryx_u32' ( c , a , b )" := (Op (AddWithGetCarry 32 (TWord 0) (TWord 5) (TWord 5) (TWord 5) (TWord 0)) (Pair (Pair c a) (Var b))).
 Notation "'addcarryx_u32' ( c , a , b )" := (Op (AddWithGetCarry 32 (TWord 0) (TWord 0) (TWord 5) (TWord 5) (TWord 0)) (Pair (Pair c a) (Var b))).
 Notation "'addcarryx_u32' ( c , a , b )" := (Op (AddWithGetCarry 32 (TWord 0) (TWord 5) (TWord 0) (TWord 5) (TWord 0)) (Pair (Pair c a) (Var b))).
+Notation "'addcarryx_u32' ( c , a , b )" := (Op (AddWithGetCarry 32 (TWord 0) (TWord 0) (TWord 0) (TWord 5) (TWord 0)) (Pair (Pair c a) (Var b))).
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 32 (TWord 0) (TWord 5) (TWord 5) (TWord 5) (TWord 0)) (Pair (Pair c a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 32 (TWord 0) (TWord 0) (TWord 5) (TWord 5) (TWord 0)) (Pair (Pair c a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 32 (TWord 0) (TWord 5) (TWord 0) (TWord 5) (TWord 0)) (Pair (Pair c a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_addcarryx_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 32 (TWord 0) (TWord 0) (TWord 0) (TWord 5) (TWord 0)) (Pair (Pair c a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 Notation "'addcarryx_u32' ( c , a , b )" := (Op (AddWithGetCarry 32 (TWord 3) (TWord 5) (TWord 5) (TWord 5) (TWord 3)) (Pair (Pair c a) (Var b))).
 Notation "'addcarryx_u32' ( c , a , b )" := (Op (AddWithGetCarry 32 (TWord 3) (TWord 3) (TWord 5) (TWord 5) (TWord 3)) (Pair (Pair c a) (Var b))).
 Notation "'addcarryx_u32' ( c , a , b )" := (Op (AddWithGetCarry 32 (TWord 3) (TWord 5) (TWord 3) (TWord 5) (TWord 3)) (Pair (Pair c a) (Var b))).
+Notation "'addcarryx_u32' ( c , a , b )" := (Op (AddWithGetCarry 32 (TWord 3) (TWord 3) (TWord 3) (TWord 5) (TWord 3)) (Pair (Pair c a) (Var b))).
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 32 (TWord 3) (TWord 5) (TWord 5) (TWord 5) (TWord 3)) (Pair (Pair c a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 32 (TWord 3) (TWord 3) (TWord 5) (TWord 5) (TWord 3)) (Pair (Pair c a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 32 (TWord 3) (TWord 5) (TWord 3) (TWord 5) (TWord 3)) (Pair (Pair c a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_addcarryx_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 32 (TWord 3) (TWord 3) (TWord 3) (TWord 5) (TWord 3)) (Pair (Pair c a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 Notation "'addcarryx_u32' ( c , a , b )" := (Op (AddWithGetCarry 32 (TWord 0) (TWord 5) (TWord 5) (TWord 5) (TWord 0)) (Pair (Pair c (Var a)) b)).
 Notation "'addcarryx_u32' ( c , a , b )" := (Op (AddWithGetCarry 32 (TWord 0) (TWord 0) (TWord 5) (TWord 5) (TWord 0)) (Pair (Pair c (Var a)) b)).
 Notation "'addcarryx_u32' ( c , a , b )" := (Op (AddWithGetCarry 32 (TWord 0) (TWord 5) (TWord 0) (TWord 5) (TWord 0)) (Pair (Pair c (Var a)) b)).
+Notation "'addcarryx_u32' ( c , a , b )" := (Op (AddWithGetCarry 32 (TWord 0) (TWord 0) (TWord 0) (TWord 5) (TWord 0)) (Pair (Pair c (Var a)) b)).
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 32 (TWord 0) (TWord 5) (TWord 5) (TWord 5) (TWord 0)) (Pair (Pair c (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 32 (TWord 0) (TWord 0) (TWord 5) (TWord 5) (TWord 0)) (Pair (Pair c (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 32 (TWord 0) (TWord 5) (TWord 0) (TWord 5) (TWord 0)) (Pair (Pair c (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_addcarryx_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 32 (TWord 0) (TWord 0) (TWord 0) (TWord 5) (TWord 0)) (Pair (Pair c (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 Notation "'addcarryx_u32' ( c , a , b )" := (Op (AddWithGetCarry 32 (TWord 3) (TWord 5) (TWord 5) (TWord 5) (TWord 3)) (Pair (Pair c (Var a)) b)).
 Notation "'addcarryx_u32' ( c , a , b )" := (Op (AddWithGetCarry 32 (TWord 3) (TWord 3) (TWord 5) (TWord 5) (TWord 3)) (Pair (Pair c (Var a)) b)).
 Notation "'addcarryx_u32' ( c , a , b )" := (Op (AddWithGetCarry 32 (TWord 3) (TWord 5) (TWord 3) (TWord 5) (TWord 3)) (Pair (Pair c (Var a)) b)).
+Notation "'addcarryx_u32' ( c , a , b )" := (Op (AddWithGetCarry 32 (TWord 3) (TWord 3) (TWord 3) (TWord 5) (TWord 3)) (Pair (Pair c (Var a)) b)).
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 32 (TWord 3) (TWord 5) (TWord 5) (TWord 5) (TWord 3)) (Pair (Pair c (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 32 (TWord 3) (TWord 3) (TWord 5) (TWord 5) (TWord 3)) (Pair (Pair c (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 32 (TWord 3) (TWord 5) (TWord 3) (TWord 5) (TWord 3)) (Pair (Pair c (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_addcarryx_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 32 (TWord 3) (TWord 3) (TWord 3) (TWord 5) (TWord 3)) (Pair (Pair c (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 Notation "'addcarryx_u32' ( c , a , b )" := (Op (AddWithGetCarry 32 (TWord 0) (TWord 5) (TWord 5) (TWord 5) (TWord 0)) (Pair (Pair c (Var a)) (Var b))).
 Notation "'addcarryx_u32' ( c , a , b )" := (Op (AddWithGetCarry 32 (TWord 0) (TWord 0) (TWord 5) (TWord 5) (TWord 0)) (Pair (Pair c (Var a)) (Var b))).
 Notation "'addcarryx_u32' ( c , a , b )" := (Op (AddWithGetCarry 32 (TWord 0) (TWord 5) (TWord 0) (TWord 5) (TWord 0)) (Pair (Pair c (Var a)) (Var b))).
+Notation "'addcarryx_u32' ( c , a , b )" := (Op (AddWithGetCarry 32 (TWord 0) (TWord 0) (TWord 0) (TWord 5) (TWord 0)) (Pair (Pair c (Var a)) (Var b))).
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 32 (TWord 0) (TWord 5) (TWord 5) (TWord 5) (TWord 0)) (Pair (Pair c (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 32 (TWord 0) (TWord 0) (TWord 5) (TWord 5) (TWord 0)) (Pair (Pair c (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 32 (TWord 0) (TWord 5) (TWord 0) (TWord 5) (TWord 0)) (Pair (Pair c (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_addcarryx_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 32 (TWord 0) (TWord 0) (TWord 0) (TWord 5) (TWord 0)) (Pair (Pair c (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 Notation "'addcarryx_u32' ( c , a , b )" := (Op (AddWithGetCarry 32 (TWord 3) (TWord 5) (TWord 5) (TWord 5) (TWord 3)) (Pair (Pair c (Var a)) (Var b))).
 Notation "'addcarryx_u32' ( c , a , b )" := (Op (AddWithGetCarry 32 (TWord 3) (TWord 3) (TWord 5) (TWord 5) (TWord 3)) (Pair (Pair c (Var a)) (Var b))).
 Notation "'addcarryx_u32' ( c , a , b )" := (Op (AddWithGetCarry 32 (TWord 3) (TWord 5) (TWord 3) (TWord 5) (TWord 3)) (Pair (Pair c (Var a)) (Var b))).
+Notation "'addcarryx_u32' ( c , a , b )" := (Op (AddWithGetCarry 32 (TWord 3) (TWord 3) (TWord 3) (TWord 5) (TWord 3)) (Pair (Pair c (Var a)) (Var b))).
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 32 (TWord 3) (TWord 5) (TWord 5) (TWord 5) (TWord 3)) (Pair (Pair c (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 32 (TWord 3) (TWord 3) (TWord 5) (TWord 5) (TWord 3)) (Pair (Pair c (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 32 (TWord 3) (TWord 5) (TWord 3) (TWord 5) (TWord 3)) (Pair (Pair c (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_addcarryx_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 32 (TWord 3) (TWord 3) (TWord 3) (TWord 5) (TWord 3)) (Pair (Pair c (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 Notation "'addcarryx_u32' ( c , a , b )" := (Op (AddWithGetCarry 32 (TWord 0) (TWord 5) (TWord 5) (TWord 5) (TWord 0)) (Pair (Pair (Var c) a) b)).
 Notation "'addcarryx_u32' ( c , a , b )" := (Op (AddWithGetCarry 32 (TWord 0) (TWord 0) (TWord 5) (TWord 5) (TWord 0)) (Pair (Pair (Var c) a) b)).
 Notation "'addcarryx_u32' ( c , a , b )" := (Op (AddWithGetCarry 32 (TWord 0) (TWord 5) (TWord 0) (TWord 5) (TWord 0)) (Pair (Pair (Var c) a) b)).
+Notation "'addcarryx_u32' ( c , a , b )" := (Op (AddWithGetCarry 32 (TWord 0) (TWord 0) (TWord 0) (TWord 5) (TWord 0)) (Pair (Pair (Var c) a) b)).
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 32 (TWord 0) (TWord 5) (TWord 5) (TWord 5) (TWord 0)) (Pair (Pair (Var c) a) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 32 (TWord 0) (TWord 0) (TWord 5) (TWord 5) (TWord 0)) (Pair (Pair (Var c) a) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 32 (TWord 0) (TWord 5) (TWord 0) (TWord 5) (TWord 0)) (Pair (Pair (Var c) a) b)) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_addcarryx_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 32 (TWord 0) (TWord 0) (TWord 0) (TWord 5) (TWord 0)) (Pair (Pair (Var c) a) b)) (fun '((out, c_out)%core) => REST)).*)
 Notation "'addcarryx_u32' ( c , a , b )" := (Op (AddWithGetCarry 32 (TWord 3) (TWord 5) (TWord 5) (TWord 5) (TWord 3)) (Pair (Pair (Var c) a) b)).
 Notation "'addcarryx_u32' ( c , a , b )" := (Op (AddWithGetCarry 32 (TWord 3) (TWord 3) (TWord 5) (TWord 5) (TWord 3)) (Pair (Pair (Var c) a) b)).
 Notation "'addcarryx_u32' ( c , a , b )" := (Op (AddWithGetCarry 32 (TWord 3) (TWord 5) (TWord 3) (TWord 5) (TWord 3)) (Pair (Pair (Var c) a) b)).
+Notation "'addcarryx_u32' ( c , a , b )" := (Op (AddWithGetCarry 32 (TWord 3) (TWord 3) (TWord 3) (TWord 5) (TWord 3)) (Pair (Pair (Var c) a) b)).
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 32 (TWord 3) (TWord 5) (TWord 5) (TWord 5) (TWord 3)) (Pair (Pair (Var c) a) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 32 (TWord 3) (TWord 3) (TWord 5) (TWord 5) (TWord 3)) (Pair (Pair (Var c) a) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 32 (TWord 3) (TWord 5) (TWord 3) (TWord 5) (TWord 3)) (Pair (Pair (Var c) a) b)) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_addcarryx_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 32 (TWord 3) (TWord 3) (TWord 3) (TWord 5) (TWord 3)) (Pair (Pair (Var c) a) b)) (fun '((out, c_out)%core) => REST)).*)
 Notation "'addcarryx_u32' ( c , a , b )" := (Op (AddWithGetCarry 32 (TWord 0) (TWord 5) (TWord 5) (TWord 5) (TWord 0)) (Pair (Pair (Var c) a) (Var b))).
 Notation "'addcarryx_u32' ( c , a , b )" := (Op (AddWithGetCarry 32 (TWord 0) (TWord 0) (TWord 5) (TWord 5) (TWord 0)) (Pair (Pair (Var c) a) (Var b))).
 Notation "'addcarryx_u32' ( c , a , b )" := (Op (AddWithGetCarry 32 (TWord 0) (TWord 5) (TWord 0) (TWord 5) (TWord 0)) (Pair (Pair (Var c) a) (Var b))).
+Notation "'addcarryx_u32' ( c , a , b )" := (Op (AddWithGetCarry 32 (TWord 0) (TWord 0) (TWord 0) (TWord 5) (TWord 0)) (Pair (Pair (Var c) a) (Var b))).
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 32 (TWord 0) (TWord 5) (TWord 5) (TWord 5) (TWord 0)) (Pair (Pair (Var c) a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 32 (TWord 0) (TWord 0) (TWord 5) (TWord 5) (TWord 0)) (Pair (Pair (Var c) a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 32 (TWord 0) (TWord 5) (TWord 0) (TWord 5) (TWord 0)) (Pair (Pair (Var c) a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_addcarryx_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 32 (TWord 0) (TWord 0) (TWord 0) (TWord 5) (TWord 0)) (Pair (Pair (Var c) a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 Notation "'addcarryx_u32' ( c , a , b )" := (Op (AddWithGetCarry 32 (TWord 3) (TWord 5) (TWord 5) (TWord 5) (TWord 3)) (Pair (Pair (Var c) a) (Var b))).
 Notation "'addcarryx_u32' ( c , a , b )" := (Op (AddWithGetCarry 32 (TWord 3) (TWord 3) (TWord 5) (TWord 5) (TWord 3)) (Pair (Pair (Var c) a) (Var b))).
 Notation "'addcarryx_u32' ( c , a , b )" := (Op (AddWithGetCarry 32 (TWord 3) (TWord 5) (TWord 3) (TWord 5) (TWord 3)) (Pair (Pair (Var c) a) (Var b))).
+Notation "'addcarryx_u32' ( c , a , b )" := (Op (AddWithGetCarry 32 (TWord 3) (TWord 3) (TWord 3) (TWord 5) (TWord 3)) (Pair (Pair (Var c) a) (Var b))).
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 32 (TWord 3) (TWord 5) (TWord 5) (TWord 5) (TWord 3)) (Pair (Pair (Var c) a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 32 (TWord 3) (TWord 3) (TWord 5) (TWord 5) (TWord 3)) (Pair (Pair (Var c) a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 32 (TWord 3) (TWord 5) (TWord 3) (TWord 5) (TWord 3)) (Pair (Pair (Var c) a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_addcarryx_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 32 (TWord 3) (TWord 3) (TWord 3) (TWord 5) (TWord 3)) (Pair (Pair (Var c) a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 Notation "'addcarryx_u32' ( c , a , b )" := (Op (AddWithGetCarry 32 (TWord 0) (TWord 5) (TWord 5) (TWord 5) (TWord 0)) (Pair (Pair (Var c) (Var a)) b)).
 Notation "'addcarryx_u32' ( c , a , b )" := (Op (AddWithGetCarry 32 (TWord 0) (TWord 0) (TWord 5) (TWord 5) (TWord 0)) (Pair (Pair (Var c) (Var a)) b)).
 Notation "'addcarryx_u32' ( c , a , b )" := (Op (AddWithGetCarry 32 (TWord 0) (TWord 5) (TWord 0) (TWord 5) (TWord 0)) (Pair (Pair (Var c) (Var a)) b)).
+Notation "'addcarryx_u32' ( c , a , b )" := (Op (AddWithGetCarry 32 (TWord 0) (TWord 0) (TWord 0) (TWord 5) (TWord 0)) (Pair (Pair (Var c) (Var a)) b)).
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 32 (TWord 0) (TWord 5) (TWord 5) (TWord 5) (TWord 0)) (Pair (Pair (Var c) (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 32 (TWord 0) (TWord 0) (TWord 5) (TWord 5) (TWord 0)) (Pair (Pair (Var c) (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 32 (TWord 0) (TWord 5) (TWord 0) (TWord 5) (TWord 0)) (Pair (Pair (Var c) (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_addcarryx_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 32 (TWord 0) (TWord 0) (TWord 0) (TWord 5) (TWord 0)) (Pair (Pair (Var c) (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 Notation "'addcarryx_u32' ( c , a , b )" := (Op (AddWithGetCarry 32 (TWord 3) (TWord 5) (TWord 5) (TWord 5) (TWord 3)) (Pair (Pair (Var c) (Var a)) b)).
 Notation "'addcarryx_u32' ( c , a , b )" := (Op (AddWithGetCarry 32 (TWord 3) (TWord 3) (TWord 5) (TWord 5) (TWord 3)) (Pair (Pair (Var c) (Var a)) b)).
 Notation "'addcarryx_u32' ( c , a , b )" := (Op (AddWithGetCarry 32 (TWord 3) (TWord 5) (TWord 3) (TWord 5) (TWord 3)) (Pair (Pair (Var c) (Var a)) b)).
+Notation "'addcarryx_u32' ( c , a , b )" := (Op (AddWithGetCarry 32 (TWord 3) (TWord 3) (TWord 3) (TWord 5) (TWord 3)) (Pair (Pair (Var c) (Var a)) b)).
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 32 (TWord 3) (TWord 5) (TWord 5) (TWord 5) (TWord 3)) (Pair (Pair (Var c) (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 32 (TWord 3) (TWord 3) (TWord 5) (TWord 5) (TWord 3)) (Pair (Pair (Var c) (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 32 (TWord 3) (TWord 5) (TWord 3) (TWord 5) (TWord 3)) (Pair (Pair (Var c) (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_addcarryx_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 32 (TWord 3) (TWord 3) (TWord 3) (TWord 5) (TWord 3)) (Pair (Pair (Var c) (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 Notation "'addcarryx_u32' ( c , a , b )" := (Op (AddWithGetCarry 32 (TWord 0) (TWord 5) (TWord 5) (TWord 5) (TWord 0)) (Pair (Pair (Var c) (Var a)) (Var b))).
 Notation "'addcarryx_u32' ( c , a , b )" := (Op (AddWithGetCarry 32 (TWord 0) (TWord 0) (TWord 5) (TWord 5) (TWord 0)) (Pair (Pair (Var c) (Var a)) (Var b))).
 Notation "'addcarryx_u32' ( c , a , b )" := (Op (AddWithGetCarry 32 (TWord 0) (TWord 5) (TWord 0) (TWord 5) (TWord 0)) (Pair (Pair (Var c) (Var a)) (Var b))).
+Notation "'addcarryx_u32' ( c , a , b )" := (Op (AddWithGetCarry 32 (TWord 0) (TWord 0) (TWord 0) (TWord 5) (TWord 0)) (Pair (Pair (Var c) (Var a)) (Var b))).
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 32 (TWord 0) (TWord 5) (TWord 5) (TWord 5) (TWord 0)) (Pair (Pair (Var c) (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 32 (TWord 0) (TWord 0) (TWord 5) (TWord 5) (TWord 0)) (Pair (Pair (Var c) (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 32 (TWord 0) (TWord 5) (TWord 0) (TWord 5) (TWord 0)) (Pair (Pair (Var c) (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_addcarryx_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 32 (TWord 0) (TWord 0) (TWord 0) (TWord 5) (TWord 0)) (Pair (Pair (Var c) (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 Notation "'addcarryx_u32' ( c , a , b )" := (Op (AddWithGetCarry 32 (TWord 3) (TWord 5) (TWord 5) (TWord 5) (TWord 3)) (Pair (Pair (Var c) (Var a)) (Var b))).
 Notation "'addcarryx_u32' ( c , a , b )" := (Op (AddWithGetCarry 32 (TWord 3) (TWord 3) (TWord 5) (TWord 5) (TWord 3)) (Pair (Pair (Var c) (Var a)) (Var b))).
 Notation "'addcarryx_u32' ( c , a , b )" := (Op (AddWithGetCarry 32 (TWord 3) (TWord 5) (TWord 3) (TWord 5) (TWord 3)) (Pair (Pair (Var c) (Var a)) (Var b))).
+Notation "'addcarryx_u32' ( c , a , b )" := (Op (AddWithGetCarry 32 (TWord 3) (TWord 3) (TWord 3) (TWord 5) (TWord 3)) (Pair (Pair (Var c) (Var a)) (Var b))).
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 32 (TWord 3) (TWord 5) (TWord 5) (TWord 5) (TWord 3)) (Pair (Pair (Var c) (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 32 (TWord 3) (TWord 3) (TWord 5) (TWord 5) (TWord 3)) (Pair (Pair (Var c) (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 32 (TWord 3) (TWord 5) (TWord 3) (TWord 5) (TWord 3)) (Pair (Pair (Var c) (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_addcarryx_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 32 (TWord 3) (TWord 3) (TWord 3) (TWord 5) (TWord 3)) (Pair (Pair (Var c) (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 Notation "'addcarryx_u64' ( c , a , b )" := (Op (AddWithGetCarry 64 (TWord 0) (TWord 6) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair c a) b)).
 Notation "'addcarryx_u64' ( c , a , b )" := (Op (AddWithGetCarry 64 (TWord 0) (TWord 0) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair c a) b)).
 Notation "'addcarryx_u64' ( c , a , b )" := (Op (AddWithGetCarry 64 (TWord 0) (TWord 6) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair c a) b)).
+Notation "'addcarryx_u64' ( c , a , b )" := (Op (AddWithGetCarry 64 (TWord 0) (TWord 0) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair c a) b)).
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 64 (TWord 0) (TWord 6) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair c a) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 64 (TWord 0) (TWord 0) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair c a) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 64 (TWord 0) (TWord 6) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair c a) b)) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_addcarryx_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 64 (TWord 0) (TWord 0) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair c a) b)) (fun '((out, c_out)%core) => REST)).*)
 Notation "'addcarryx_u64' ( c , a , b )" := (Op (AddWithGetCarry 64 (TWord 3) (TWord 6) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair c a) b)).
 Notation "'addcarryx_u64' ( c , a , b )" := (Op (AddWithGetCarry 64 (TWord 3) (TWord 3) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair c a) b)).
 Notation "'addcarryx_u64' ( c , a , b )" := (Op (AddWithGetCarry 64 (TWord 3) (TWord 6) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair c a) b)).
+Notation "'addcarryx_u64' ( c , a , b )" := (Op (AddWithGetCarry 64 (TWord 3) (TWord 3) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair c a) b)).
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 64 (TWord 3) (TWord 6) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair c a) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 64 (TWord 3) (TWord 3) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair c a) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 64 (TWord 3) (TWord 6) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair c a) b)) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_addcarryx_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 64 (TWord 3) (TWord 3) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair c a) b)) (fun '((out, c_out)%core) => REST)).*)
 Notation "'addcarryx_u64' ( c , a , b )" := (Op (AddWithGetCarry 64 (TWord 0) (TWord 6) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair c a) (Var b))).
 Notation "'addcarryx_u64' ( c , a , b )" := (Op (AddWithGetCarry 64 (TWord 0) (TWord 0) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair c a) (Var b))).
 Notation "'addcarryx_u64' ( c , a , b )" := (Op (AddWithGetCarry 64 (TWord 0) (TWord 6) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair c a) (Var b))).
+Notation "'addcarryx_u64' ( c , a , b )" := (Op (AddWithGetCarry 64 (TWord 0) (TWord 0) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair c a) (Var b))).
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 64 (TWord 0) (TWord 6) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair c a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 64 (TWord 0) (TWord 0) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair c a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 64 (TWord 0) (TWord 6) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair c a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_addcarryx_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 64 (TWord 0) (TWord 0) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair c a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 Notation "'addcarryx_u64' ( c , a , b )" := (Op (AddWithGetCarry 64 (TWord 3) (TWord 6) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair c a) (Var b))).
 Notation "'addcarryx_u64' ( c , a , b )" := (Op (AddWithGetCarry 64 (TWord 3) (TWord 3) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair c a) (Var b))).
 Notation "'addcarryx_u64' ( c , a , b )" := (Op (AddWithGetCarry 64 (TWord 3) (TWord 6) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair c a) (Var b))).
+Notation "'addcarryx_u64' ( c , a , b )" := (Op (AddWithGetCarry 64 (TWord 3) (TWord 3) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair c a) (Var b))).
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 64 (TWord 3) (TWord 6) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair c a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 64 (TWord 3) (TWord 3) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair c a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 64 (TWord 3) (TWord 6) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair c a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_addcarryx_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 64 (TWord 3) (TWord 3) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair c a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 Notation "'addcarryx_u64' ( c , a , b )" := (Op (AddWithGetCarry 64 (TWord 0) (TWord 6) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair c (Var a)) b)).
 Notation "'addcarryx_u64' ( c , a , b )" := (Op (AddWithGetCarry 64 (TWord 0) (TWord 0) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair c (Var a)) b)).
 Notation "'addcarryx_u64' ( c , a , b )" := (Op (AddWithGetCarry 64 (TWord 0) (TWord 6) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair c (Var a)) b)).
+Notation "'addcarryx_u64' ( c , a , b )" := (Op (AddWithGetCarry 64 (TWord 0) (TWord 0) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair c (Var a)) b)).
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 64 (TWord 0) (TWord 6) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair c (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 64 (TWord 0) (TWord 0) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair c (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 64 (TWord 0) (TWord 6) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair c (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_addcarryx_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 64 (TWord 0) (TWord 0) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair c (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 Notation "'addcarryx_u64' ( c , a , b )" := (Op (AddWithGetCarry 64 (TWord 3) (TWord 6) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair c (Var a)) b)).
 Notation "'addcarryx_u64' ( c , a , b )" := (Op (AddWithGetCarry 64 (TWord 3) (TWord 3) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair c (Var a)) b)).
 Notation "'addcarryx_u64' ( c , a , b )" := (Op (AddWithGetCarry 64 (TWord 3) (TWord 6) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair c (Var a)) b)).
+Notation "'addcarryx_u64' ( c , a , b )" := (Op (AddWithGetCarry 64 (TWord 3) (TWord 3) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair c (Var a)) b)).
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 64 (TWord 3) (TWord 6) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair c (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 64 (TWord 3) (TWord 3) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair c (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 64 (TWord 3) (TWord 6) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair c (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_addcarryx_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 64 (TWord 3) (TWord 3) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair c (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 Notation "'addcarryx_u64' ( c , a , b )" := (Op (AddWithGetCarry 64 (TWord 0) (TWord 6) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair c (Var a)) (Var b))).
 Notation "'addcarryx_u64' ( c , a , b )" := (Op (AddWithGetCarry 64 (TWord 0) (TWord 0) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair c (Var a)) (Var b))).
 Notation "'addcarryx_u64' ( c , a , b )" := (Op (AddWithGetCarry 64 (TWord 0) (TWord 6) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair c (Var a)) (Var b))).
+Notation "'addcarryx_u64' ( c , a , b )" := (Op (AddWithGetCarry 64 (TWord 0) (TWord 0) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair c (Var a)) (Var b))).
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 64 (TWord 0) (TWord 6) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair c (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 64 (TWord 0) (TWord 0) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair c (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 64 (TWord 0) (TWord 6) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair c (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_addcarryx_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 64 (TWord 0) (TWord 0) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair c (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 Notation "'addcarryx_u64' ( c , a , b )" := (Op (AddWithGetCarry 64 (TWord 3) (TWord 6) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair c (Var a)) (Var b))).
 Notation "'addcarryx_u64' ( c , a , b )" := (Op (AddWithGetCarry 64 (TWord 3) (TWord 3) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair c (Var a)) (Var b))).
 Notation "'addcarryx_u64' ( c , a , b )" := (Op (AddWithGetCarry 64 (TWord 3) (TWord 6) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair c (Var a)) (Var b))).
+Notation "'addcarryx_u64' ( c , a , b )" := (Op (AddWithGetCarry 64 (TWord 3) (TWord 3) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair c (Var a)) (Var b))).
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 64 (TWord 3) (TWord 6) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair c (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 64 (TWord 3) (TWord 3) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair c (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 64 (TWord 3) (TWord 6) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair c (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_addcarryx_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 64 (TWord 3) (TWord 3) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair c (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 Notation "'addcarryx_u64' ( c , a , b )" := (Op (AddWithGetCarry 64 (TWord 0) (TWord 6) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair (Var c) a) b)).
 Notation "'addcarryx_u64' ( c , a , b )" := (Op (AddWithGetCarry 64 (TWord 0) (TWord 0) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair (Var c) a) b)).
 Notation "'addcarryx_u64' ( c , a , b )" := (Op (AddWithGetCarry 64 (TWord 0) (TWord 6) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair (Var c) a) b)).
+Notation "'addcarryx_u64' ( c , a , b )" := (Op (AddWithGetCarry 64 (TWord 0) (TWord 0) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair (Var c) a) b)).
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 64 (TWord 0) (TWord 6) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair (Var c) a) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 64 (TWord 0) (TWord 0) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair (Var c) a) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 64 (TWord 0) (TWord 6) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair (Var c) a) b)) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_addcarryx_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 64 (TWord 0) (TWord 0) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair (Var c) a) b)) (fun '((out, c_out)%core) => REST)).*)
 Notation "'addcarryx_u64' ( c , a , b )" := (Op (AddWithGetCarry 64 (TWord 3) (TWord 6) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair (Var c) a) b)).
 Notation "'addcarryx_u64' ( c , a , b )" := (Op (AddWithGetCarry 64 (TWord 3) (TWord 3) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair (Var c) a) b)).
 Notation "'addcarryx_u64' ( c , a , b )" := (Op (AddWithGetCarry 64 (TWord 3) (TWord 6) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair (Var c) a) b)).
+Notation "'addcarryx_u64' ( c , a , b )" := (Op (AddWithGetCarry 64 (TWord 3) (TWord 3) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair (Var c) a) b)).
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 64 (TWord 3) (TWord 6) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair (Var c) a) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 64 (TWord 3) (TWord 3) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair (Var c) a) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 64 (TWord 3) (TWord 6) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair (Var c) a) b)) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_addcarryx_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 64 (TWord 3) (TWord 3) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair (Var c) a) b)) (fun '((out, c_out)%core) => REST)).*)
 Notation "'addcarryx_u64' ( c , a , b )" := (Op (AddWithGetCarry 64 (TWord 0) (TWord 6) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair (Var c) a) (Var b))).
 Notation "'addcarryx_u64' ( c , a , b )" := (Op (AddWithGetCarry 64 (TWord 0) (TWord 0) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair (Var c) a) (Var b))).
 Notation "'addcarryx_u64' ( c , a , b )" := (Op (AddWithGetCarry 64 (TWord 0) (TWord 6) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair (Var c) a) (Var b))).
+Notation "'addcarryx_u64' ( c , a , b )" := (Op (AddWithGetCarry 64 (TWord 0) (TWord 0) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair (Var c) a) (Var b))).
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 64 (TWord 0) (TWord 6) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair (Var c) a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 64 (TWord 0) (TWord 0) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair (Var c) a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 64 (TWord 0) (TWord 6) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair (Var c) a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_addcarryx_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 64 (TWord 0) (TWord 0) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair (Var c) a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 Notation "'addcarryx_u64' ( c , a , b )" := (Op (AddWithGetCarry 64 (TWord 3) (TWord 6) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair (Var c) a) (Var b))).
 Notation "'addcarryx_u64' ( c , a , b )" := (Op (AddWithGetCarry 64 (TWord 3) (TWord 3) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair (Var c) a) (Var b))).
 Notation "'addcarryx_u64' ( c , a , b )" := (Op (AddWithGetCarry 64 (TWord 3) (TWord 6) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair (Var c) a) (Var b))).
+Notation "'addcarryx_u64' ( c , a , b )" := (Op (AddWithGetCarry 64 (TWord 3) (TWord 3) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair (Var c) a) (Var b))).
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 64 (TWord 3) (TWord 6) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair (Var c) a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 64 (TWord 3) (TWord 3) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair (Var c) a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 64 (TWord 3) (TWord 6) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair (Var c) a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_addcarryx_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 64 (TWord 3) (TWord 3) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair (Var c) a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 Notation "'addcarryx_u64' ( c , a , b )" := (Op (AddWithGetCarry 64 (TWord 0) (TWord 6) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair (Var c) (Var a)) b)).
 Notation "'addcarryx_u64' ( c , a , b )" := (Op (AddWithGetCarry 64 (TWord 0) (TWord 0) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair (Var c) (Var a)) b)).
 Notation "'addcarryx_u64' ( c , a , b )" := (Op (AddWithGetCarry 64 (TWord 0) (TWord 6) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair (Var c) (Var a)) b)).
+Notation "'addcarryx_u64' ( c , a , b )" := (Op (AddWithGetCarry 64 (TWord 0) (TWord 0) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair (Var c) (Var a)) b)).
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 64 (TWord 0) (TWord 6) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair (Var c) (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 64 (TWord 0) (TWord 0) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair (Var c) (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 64 (TWord 0) (TWord 6) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair (Var c) (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_addcarryx_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 64 (TWord 0) (TWord 0) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair (Var c) (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 Notation "'addcarryx_u64' ( c , a , b )" := (Op (AddWithGetCarry 64 (TWord 3) (TWord 6) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair (Var c) (Var a)) b)).
 Notation "'addcarryx_u64' ( c , a , b )" := (Op (AddWithGetCarry 64 (TWord 3) (TWord 3) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair (Var c) (Var a)) b)).
 Notation "'addcarryx_u64' ( c , a , b )" := (Op (AddWithGetCarry 64 (TWord 3) (TWord 6) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair (Var c) (Var a)) b)).
+Notation "'addcarryx_u64' ( c , a , b )" := (Op (AddWithGetCarry 64 (TWord 3) (TWord 3) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair (Var c) (Var a)) b)).
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 64 (TWord 3) (TWord 6) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair (Var c) (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 64 (TWord 3) (TWord 3) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair (Var c) (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 64 (TWord 3) (TWord 6) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair (Var c) (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_addcarryx_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 64 (TWord 3) (TWord 3) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair (Var c) (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 Notation "'addcarryx_u64' ( c , a , b )" := (Op (AddWithGetCarry 64 (TWord 0) (TWord 6) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair (Var c) (Var a)) (Var b))).
 Notation "'addcarryx_u64' ( c , a , b )" := (Op (AddWithGetCarry 64 (TWord 0) (TWord 0) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair (Var c) (Var a)) (Var b))).
 Notation "'addcarryx_u64' ( c , a , b )" := (Op (AddWithGetCarry 64 (TWord 0) (TWord 6) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair (Var c) (Var a)) (Var b))).
+Notation "'addcarryx_u64' ( c , a , b )" := (Op (AddWithGetCarry 64 (TWord 0) (TWord 0) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair (Var c) (Var a)) (Var b))).
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 64 (TWord 0) (TWord 6) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair (Var c) (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 64 (TWord 0) (TWord 0) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair (Var c) (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 64 (TWord 0) (TWord 6) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair (Var c) (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_addcarryx_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 64 (TWord 0) (TWord 0) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair (Var c) (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 Notation "'addcarryx_u64' ( c , a , b )" := (Op (AddWithGetCarry 64 (TWord 3) (TWord 6) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair (Var c) (Var a)) (Var b))).
 Notation "'addcarryx_u64' ( c , a , b )" := (Op (AddWithGetCarry 64 (TWord 3) (TWord 3) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair (Var c) (Var a)) (Var b))).
 Notation "'addcarryx_u64' ( c , a , b )" := (Op (AddWithGetCarry 64 (TWord 3) (TWord 6) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair (Var c) (Var a)) (Var b))).
+Notation "'addcarryx_u64' ( c , a , b )" := (Op (AddWithGetCarry 64 (TWord 3) (TWord 3) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair (Var c) (Var a)) (Var b))).
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 64 (TWord 3) (TWord 6) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair (Var c) (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 64 (TWord 3) (TWord 3) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair (Var c) (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 64 (TWord 3) (TWord 6) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair (Var c) (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_addcarryx_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 64 (TWord 3) (TWord 3) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair (Var c) (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 Notation "'addcarryx_u128' ( c , a , b )" := (Op (AddWithGetCarry 128 (TWord 0) (TWord 7) (TWord 7) (TWord 7) (TWord 0)) (Pair (Pair c a) b)).
 Notation "'addcarryx_u128' ( c , a , b )" := (Op (AddWithGetCarry 128 (TWord 0) (TWord 0) (TWord 7) (TWord 7) (TWord 0)) (Pair (Pair c a) b)).
 Notation "'addcarryx_u128' ( c , a , b )" := (Op (AddWithGetCarry 128 (TWord 0) (TWord 7) (TWord 0) (TWord 7) (TWord 0)) (Pair (Pair c a) b)).
+Notation "'addcarryx_u128' ( c , a , b )" := (Op (AddWithGetCarry 128 (TWord 0) (TWord 0) (TWord 0) (TWord 7) (TWord 0)) (Pair (Pair c a) b)).
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 128 (TWord 0) (TWord 7) (TWord 7) (TWord 7) (TWord 0)) (Pair (Pair c a) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 128 (TWord 0) (TWord 0) (TWord 7) (TWord 7) (TWord 0)) (Pair (Pair c a) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 128 (TWord 0) (TWord 7) (TWord 0) (TWord 7) (TWord 0)) (Pair (Pair c a) b)) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_addcarryx_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 128 (TWord 0) (TWord 0) (TWord 0) (TWord 7) (TWord 0)) (Pair (Pair c a) b)) (fun '((out, c_out)%core) => REST)).*)
 Notation "'addcarryx_u128' ( c , a , b )" := (Op (AddWithGetCarry 128 (TWord 3) (TWord 7) (TWord 7) (TWord 7) (TWord 3)) (Pair (Pair c a) b)).
 Notation "'addcarryx_u128' ( c , a , b )" := (Op (AddWithGetCarry 128 (TWord 3) (TWord 3) (TWord 7) (TWord 7) (TWord 3)) (Pair (Pair c a) b)).
 Notation "'addcarryx_u128' ( c , a , b )" := (Op (AddWithGetCarry 128 (TWord 3) (TWord 7) (TWord 3) (TWord 7) (TWord 3)) (Pair (Pair c a) b)).
+Notation "'addcarryx_u128' ( c , a , b )" := (Op (AddWithGetCarry 128 (TWord 3) (TWord 3) (TWord 3) (TWord 7) (TWord 3)) (Pair (Pair c a) b)).
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 128 (TWord 3) (TWord 7) (TWord 7) (TWord 7) (TWord 3)) (Pair (Pair c a) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 128 (TWord 3) (TWord 3) (TWord 7) (TWord 7) (TWord 3)) (Pair (Pair c a) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 128 (TWord 3) (TWord 7) (TWord 3) (TWord 7) (TWord 3)) (Pair (Pair c a) b)) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_addcarryx_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 128 (TWord 3) (TWord 3) (TWord 3) (TWord 7) (TWord 3)) (Pair (Pair c a) b)) (fun '((out, c_out)%core) => REST)).*)
 Notation "'addcarryx_u128' ( c , a , b )" := (Op (AddWithGetCarry 128 (TWord 0) (TWord 7) (TWord 7) (TWord 7) (TWord 0)) (Pair (Pair c a) (Var b))).
 Notation "'addcarryx_u128' ( c , a , b )" := (Op (AddWithGetCarry 128 (TWord 0) (TWord 0) (TWord 7) (TWord 7) (TWord 0)) (Pair (Pair c a) (Var b))).
 Notation "'addcarryx_u128' ( c , a , b )" := (Op (AddWithGetCarry 128 (TWord 0) (TWord 7) (TWord 0) (TWord 7) (TWord 0)) (Pair (Pair c a) (Var b))).
+Notation "'addcarryx_u128' ( c , a , b )" := (Op (AddWithGetCarry 128 (TWord 0) (TWord 0) (TWord 0) (TWord 7) (TWord 0)) (Pair (Pair c a) (Var b))).
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 128 (TWord 0) (TWord 7) (TWord 7) (TWord 7) (TWord 0)) (Pair (Pair c a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 128 (TWord 0) (TWord 0) (TWord 7) (TWord 7) (TWord 0)) (Pair (Pair c a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 128 (TWord 0) (TWord 7) (TWord 0) (TWord 7) (TWord 0)) (Pair (Pair c a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_addcarryx_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 128 (TWord 0) (TWord 0) (TWord 0) (TWord 7) (TWord 0)) (Pair (Pair c a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 Notation "'addcarryx_u128' ( c , a , b )" := (Op (AddWithGetCarry 128 (TWord 3) (TWord 7) (TWord 7) (TWord 7) (TWord 3)) (Pair (Pair c a) (Var b))).
 Notation "'addcarryx_u128' ( c , a , b )" := (Op (AddWithGetCarry 128 (TWord 3) (TWord 3) (TWord 7) (TWord 7) (TWord 3)) (Pair (Pair c a) (Var b))).
 Notation "'addcarryx_u128' ( c , a , b )" := (Op (AddWithGetCarry 128 (TWord 3) (TWord 7) (TWord 3) (TWord 7) (TWord 3)) (Pair (Pair c a) (Var b))).
+Notation "'addcarryx_u128' ( c , a , b )" := (Op (AddWithGetCarry 128 (TWord 3) (TWord 3) (TWord 3) (TWord 7) (TWord 3)) (Pair (Pair c a) (Var b))).
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 128 (TWord 3) (TWord 7) (TWord 7) (TWord 7) (TWord 3)) (Pair (Pair c a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 128 (TWord 3) (TWord 3) (TWord 7) (TWord 7) (TWord 3)) (Pair (Pair c a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 128 (TWord 3) (TWord 7) (TWord 3) (TWord 7) (TWord 3)) (Pair (Pair c a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_addcarryx_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 128 (TWord 3) (TWord 3) (TWord 3) (TWord 7) (TWord 3)) (Pair (Pair c a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 Notation "'addcarryx_u128' ( c , a , b )" := (Op (AddWithGetCarry 128 (TWord 0) (TWord 7) (TWord 7) (TWord 7) (TWord 0)) (Pair (Pair c (Var a)) b)).
 Notation "'addcarryx_u128' ( c , a , b )" := (Op (AddWithGetCarry 128 (TWord 0) (TWord 0) (TWord 7) (TWord 7) (TWord 0)) (Pair (Pair c (Var a)) b)).
 Notation "'addcarryx_u128' ( c , a , b )" := (Op (AddWithGetCarry 128 (TWord 0) (TWord 7) (TWord 0) (TWord 7) (TWord 0)) (Pair (Pair c (Var a)) b)).
+Notation "'addcarryx_u128' ( c , a , b )" := (Op (AddWithGetCarry 128 (TWord 0) (TWord 0) (TWord 0) (TWord 7) (TWord 0)) (Pair (Pair c (Var a)) b)).
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 128 (TWord 0) (TWord 7) (TWord 7) (TWord 7) (TWord 0)) (Pair (Pair c (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 128 (TWord 0) (TWord 0) (TWord 7) (TWord 7) (TWord 0)) (Pair (Pair c (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 128 (TWord 0) (TWord 7) (TWord 0) (TWord 7) (TWord 0)) (Pair (Pair c (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_addcarryx_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 128 (TWord 0) (TWord 0) (TWord 0) (TWord 7) (TWord 0)) (Pair (Pair c (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 Notation "'addcarryx_u128' ( c , a , b )" := (Op (AddWithGetCarry 128 (TWord 3) (TWord 7) (TWord 7) (TWord 7) (TWord 3)) (Pair (Pair c (Var a)) b)).
 Notation "'addcarryx_u128' ( c , a , b )" := (Op (AddWithGetCarry 128 (TWord 3) (TWord 3) (TWord 7) (TWord 7) (TWord 3)) (Pair (Pair c (Var a)) b)).
 Notation "'addcarryx_u128' ( c , a , b )" := (Op (AddWithGetCarry 128 (TWord 3) (TWord 7) (TWord 3) (TWord 7) (TWord 3)) (Pair (Pair c (Var a)) b)).
+Notation "'addcarryx_u128' ( c , a , b )" := (Op (AddWithGetCarry 128 (TWord 3) (TWord 3) (TWord 3) (TWord 7) (TWord 3)) (Pair (Pair c (Var a)) b)).
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 128 (TWord 3) (TWord 7) (TWord 7) (TWord 7) (TWord 3)) (Pair (Pair c (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 128 (TWord 3) (TWord 3) (TWord 7) (TWord 7) (TWord 3)) (Pair (Pair c (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 128 (TWord 3) (TWord 7) (TWord 3) (TWord 7) (TWord 3)) (Pair (Pair c (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_addcarryx_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 128 (TWord 3) (TWord 3) (TWord 3) (TWord 7) (TWord 3)) (Pair (Pair c (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 Notation "'addcarryx_u128' ( c , a , b )" := (Op (AddWithGetCarry 128 (TWord 0) (TWord 7) (TWord 7) (TWord 7) (TWord 0)) (Pair (Pair c (Var a)) (Var b))).
 Notation "'addcarryx_u128' ( c , a , b )" := (Op (AddWithGetCarry 128 (TWord 0) (TWord 0) (TWord 7) (TWord 7) (TWord 0)) (Pair (Pair c (Var a)) (Var b))).
 Notation "'addcarryx_u128' ( c , a , b )" := (Op (AddWithGetCarry 128 (TWord 0) (TWord 7) (TWord 0) (TWord 7) (TWord 0)) (Pair (Pair c (Var a)) (Var b))).
+Notation "'addcarryx_u128' ( c , a , b )" := (Op (AddWithGetCarry 128 (TWord 0) (TWord 0) (TWord 0) (TWord 7) (TWord 0)) (Pair (Pair c (Var a)) (Var b))).
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 128 (TWord 0) (TWord 7) (TWord 7) (TWord 7) (TWord 0)) (Pair (Pair c (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 128 (TWord 0) (TWord 0) (TWord 7) (TWord 7) (TWord 0)) (Pair (Pair c (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 128 (TWord 0) (TWord 7) (TWord 0) (TWord 7) (TWord 0)) (Pair (Pair c (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_addcarryx_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 128 (TWord 0) (TWord 0) (TWord 0) (TWord 7) (TWord 0)) (Pair (Pair c (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 Notation "'addcarryx_u128' ( c , a , b )" := (Op (AddWithGetCarry 128 (TWord 3) (TWord 7) (TWord 7) (TWord 7) (TWord 3)) (Pair (Pair c (Var a)) (Var b))).
 Notation "'addcarryx_u128' ( c , a , b )" := (Op (AddWithGetCarry 128 (TWord 3) (TWord 3) (TWord 7) (TWord 7) (TWord 3)) (Pair (Pair c (Var a)) (Var b))).
 Notation "'addcarryx_u128' ( c , a , b )" := (Op (AddWithGetCarry 128 (TWord 3) (TWord 7) (TWord 3) (TWord 7) (TWord 3)) (Pair (Pair c (Var a)) (Var b))).
+Notation "'addcarryx_u128' ( c , a , b )" := (Op (AddWithGetCarry 128 (TWord 3) (TWord 3) (TWord 3) (TWord 7) (TWord 3)) (Pair (Pair c (Var a)) (Var b))).
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 128 (TWord 3) (TWord 7) (TWord 7) (TWord 7) (TWord 3)) (Pair (Pair c (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 128 (TWord 3) (TWord 3) (TWord 7) (TWord 7) (TWord 3)) (Pair (Pair c (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 128 (TWord 3) (TWord 7) (TWord 3) (TWord 7) (TWord 3)) (Pair (Pair c (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_addcarryx_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 128 (TWord 3) (TWord 3) (TWord 3) (TWord 7) (TWord 3)) (Pair (Pair c (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 Notation "'addcarryx_u128' ( c , a , b )" := (Op (AddWithGetCarry 128 (TWord 0) (TWord 7) (TWord 7) (TWord 7) (TWord 0)) (Pair (Pair (Var c) a) b)).
 Notation "'addcarryx_u128' ( c , a , b )" := (Op (AddWithGetCarry 128 (TWord 0) (TWord 0) (TWord 7) (TWord 7) (TWord 0)) (Pair (Pair (Var c) a) b)).
 Notation "'addcarryx_u128' ( c , a , b )" := (Op (AddWithGetCarry 128 (TWord 0) (TWord 7) (TWord 0) (TWord 7) (TWord 0)) (Pair (Pair (Var c) a) b)).
+Notation "'addcarryx_u128' ( c , a , b )" := (Op (AddWithGetCarry 128 (TWord 0) (TWord 0) (TWord 0) (TWord 7) (TWord 0)) (Pair (Pair (Var c) a) b)).
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 128 (TWord 0) (TWord 7) (TWord 7) (TWord 7) (TWord 0)) (Pair (Pair (Var c) a) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 128 (TWord 0) (TWord 0) (TWord 7) (TWord 7) (TWord 0)) (Pair (Pair (Var c) a) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 128 (TWord 0) (TWord 7) (TWord 0) (TWord 7) (TWord 0)) (Pair (Pair (Var c) a) b)) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_addcarryx_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 128 (TWord 0) (TWord 0) (TWord 0) (TWord 7) (TWord 0)) (Pair (Pair (Var c) a) b)) (fun '((out, c_out)%core) => REST)).*)
 Notation "'addcarryx_u128' ( c , a , b )" := (Op (AddWithGetCarry 128 (TWord 3) (TWord 7) (TWord 7) (TWord 7) (TWord 3)) (Pair (Pair (Var c) a) b)).
 Notation "'addcarryx_u128' ( c , a , b )" := (Op (AddWithGetCarry 128 (TWord 3) (TWord 3) (TWord 7) (TWord 7) (TWord 3)) (Pair (Pair (Var c) a) b)).
 Notation "'addcarryx_u128' ( c , a , b )" := (Op (AddWithGetCarry 128 (TWord 3) (TWord 7) (TWord 3) (TWord 7) (TWord 3)) (Pair (Pair (Var c) a) b)).
+Notation "'addcarryx_u128' ( c , a , b )" := (Op (AddWithGetCarry 128 (TWord 3) (TWord 3) (TWord 3) (TWord 7) (TWord 3)) (Pair (Pair (Var c) a) b)).
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 128 (TWord 3) (TWord 7) (TWord 7) (TWord 7) (TWord 3)) (Pair (Pair (Var c) a) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 128 (TWord 3) (TWord 3) (TWord 7) (TWord 7) (TWord 3)) (Pair (Pair (Var c) a) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 128 (TWord 3) (TWord 7) (TWord 3) (TWord 7) (TWord 3)) (Pair (Pair (Var c) a) b)) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_addcarryx_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 128 (TWord 3) (TWord 3) (TWord 3) (TWord 7) (TWord 3)) (Pair (Pair (Var c) a) b)) (fun '((out, c_out)%core) => REST)).*)
 Notation "'addcarryx_u128' ( c , a , b )" := (Op (AddWithGetCarry 128 (TWord 0) (TWord 7) (TWord 7) (TWord 7) (TWord 0)) (Pair (Pair (Var c) a) (Var b))).
 Notation "'addcarryx_u128' ( c , a , b )" := (Op (AddWithGetCarry 128 (TWord 0) (TWord 0) (TWord 7) (TWord 7) (TWord 0)) (Pair (Pair (Var c) a) (Var b))).
 Notation "'addcarryx_u128' ( c , a , b )" := (Op (AddWithGetCarry 128 (TWord 0) (TWord 7) (TWord 0) (TWord 7) (TWord 0)) (Pair (Pair (Var c) a) (Var b))).
+Notation "'addcarryx_u128' ( c , a , b )" := (Op (AddWithGetCarry 128 (TWord 0) (TWord 0) (TWord 0) (TWord 7) (TWord 0)) (Pair (Pair (Var c) a) (Var b))).
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 128 (TWord 0) (TWord 7) (TWord 7) (TWord 7) (TWord 0)) (Pair (Pair (Var c) a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 128 (TWord 0) (TWord 0) (TWord 7) (TWord 7) (TWord 0)) (Pair (Pair (Var c) a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 128 (TWord 0) (TWord 7) (TWord 0) (TWord 7) (TWord 0)) (Pair (Pair (Var c) a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_addcarryx_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 128 (TWord 0) (TWord 0) (TWord 0) (TWord 7) (TWord 0)) (Pair (Pair (Var c) a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 Notation "'addcarryx_u128' ( c , a , b )" := (Op (AddWithGetCarry 128 (TWord 3) (TWord 7) (TWord 7) (TWord 7) (TWord 3)) (Pair (Pair (Var c) a) (Var b))).
 Notation "'addcarryx_u128' ( c , a , b )" := (Op (AddWithGetCarry 128 (TWord 3) (TWord 3) (TWord 7) (TWord 7) (TWord 3)) (Pair (Pair (Var c) a) (Var b))).
 Notation "'addcarryx_u128' ( c , a , b )" := (Op (AddWithGetCarry 128 (TWord 3) (TWord 7) (TWord 3) (TWord 7) (TWord 3)) (Pair (Pair (Var c) a) (Var b))).
+Notation "'addcarryx_u128' ( c , a , b )" := (Op (AddWithGetCarry 128 (TWord 3) (TWord 3) (TWord 3) (TWord 7) (TWord 3)) (Pair (Pair (Var c) a) (Var b))).
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 128 (TWord 3) (TWord 7) (TWord 7) (TWord 7) (TWord 3)) (Pair (Pair (Var c) a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 128 (TWord 3) (TWord 3) (TWord 7) (TWord 7) (TWord 3)) (Pair (Pair (Var c) a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 128 (TWord 3) (TWord 7) (TWord 3) (TWord 7) (TWord 3)) (Pair (Pair (Var c) a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_addcarryx_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 128 (TWord 3) (TWord 3) (TWord 3) (TWord 7) (TWord 3)) (Pair (Pair (Var c) a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 Notation "'addcarryx_u128' ( c , a , b )" := (Op (AddWithGetCarry 128 (TWord 0) (TWord 7) (TWord 7) (TWord 7) (TWord 0)) (Pair (Pair (Var c) (Var a)) b)).
 Notation "'addcarryx_u128' ( c , a , b )" := (Op (AddWithGetCarry 128 (TWord 0) (TWord 0) (TWord 7) (TWord 7) (TWord 0)) (Pair (Pair (Var c) (Var a)) b)).
 Notation "'addcarryx_u128' ( c , a , b )" := (Op (AddWithGetCarry 128 (TWord 0) (TWord 7) (TWord 0) (TWord 7) (TWord 0)) (Pair (Pair (Var c) (Var a)) b)).
+Notation "'addcarryx_u128' ( c , a , b )" := (Op (AddWithGetCarry 128 (TWord 0) (TWord 0) (TWord 0) (TWord 7) (TWord 0)) (Pair (Pair (Var c) (Var a)) b)).
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 128 (TWord 0) (TWord 7) (TWord 7) (TWord 7) (TWord 0)) (Pair (Pair (Var c) (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 128 (TWord 0) (TWord 0) (TWord 7) (TWord 7) (TWord 0)) (Pair (Pair (Var c) (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 128 (TWord 0) (TWord 7) (TWord 0) (TWord 7) (TWord 0)) (Pair (Pair (Var c) (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_addcarryx_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 128 (TWord 0) (TWord 0) (TWord 0) (TWord 7) (TWord 0)) (Pair (Pair (Var c) (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 Notation "'addcarryx_u128' ( c , a , b )" := (Op (AddWithGetCarry 128 (TWord 3) (TWord 7) (TWord 7) (TWord 7) (TWord 3)) (Pair (Pair (Var c) (Var a)) b)).
 Notation "'addcarryx_u128' ( c , a , b )" := (Op (AddWithGetCarry 128 (TWord 3) (TWord 3) (TWord 7) (TWord 7) (TWord 3)) (Pair (Pair (Var c) (Var a)) b)).
 Notation "'addcarryx_u128' ( c , a , b )" := (Op (AddWithGetCarry 128 (TWord 3) (TWord 7) (TWord 3) (TWord 7) (TWord 3)) (Pair (Pair (Var c) (Var a)) b)).
+Notation "'addcarryx_u128' ( c , a , b )" := (Op (AddWithGetCarry 128 (TWord 3) (TWord 3) (TWord 3) (TWord 7) (TWord 3)) (Pair (Pair (Var c) (Var a)) b)).
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 128 (TWord 3) (TWord 7) (TWord 7) (TWord 7) (TWord 3)) (Pair (Pair (Var c) (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 128 (TWord 3) (TWord 3) (TWord 7) (TWord 7) (TWord 3)) (Pair (Pair (Var c) (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 128 (TWord 3) (TWord 7) (TWord 3) (TWord 7) (TWord 3)) (Pair (Pair (Var c) (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_addcarryx_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 128 (TWord 3) (TWord 3) (TWord 3) (TWord 7) (TWord 3)) (Pair (Pair (Var c) (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 Notation "'addcarryx_u128' ( c , a , b )" := (Op (AddWithGetCarry 128 (TWord 0) (TWord 7) (TWord 7) (TWord 7) (TWord 0)) (Pair (Pair (Var c) (Var a)) (Var b))).
 Notation "'addcarryx_u128' ( c , a , b )" := (Op (AddWithGetCarry 128 (TWord 0) (TWord 0) (TWord 7) (TWord 7) (TWord 0)) (Pair (Pair (Var c) (Var a)) (Var b))).
 Notation "'addcarryx_u128' ( c , a , b )" := (Op (AddWithGetCarry 128 (TWord 0) (TWord 7) (TWord 0) (TWord 7) (TWord 0)) (Pair (Pair (Var c) (Var a)) (Var b))).
+Notation "'addcarryx_u128' ( c , a , b )" := (Op (AddWithGetCarry 128 (TWord 0) (TWord 0) (TWord 0) (TWord 7) (TWord 0)) (Pair (Pair (Var c) (Var a)) (Var b))).
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 128 (TWord 0) (TWord 7) (TWord 7) (TWord 7) (TWord 0)) (Pair (Pair (Var c) (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 128 (TWord 0) (TWord 0) (TWord 7) (TWord 7) (TWord 0)) (Pair (Pair (Var c) (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 128 (TWord 0) (TWord 7) (TWord 0) (TWord 7) (TWord 0)) (Pair (Pair (Var c) (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_addcarryx_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 128 (TWord 0) (TWord 0) (TWord 0) (TWord 7) (TWord 0)) (Pair (Pair (Var c) (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 Notation "'addcarryx_u128' ( c , a , b )" := (Op (AddWithGetCarry 128 (TWord 3) (TWord 7) (TWord 7) (TWord 7) (TWord 3)) (Pair (Pair (Var c) (Var a)) (Var b))).
 Notation "'addcarryx_u128' ( c , a , b )" := (Op (AddWithGetCarry 128 (TWord 3) (TWord 3) (TWord 7) (TWord 7) (TWord 3)) (Pair (Pair (Var c) (Var a)) (Var b))).
 Notation "'addcarryx_u128' ( c , a , b )" := (Op (AddWithGetCarry 128 (TWord 3) (TWord 7) (TWord 3) (TWord 7) (TWord 3)) (Pair (Pair (Var c) (Var a)) (Var b))).
+Notation "'addcarryx_u128' ( c , a , b )" := (Op (AddWithGetCarry 128 (TWord 3) (TWord 3) (TWord 3) (TWord 7) (TWord 3)) (Pair (Pair (Var c) (Var a)) (Var b))).
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 128 (TWord 3) (TWord 7) (TWord 7) (TWord 7) (TWord 3)) (Pair (Pair (Var c) (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 128 (TWord 3) (TWord 3) (TWord 7) (TWord 7) (TWord 3)) (Pair (Pair (Var c) (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 128 (TWord 3) (TWord 7) (TWord 3) (TWord 7) (TWord 3)) (Pair (Pair (Var c) (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_addcarryx_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 128 (TWord 3) (TWord 3) (TWord 3) (TWord 7) (TWord 3)) (Pair (Pair (Var c) (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 Notation "'addcarryx_u51' ( c , a , b )" := (Op (AddWithGetCarry 51 (TWord 0) (TWord 6) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair c a) b)).
 Notation "'addcarryx_u51' ( c , a , b )" := (Op (AddWithGetCarry 51 (TWord 0) (TWord 0) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair c a) b)).
 Notation "'addcarryx_u51' ( c , a , b )" := (Op (AddWithGetCarry 51 (TWord 0) (TWord 6) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair c a) b)).
+Notation "'addcarryx_u51' ( c , a , b )" := (Op (AddWithGetCarry 51 (TWord 0) (TWord 0) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair c a) b)).
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 51 (TWord 0) (TWord 6) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair c a) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 51 (TWord 0) (TWord 0) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair c a) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 51 (TWord 0) (TWord 6) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair c a) b)) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_addcarryx_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 51 (TWord 0) (TWord 0) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair c a) b)) (fun '((out, c_out)%core) => REST)).*)
 Notation "'addcarryx_u51' ( c , a , b )" := (Op (AddWithGetCarry 51 (TWord 3) (TWord 6) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair c a) b)).
 Notation "'addcarryx_u51' ( c , a , b )" := (Op (AddWithGetCarry 51 (TWord 3) (TWord 3) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair c a) b)).
 Notation "'addcarryx_u51' ( c , a , b )" := (Op (AddWithGetCarry 51 (TWord 3) (TWord 6) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair c a) b)).
+Notation "'addcarryx_u51' ( c , a , b )" := (Op (AddWithGetCarry 51 (TWord 3) (TWord 3) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair c a) b)).
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 51 (TWord 3) (TWord 6) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair c a) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 51 (TWord 3) (TWord 3) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair c a) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 51 (TWord 3) (TWord 6) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair c a) b)) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_addcarryx_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 51 (TWord 3) (TWord 3) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair c a) b)) (fun '((out, c_out)%core) => REST)).*)
 Notation "'addcarryx_u51' ( c , a , b )" := (Op (AddWithGetCarry 51 (TWord 0) (TWord 6) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair c a) (Var b))).
 Notation "'addcarryx_u51' ( c , a , b )" := (Op (AddWithGetCarry 51 (TWord 0) (TWord 0) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair c a) (Var b))).
 Notation "'addcarryx_u51' ( c , a , b )" := (Op (AddWithGetCarry 51 (TWord 0) (TWord 6) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair c a) (Var b))).
+Notation "'addcarryx_u51' ( c , a , b )" := (Op (AddWithGetCarry 51 (TWord 0) (TWord 0) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair c a) (Var b))).
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 51 (TWord 0) (TWord 6) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair c a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 51 (TWord 0) (TWord 0) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair c a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 51 (TWord 0) (TWord 6) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair c a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_addcarryx_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 51 (TWord 0) (TWord 0) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair c a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 Notation "'addcarryx_u51' ( c , a , b )" := (Op (AddWithGetCarry 51 (TWord 3) (TWord 6) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair c a) (Var b))).
 Notation "'addcarryx_u51' ( c , a , b )" := (Op (AddWithGetCarry 51 (TWord 3) (TWord 3) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair c a) (Var b))).
 Notation "'addcarryx_u51' ( c , a , b )" := (Op (AddWithGetCarry 51 (TWord 3) (TWord 6) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair c a) (Var b))).
+Notation "'addcarryx_u51' ( c , a , b )" := (Op (AddWithGetCarry 51 (TWord 3) (TWord 3) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair c a) (Var b))).
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 51 (TWord 3) (TWord 6) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair c a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 51 (TWord 3) (TWord 3) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair c a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 51 (TWord 3) (TWord 6) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair c a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_addcarryx_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 51 (TWord 3) (TWord 3) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair c a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 Notation "'addcarryx_u51' ( c , a , b )" := (Op (AddWithGetCarry 51 (TWord 0) (TWord 6) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair c (Var a)) b)).
 Notation "'addcarryx_u51' ( c , a , b )" := (Op (AddWithGetCarry 51 (TWord 0) (TWord 0) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair c (Var a)) b)).
 Notation "'addcarryx_u51' ( c , a , b )" := (Op (AddWithGetCarry 51 (TWord 0) (TWord 6) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair c (Var a)) b)).
+Notation "'addcarryx_u51' ( c , a , b )" := (Op (AddWithGetCarry 51 (TWord 0) (TWord 0) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair c (Var a)) b)).
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 51 (TWord 0) (TWord 6) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair c (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 51 (TWord 0) (TWord 0) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair c (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 51 (TWord 0) (TWord 6) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair c (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_addcarryx_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 51 (TWord 0) (TWord 0) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair c (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 Notation "'addcarryx_u51' ( c , a , b )" := (Op (AddWithGetCarry 51 (TWord 3) (TWord 6) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair c (Var a)) b)).
 Notation "'addcarryx_u51' ( c , a , b )" := (Op (AddWithGetCarry 51 (TWord 3) (TWord 3) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair c (Var a)) b)).
 Notation "'addcarryx_u51' ( c , a , b )" := (Op (AddWithGetCarry 51 (TWord 3) (TWord 6) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair c (Var a)) b)).
+Notation "'addcarryx_u51' ( c , a , b )" := (Op (AddWithGetCarry 51 (TWord 3) (TWord 3) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair c (Var a)) b)).
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 51 (TWord 3) (TWord 6) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair c (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 51 (TWord 3) (TWord 3) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair c (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 51 (TWord 3) (TWord 6) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair c (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_addcarryx_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 51 (TWord 3) (TWord 3) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair c (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 Notation "'addcarryx_u51' ( c , a , b )" := (Op (AddWithGetCarry 51 (TWord 0) (TWord 6) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair c (Var a)) (Var b))).
 Notation "'addcarryx_u51' ( c , a , b )" := (Op (AddWithGetCarry 51 (TWord 0) (TWord 0) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair c (Var a)) (Var b))).
 Notation "'addcarryx_u51' ( c , a , b )" := (Op (AddWithGetCarry 51 (TWord 0) (TWord 6) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair c (Var a)) (Var b))).
+Notation "'addcarryx_u51' ( c , a , b )" := (Op (AddWithGetCarry 51 (TWord 0) (TWord 0) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair c (Var a)) (Var b))).
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 51 (TWord 0) (TWord 6) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair c (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 51 (TWord 0) (TWord 0) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair c (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 51 (TWord 0) (TWord 6) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair c (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_addcarryx_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 51 (TWord 0) (TWord 0) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair c (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 Notation "'addcarryx_u51' ( c , a , b )" := (Op (AddWithGetCarry 51 (TWord 3) (TWord 6) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair c (Var a)) (Var b))).
 Notation "'addcarryx_u51' ( c , a , b )" := (Op (AddWithGetCarry 51 (TWord 3) (TWord 3) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair c (Var a)) (Var b))).
 Notation "'addcarryx_u51' ( c , a , b )" := (Op (AddWithGetCarry 51 (TWord 3) (TWord 6) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair c (Var a)) (Var b))).
+Notation "'addcarryx_u51' ( c , a , b )" := (Op (AddWithGetCarry 51 (TWord 3) (TWord 3) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair c (Var a)) (Var b))).
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 51 (TWord 3) (TWord 6) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair c (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 51 (TWord 3) (TWord 3) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair c (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 51 (TWord 3) (TWord 6) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair c (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_addcarryx_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 51 (TWord 3) (TWord 3) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair c (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 Notation "'addcarryx_u51' ( c , a , b )" := (Op (AddWithGetCarry 51 (TWord 0) (TWord 6) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair (Var c) a) b)).
 Notation "'addcarryx_u51' ( c , a , b )" := (Op (AddWithGetCarry 51 (TWord 0) (TWord 0) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair (Var c) a) b)).
 Notation "'addcarryx_u51' ( c , a , b )" := (Op (AddWithGetCarry 51 (TWord 0) (TWord 6) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair (Var c) a) b)).
+Notation "'addcarryx_u51' ( c , a , b )" := (Op (AddWithGetCarry 51 (TWord 0) (TWord 0) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair (Var c) a) b)).
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 51 (TWord 0) (TWord 6) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair (Var c) a) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 51 (TWord 0) (TWord 0) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair (Var c) a) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 51 (TWord 0) (TWord 6) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair (Var c) a) b)) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_addcarryx_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 51 (TWord 0) (TWord 0) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair (Var c) a) b)) (fun '((out, c_out)%core) => REST)).*)
 Notation "'addcarryx_u51' ( c , a , b )" := (Op (AddWithGetCarry 51 (TWord 3) (TWord 6) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair (Var c) a) b)).
 Notation "'addcarryx_u51' ( c , a , b )" := (Op (AddWithGetCarry 51 (TWord 3) (TWord 3) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair (Var c) a) b)).
 Notation "'addcarryx_u51' ( c , a , b )" := (Op (AddWithGetCarry 51 (TWord 3) (TWord 6) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair (Var c) a) b)).
+Notation "'addcarryx_u51' ( c , a , b )" := (Op (AddWithGetCarry 51 (TWord 3) (TWord 3) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair (Var c) a) b)).
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 51 (TWord 3) (TWord 6) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair (Var c) a) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 51 (TWord 3) (TWord 3) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair (Var c) a) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 51 (TWord 3) (TWord 6) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair (Var c) a) b)) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_addcarryx_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 51 (TWord 3) (TWord 3) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair (Var c) a) b)) (fun '((out, c_out)%core) => REST)).*)
 Notation "'addcarryx_u51' ( c , a , b )" := (Op (AddWithGetCarry 51 (TWord 0) (TWord 6) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair (Var c) a) (Var b))).
 Notation "'addcarryx_u51' ( c , a , b )" := (Op (AddWithGetCarry 51 (TWord 0) (TWord 0) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair (Var c) a) (Var b))).
 Notation "'addcarryx_u51' ( c , a , b )" := (Op (AddWithGetCarry 51 (TWord 0) (TWord 6) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair (Var c) a) (Var b))).
+Notation "'addcarryx_u51' ( c , a , b )" := (Op (AddWithGetCarry 51 (TWord 0) (TWord 0) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair (Var c) a) (Var b))).
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 51 (TWord 0) (TWord 6) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair (Var c) a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 51 (TWord 0) (TWord 0) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair (Var c) a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 51 (TWord 0) (TWord 6) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair (Var c) a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_addcarryx_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 51 (TWord 0) (TWord 0) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair (Var c) a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 Notation "'addcarryx_u51' ( c , a , b )" := (Op (AddWithGetCarry 51 (TWord 3) (TWord 6) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair (Var c) a) (Var b))).
 Notation "'addcarryx_u51' ( c , a , b )" := (Op (AddWithGetCarry 51 (TWord 3) (TWord 3) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair (Var c) a) (Var b))).
 Notation "'addcarryx_u51' ( c , a , b )" := (Op (AddWithGetCarry 51 (TWord 3) (TWord 6) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair (Var c) a) (Var b))).
+Notation "'addcarryx_u51' ( c , a , b )" := (Op (AddWithGetCarry 51 (TWord 3) (TWord 3) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair (Var c) a) (Var b))).
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 51 (TWord 3) (TWord 6) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair (Var c) a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 51 (TWord 3) (TWord 3) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair (Var c) a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 51 (TWord 3) (TWord 6) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair (Var c) a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_addcarryx_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 51 (TWord 3) (TWord 3) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair (Var c) a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 Notation "'addcarryx_u51' ( c , a , b )" := (Op (AddWithGetCarry 51 (TWord 0) (TWord 6) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair (Var c) (Var a)) b)).
 Notation "'addcarryx_u51' ( c , a , b )" := (Op (AddWithGetCarry 51 (TWord 0) (TWord 0) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair (Var c) (Var a)) b)).
 Notation "'addcarryx_u51' ( c , a , b )" := (Op (AddWithGetCarry 51 (TWord 0) (TWord 6) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair (Var c) (Var a)) b)).
+Notation "'addcarryx_u51' ( c , a , b )" := (Op (AddWithGetCarry 51 (TWord 0) (TWord 0) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair (Var c) (Var a)) b)).
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 51 (TWord 0) (TWord 6) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair (Var c) (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 51 (TWord 0) (TWord 0) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair (Var c) (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 51 (TWord 0) (TWord 6) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair (Var c) (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_addcarryx_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 51 (TWord 0) (TWord 0) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair (Var c) (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 Notation "'addcarryx_u51' ( c , a , b )" := (Op (AddWithGetCarry 51 (TWord 3) (TWord 6) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair (Var c) (Var a)) b)).
 Notation "'addcarryx_u51' ( c , a , b )" := (Op (AddWithGetCarry 51 (TWord 3) (TWord 3) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair (Var c) (Var a)) b)).
 Notation "'addcarryx_u51' ( c , a , b )" := (Op (AddWithGetCarry 51 (TWord 3) (TWord 6) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair (Var c) (Var a)) b)).
+Notation "'addcarryx_u51' ( c , a , b )" := (Op (AddWithGetCarry 51 (TWord 3) (TWord 3) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair (Var c) (Var a)) b)).
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 51 (TWord 3) (TWord 6) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair (Var c) (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 51 (TWord 3) (TWord 3) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair (Var c) (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 51 (TWord 3) (TWord 6) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair (Var c) (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_addcarryx_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 51 (TWord 3) (TWord 3) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair (Var c) (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 Notation "'addcarryx_u51' ( c , a , b )" := (Op (AddWithGetCarry 51 (TWord 0) (TWord 6) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair (Var c) (Var a)) (Var b))).
 Notation "'addcarryx_u51' ( c , a , b )" := (Op (AddWithGetCarry 51 (TWord 0) (TWord 0) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair (Var c) (Var a)) (Var b))).
 Notation "'addcarryx_u51' ( c , a , b )" := (Op (AddWithGetCarry 51 (TWord 0) (TWord 6) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair (Var c) (Var a)) (Var b))).
+Notation "'addcarryx_u51' ( c , a , b )" := (Op (AddWithGetCarry 51 (TWord 0) (TWord 0) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair (Var c) (Var a)) (Var b))).
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 51 (TWord 0) (TWord 6) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair (Var c) (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 51 (TWord 0) (TWord 0) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair (Var c) (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 51 (TWord 0) (TWord 6) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair (Var c) (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_addcarryx_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 51 (TWord 0) (TWord 0) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair (Var c) (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 Notation "'addcarryx_u51' ( c , a , b )" := (Op (AddWithGetCarry 51 (TWord 3) (TWord 6) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair (Var c) (Var a)) (Var b))).
 Notation "'addcarryx_u51' ( c , a , b )" := (Op (AddWithGetCarry 51 (TWord 3) (TWord 3) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair (Var c) (Var a)) (Var b))).
 Notation "'addcarryx_u51' ( c , a , b )" := (Op (AddWithGetCarry 51 (TWord 3) (TWord 6) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair (Var c) (Var a)) (Var b))).
+Notation "'addcarryx_u51' ( c , a , b )" := (Op (AddWithGetCarry 51 (TWord 3) (TWord 3) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair (Var c) (Var a)) (Var b))).
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 51 (TWord 3) (TWord 6) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair (Var c) (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 51 (TWord 3) (TWord 3) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair (Var c) (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_addcarryx_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 51 (TWord 3) (TWord 6) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair (Var c) (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_addcarryx_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (AddWithGetCarry 51 (TWord 3) (TWord 3) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair (Var c) (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 Notation "'subborrow_u32' ( c , a , b )" := (Op (SubWithGetBorrow 32 (TWord 0) (TWord 5) (TWord 5) (TWord 5) (TWord 0)) (Pair (Pair c a) b)).
 Notation "'subborrow_u32' ( c , a , b )" := (Op (SubWithGetBorrow 32 (TWord 0) (TWord 0) (TWord 5) (TWord 5) (TWord 0)) (Pair (Pair c a) b)).
 Notation "'subborrow_u32' ( c , a , b )" := (Op (SubWithGetBorrow 32 (TWord 0) (TWord 5) (TWord 0) (TWord 5) (TWord 0)) (Pair (Pair c a) b)).
+Notation "'subborrow_u32' ( c , a , b )" := (Op (SubWithGetBorrow 32 (TWord 0) (TWord 0) (TWord 0) (TWord 5) (TWord 0)) (Pair (Pair c a) b)).
 (*Notation "T0 out ; T1 c_out = '_subborrow_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 32 (TWord 0) (TWord 5) (TWord 5) (TWord 5) (TWord 0)) (Pair (Pair c a) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 32 (TWord 0) (TWord 0) (TWord 5) (TWord 5) (TWord 0)) (Pair (Pair c a) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 32 (TWord 0) (TWord 5) (TWord 0) (TWord 5) (TWord 0)) (Pair (Pair c a) b)) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_subborrow_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 32 (TWord 0) (TWord 0) (TWord 0) (TWord 5) (TWord 0)) (Pair (Pair c a) b)) (fun '((out, c_out)%core) => REST)).*)
 Notation "'subborrow_u32' ( c , a , b )" := (Op (SubWithGetBorrow 32 (TWord 3) (TWord 5) (TWord 5) (TWord 5) (TWord 3)) (Pair (Pair c a) b)).
 Notation "'subborrow_u32' ( c , a , b )" := (Op (SubWithGetBorrow 32 (TWord 3) (TWord 3) (TWord 5) (TWord 5) (TWord 3)) (Pair (Pair c a) b)).
 Notation "'subborrow_u32' ( c , a , b )" := (Op (SubWithGetBorrow 32 (TWord 3) (TWord 5) (TWord 3) (TWord 5) (TWord 3)) (Pair (Pair c a) b)).
+Notation "'subborrow_u32' ( c , a , b )" := (Op (SubWithGetBorrow 32 (TWord 3) (TWord 3) (TWord 3) (TWord 5) (TWord 3)) (Pair (Pair c a) b)).
 (*Notation "T0 out ; T1 c_out = '_subborrow_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 32 (TWord 3) (TWord 5) (TWord 5) (TWord 5) (TWord 3)) (Pair (Pair c a) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 32 (TWord 3) (TWord 3) (TWord 5) (TWord 5) (TWord 3)) (Pair (Pair c a) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 32 (TWord 3) (TWord 5) (TWord 3) (TWord 5) (TWord 3)) (Pair (Pair c a) b)) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_subborrow_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 32 (TWord 3) (TWord 3) (TWord 3) (TWord 5) (TWord 3)) (Pair (Pair c a) b)) (fun '((out, c_out)%core) => REST)).*)
 Notation "'subborrow_u32' ( c , a , b )" := (Op (SubWithGetBorrow 32 (TWord 0) (TWord 5) (TWord 5) (TWord 5) (TWord 0)) (Pair (Pair c a) (Var b))).
 Notation "'subborrow_u32' ( c , a , b )" := (Op (SubWithGetBorrow 32 (TWord 0) (TWord 0) (TWord 5) (TWord 5) (TWord 0)) (Pair (Pair c a) (Var b))).
 Notation "'subborrow_u32' ( c , a , b )" := (Op (SubWithGetBorrow 32 (TWord 0) (TWord 5) (TWord 0) (TWord 5) (TWord 0)) (Pair (Pair c a) (Var b))).
+Notation "'subborrow_u32' ( c , a , b )" := (Op (SubWithGetBorrow 32 (TWord 0) (TWord 0) (TWord 0) (TWord 5) (TWord 0)) (Pair (Pair c a) (Var b))).
 (*Notation "T0 out ; T1 c_out = '_subborrow_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 32 (TWord 0) (TWord 5) (TWord 5) (TWord 5) (TWord 0)) (Pair (Pair c a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 32 (TWord 0) (TWord 0) (TWord 5) (TWord 5) (TWord 0)) (Pair (Pair c a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 32 (TWord 0) (TWord 5) (TWord 0) (TWord 5) (TWord 0)) (Pair (Pair c a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_subborrow_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 32 (TWord 0) (TWord 0) (TWord 0) (TWord 5) (TWord 0)) (Pair (Pair c a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 Notation "'subborrow_u32' ( c , a , b )" := (Op (SubWithGetBorrow 32 (TWord 3) (TWord 5) (TWord 5) (TWord 5) (TWord 3)) (Pair (Pair c a) (Var b))).
 Notation "'subborrow_u32' ( c , a , b )" := (Op (SubWithGetBorrow 32 (TWord 3) (TWord 3) (TWord 5) (TWord 5) (TWord 3)) (Pair (Pair c a) (Var b))).
 Notation "'subborrow_u32' ( c , a , b )" := (Op (SubWithGetBorrow 32 (TWord 3) (TWord 5) (TWord 3) (TWord 5) (TWord 3)) (Pair (Pair c a) (Var b))).
+Notation "'subborrow_u32' ( c , a , b )" := (Op (SubWithGetBorrow 32 (TWord 3) (TWord 3) (TWord 3) (TWord 5) (TWord 3)) (Pair (Pair c a) (Var b))).
 (*Notation "T0 out ; T1 c_out = '_subborrow_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 32 (TWord 3) (TWord 5) (TWord 5) (TWord 5) (TWord 3)) (Pair (Pair c a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 32 (TWord 3) (TWord 3) (TWord 5) (TWord 5) (TWord 3)) (Pair (Pair c a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 32 (TWord 3) (TWord 5) (TWord 3) (TWord 5) (TWord 3)) (Pair (Pair c a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_subborrow_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 32 (TWord 3) (TWord 3) (TWord 3) (TWord 5) (TWord 3)) (Pair (Pair c a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 Notation "'subborrow_u32' ( c , a , b )" := (Op (SubWithGetBorrow 32 (TWord 0) (TWord 5) (TWord 5) (TWord 5) (TWord 0)) (Pair (Pair c (Var a)) b)).
 Notation "'subborrow_u32' ( c , a , b )" := (Op (SubWithGetBorrow 32 (TWord 0) (TWord 0) (TWord 5) (TWord 5) (TWord 0)) (Pair (Pair c (Var a)) b)).
 Notation "'subborrow_u32' ( c , a , b )" := (Op (SubWithGetBorrow 32 (TWord 0) (TWord 5) (TWord 0) (TWord 5) (TWord 0)) (Pair (Pair c (Var a)) b)).
+Notation "'subborrow_u32' ( c , a , b )" := (Op (SubWithGetBorrow 32 (TWord 0) (TWord 0) (TWord 0) (TWord 5) (TWord 0)) (Pair (Pair c (Var a)) b)).
 (*Notation "T0 out ; T1 c_out = '_subborrow_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 32 (TWord 0) (TWord 5) (TWord 5) (TWord 5) (TWord 0)) (Pair (Pair c (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 32 (TWord 0) (TWord 0) (TWord 5) (TWord 5) (TWord 0)) (Pair (Pair c (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 32 (TWord 0) (TWord 5) (TWord 0) (TWord 5) (TWord 0)) (Pair (Pair c (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_subborrow_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 32 (TWord 0) (TWord 0) (TWord 0) (TWord 5) (TWord 0)) (Pair (Pair c (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 Notation "'subborrow_u32' ( c , a , b )" := (Op (SubWithGetBorrow 32 (TWord 3) (TWord 5) (TWord 5) (TWord 5) (TWord 3)) (Pair (Pair c (Var a)) b)).
 Notation "'subborrow_u32' ( c , a , b )" := (Op (SubWithGetBorrow 32 (TWord 3) (TWord 3) (TWord 5) (TWord 5) (TWord 3)) (Pair (Pair c (Var a)) b)).
 Notation "'subborrow_u32' ( c , a , b )" := (Op (SubWithGetBorrow 32 (TWord 3) (TWord 5) (TWord 3) (TWord 5) (TWord 3)) (Pair (Pair c (Var a)) b)).
+Notation "'subborrow_u32' ( c , a , b )" := (Op (SubWithGetBorrow 32 (TWord 3) (TWord 3) (TWord 3) (TWord 5) (TWord 3)) (Pair (Pair c (Var a)) b)).
 (*Notation "T0 out ; T1 c_out = '_subborrow_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 32 (TWord 3) (TWord 5) (TWord 5) (TWord 5) (TWord 3)) (Pair (Pair c (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 32 (TWord 3) (TWord 3) (TWord 5) (TWord 5) (TWord 3)) (Pair (Pair c (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 32 (TWord 3) (TWord 5) (TWord 3) (TWord 5) (TWord 3)) (Pair (Pair c (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_subborrow_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 32 (TWord 3) (TWord 3) (TWord 3) (TWord 5) (TWord 3)) (Pair (Pair c (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 Notation "'subborrow_u32' ( c , a , b )" := (Op (SubWithGetBorrow 32 (TWord 0) (TWord 5) (TWord 5) (TWord 5) (TWord 0)) (Pair (Pair c (Var a)) (Var b))).
 Notation "'subborrow_u32' ( c , a , b )" := (Op (SubWithGetBorrow 32 (TWord 0) (TWord 0) (TWord 5) (TWord 5) (TWord 0)) (Pair (Pair c (Var a)) (Var b))).
 Notation "'subborrow_u32' ( c , a , b )" := (Op (SubWithGetBorrow 32 (TWord 0) (TWord 5) (TWord 0) (TWord 5) (TWord 0)) (Pair (Pair c (Var a)) (Var b))).
+Notation "'subborrow_u32' ( c , a , b )" := (Op (SubWithGetBorrow 32 (TWord 0) (TWord 0) (TWord 0) (TWord 5) (TWord 0)) (Pair (Pair c (Var a)) (Var b))).
 (*Notation "T0 out ; T1 c_out = '_subborrow_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 32 (TWord 0) (TWord 5) (TWord 5) (TWord 5) (TWord 0)) (Pair (Pair c (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 32 (TWord 0) (TWord 0) (TWord 5) (TWord 5) (TWord 0)) (Pair (Pair c (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 32 (TWord 0) (TWord 5) (TWord 0) (TWord 5) (TWord 0)) (Pair (Pair c (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_subborrow_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 32 (TWord 0) (TWord 0) (TWord 0) (TWord 5) (TWord 0)) (Pair (Pair c (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 Notation "'subborrow_u32' ( c , a , b )" := (Op (SubWithGetBorrow 32 (TWord 3) (TWord 5) (TWord 5) (TWord 5) (TWord 3)) (Pair (Pair c (Var a)) (Var b))).
 Notation "'subborrow_u32' ( c , a , b )" := (Op (SubWithGetBorrow 32 (TWord 3) (TWord 3) (TWord 5) (TWord 5) (TWord 3)) (Pair (Pair c (Var a)) (Var b))).
 Notation "'subborrow_u32' ( c , a , b )" := (Op (SubWithGetBorrow 32 (TWord 3) (TWord 5) (TWord 3) (TWord 5) (TWord 3)) (Pair (Pair c (Var a)) (Var b))).
+Notation "'subborrow_u32' ( c , a , b )" := (Op (SubWithGetBorrow 32 (TWord 3) (TWord 3) (TWord 3) (TWord 5) (TWord 3)) (Pair (Pair c (Var a)) (Var b))).
 (*Notation "T0 out ; T1 c_out = '_subborrow_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 32 (TWord 3) (TWord 5) (TWord 5) (TWord 5) (TWord 3)) (Pair (Pair c (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 32 (TWord 3) (TWord 3) (TWord 5) (TWord 5) (TWord 3)) (Pair (Pair c (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 32 (TWord 3) (TWord 5) (TWord 3) (TWord 5) (TWord 3)) (Pair (Pair c (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_subborrow_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 32 (TWord 3) (TWord 3) (TWord 3) (TWord 5) (TWord 3)) (Pair (Pair c (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 Notation "'subborrow_u32' ( c , a , b )" := (Op (SubWithGetBorrow 32 (TWord 0) (TWord 5) (TWord 5) (TWord 5) (TWord 0)) (Pair (Pair (Var c) a) b)).
 Notation "'subborrow_u32' ( c , a , b )" := (Op (SubWithGetBorrow 32 (TWord 0) (TWord 0) (TWord 5) (TWord 5) (TWord 0)) (Pair (Pair (Var c) a) b)).
 Notation "'subborrow_u32' ( c , a , b )" := (Op (SubWithGetBorrow 32 (TWord 0) (TWord 5) (TWord 0) (TWord 5) (TWord 0)) (Pair (Pair (Var c) a) b)).
+Notation "'subborrow_u32' ( c , a , b )" := (Op (SubWithGetBorrow 32 (TWord 0) (TWord 0) (TWord 0) (TWord 5) (TWord 0)) (Pair (Pair (Var c) a) b)).
 (*Notation "T0 out ; T1 c_out = '_subborrow_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 32 (TWord 0) (TWord 5) (TWord 5) (TWord 5) (TWord 0)) (Pair (Pair (Var c) a) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 32 (TWord 0) (TWord 0) (TWord 5) (TWord 5) (TWord 0)) (Pair (Pair (Var c) a) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 32 (TWord 0) (TWord 5) (TWord 0) (TWord 5) (TWord 0)) (Pair (Pair (Var c) a) b)) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_subborrow_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 32 (TWord 0) (TWord 0) (TWord 0) (TWord 5) (TWord 0)) (Pair (Pair (Var c) a) b)) (fun '((out, c_out)%core) => REST)).*)
 Notation "'subborrow_u32' ( c , a , b )" := (Op (SubWithGetBorrow 32 (TWord 3) (TWord 5) (TWord 5) (TWord 5) (TWord 3)) (Pair (Pair (Var c) a) b)).
 Notation "'subborrow_u32' ( c , a , b )" := (Op (SubWithGetBorrow 32 (TWord 3) (TWord 3) (TWord 5) (TWord 5) (TWord 3)) (Pair (Pair (Var c) a) b)).
 Notation "'subborrow_u32' ( c , a , b )" := (Op (SubWithGetBorrow 32 (TWord 3) (TWord 5) (TWord 3) (TWord 5) (TWord 3)) (Pair (Pair (Var c) a) b)).
+Notation "'subborrow_u32' ( c , a , b )" := (Op (SubWithGetBorrow 32 (TWord 3) (TWord 3) (TWord 3) (TWord 5) (TWord 3)) (Pair (Pair (Var c) a) b)).
 (*Notation "T0 out ; T1 c_out = '_subborrow_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 32 (TWord 3) (TWord 5) (TWord 5) (TWord 5) (TWord 3)) (Pair (Pair (Var c) a) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 32 (TWord 3) (TWord 3) (TWord 5) (TWord 5) (TWord 3)) (Pair (Pair (Var c) a) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 32 (TWord 3) (TWord 5) (TWord 3) (TWord 5) (TWord 3)) (Pair (Pair (Var c) a) b)) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_subborrow_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 32 (TWord 3) (TWord 3) (TWord 3) (TWord 5) (TWord 3)) (Pair (Pair (Var c) a) b)) (fun '((out, c_out)%core) => REST)).*)
 Notation "'subborrow_u32' ( c , a , b )" := (Op (SubWithGetBorrow 32 (TWord 0) (TWord 5) (TWord 5) (TWord 5) (TWord 0)) (Pair (Pair (Var c) a) (Var b))).
 Notation "'subborrow_u32' ( c , a , b )" := (Op (SubWithGetBorrow 32 (TWord 0) (TWord 0) (TWord 5) (TWord 5) (TWord 0)) (Pair (Pair (Var c) a) (Var b))).
 Notation "'subborrow_u32' ( c , a , b )" := (Op (SubWithGetBorrow 32 (TWord 0) (TWord 5) (TWord 0) (TWord 5) (TWord 0)) (Pair (Pair (Var c) a) (Var b))).
+Notation "'subborrow_u32' ( c , a , b )" := (Op (SubWithGetBorrow 32 (TWord 0) (TWord 0) (TWord 0) (TWord 5) (TWord 0)) (Pair (Pair (Var c) a) (Var b))).
 (*Notation "T0 out ; T1 c_out = '_subborrow_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 32 (TWord 0) (TWord 5) (TWord 5) (TWord 5) (TWord 0)) (Pair (Pair (Var c) a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 32 (TWord 0) (TWord 0) (TWord 5) (TWord 5) (TWord 0)) (Pair (Pair (Var c) a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 32 (TWord 0) (TWord 5) (TWord 0) (TWord 5) (TWord 0)) (Pair (Pair (Var c) a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_subborrow_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 32 (TWord 0) (TWord 0) (TWord 0) (TWord 5) (TWord 0)) (Pair (Pair (Var c) a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 Notation "'subborrow_u32' ( c , a , b )" := (Op (SubWithGetBorrow 32 (TWord 3) (TWord 5) (TWord 5) (TWord 5) (TWord 3)) (Pair (Pair (Var c) a) (Var b))).
 Notation "'subborrow_u32' ( c , a , b )" := (Op (SubWithGetBorrow 32 (TWord 3) (TWord 3) (TWord 5) (TWord 5) (TWord 3)) (Pair (Pair (Var c) a) (Var b))).
 Notation "'subborrow_u32' ( c , a , b )" := (Op (SubWithGetBorrow 32 (TWord 3) (TWord 5) (TWord 3) (TWord 5) (TWord 3)) (Pair (Pair (Var c) a) (Var b))).
+Notation "'subborrow_u32' ( c , a , b )" := (Op (SubWithGetBorrow 32 (TWord 3) (TWord 3) (TWord 3) (TWord 5) (TWord 3)) (Pair (Pair (Var c) a) (Var b))).
 (*Notation "T0 out ; T1 c_out = '_subborrow_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 32 (TWord 3) (TWord 5) (TWord 5) (TWord 5) (TWord 3)) (Pair (Pair (Var c) a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 32 (TWord 3) (TWord 3) (TWord 5) (TWord 5) (TWord 3)) (Pair (Pair (Var c) a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 32 (TWord 3) (TWord 5) (TWord 3) (TWord 5) (TWord 3)) (Pair (Pair (Var c) a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_subborrow_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 32 (TWord 3) (TWord 3) (TWord 3) (TWord 5) (TWord 3)) (Pair (Pair (Var c) a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 Notation "'subborrow_u32' ( c , a , b )" := (Op (SubWithGetBorrow 32 (TWord 0) (TWord 5) (TWord 5) (TWord 5) (TWord 0)) (Pair (Pair (Var c) (Var a)) b)).
 Notation "'subborrow_u32' ( c , a , b )" := (Op (SubWithGetBorrow 32 (TWord 0) (TWord 0) (TWord 5) (TWord 5) (TWord 0)) (Pair (Pair (Var c) (Var a)) b)).
 Notation "'subborrow_u32' ( c , a , b )" := (Op (SubWithGetBorrow 32 (TWord 0) (TWord 5) (TWord 0) (TWord 5) (TWord 0)) (Pair (Pair (Var c) (Var a)) b)).
+Notation "'subborrow_u32' ( c , a , b )" := (Op (SubWithGetBorrow 32 (TWord 0) (TWord 0) (TWord 0) (TWord 5) (TWord 0)) (Pair (Pair (Var c) (Var a)) b)).
 (*Notation "T0 out ; T1 c_out = '_subborrow_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 32 (TWord 0) (TWord 5) (TWord 5) (TWord 5) (TWord 0)) (Pair (Pair (Var c) (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 32 (TWord 0) (TWord 0) (TWord 5) (TWord 5) (TWord 0)) (Pair (Pair (Var c) (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 32 (TWord 0) (TWord 5) (TWord 0) (TWord 5) (TWord 0)) (Pair (Pair (Var c) (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_subborrow_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 32 (TWord 0) (TWord 0) (TWord 0) (TWord 5) (TWord 0)) (Pair (Pair (Var c) (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 Notation "'subborrow_u32' ( c , a , b )" := (Op (SubWithGetBorrow 32 (TWord 3) (TWord 5) (TWord 5) (TWord 5) (TWord 3)) (Pair (Pair (Var c) (Var a)) b)).
 Notation "'subborrow_u32' ( c , a , b )" := (Op (SubWithGetBorrow 32 (TWord 3) (TWord 3) (TWord 5) (TWord 5) (TWord 3)) (Pair (Pair (Var c) (Var a)) b)).
 Notation "'subborrow_u32' ( c , a , b )" := (Op (SubWithGetBorrow 32 (TWord 3) (TWord 5) (TWord 3) (TWord 5) (TWord 3)) (Pair (Pair (Var c) (Var a)) b)).
+Notation "'subborrow_u32' ( c , a , b )" := (Op (SubWithGetBorrow 32 (TWord 3) (TWord 3) (TWord 3) (TWord 5) (TWord 3)) (Pair (Pair (Var c) (Var a)) b)).
 (*Notation "T0 out ; T1 c_out = '_subborrow_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 32 (TWord 3) (TWord 5) (TWord 5) (TWord 5) (TWord 3)) (Pair (Pair (Var c) (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 32 (TWord 3) (TWord 3) (TWord 5) (TWord 5) (TWord 3)) (Pair (Pair (Var c) (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 32 (TWord 3) (TWord 5) (TWord 3) (TWord 5) (TWord 3)) (Pair (Pair (Var c) (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_subborrow_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 32 (TWord 3) (TWord 3) (TWord 3) (TWord 5) (TWord 3)) (Pair (Pair (Var c) (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 Notation "'subborrow_u32' ( c , a , b )" := (Op (SubWithGetBorrow 32 (TWord 0) (TWord 5) (TWord 5) (TWord 5) (TWord 0)) (Pair (Pair (Var c) (Var a)) (Var b))).
 Notation "'subborrow_u32' ( c , a , b )" := (Op (SubWithGetBorrow 32 (TWord 0) (TWord 0) (TWord 5) (TWord 5) (TWord 0)) (Pair (Pair (Var c) (Var a)) (Var b))).
 Notation "'subborrow_u32' ( c , a , b )" := (Op (SubWithGetBorrow 32 (TWord 0) (TWord 5) (TWord 0) (TWord 5) (TWord 0)) (Pair (Pair (Var c) (Var a)) (Var b))).
+Notation "'subborrow_u32' ( c , a , b )" := (Op (SubWithGetBorrow 32 (TWord 0) (TWord 0) (TWord 0) (TWord 5) (TWord 0)) (Pair (Pair (Var c) (Var a)) (Var b))).
 (*Notation "T0 out ; T1 c_out = '_subborrow_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 32 (TWord 0) (TWord 5) (TWord 5) (TWord 5) (TWord 0)) (Pair (Pair (Var c) (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 32 (TWord 0) (TWord 0) (TWord 5) (TWord 5) (TWord 0)) (Pair (Pair (Var c) (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 32 (TWord 0) (TWord 5) (TWord 0) (TWord 5) (TWord 0)) (Pair (Pair (Var c) (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_subborrow_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 32 (TWord 0) (TWord 0) (TWord 0) (TWord 5) (TWord 0)) (Pair (Pair (Var c) (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 Notation "'subborrow_u32' ( c , a , b )" := (Op (SubWithGetBorrow 32 (TWord 3) (TWord 5) (TWord 5) (TWord 5) (TWord 3)) (Pair (Pair (Var c) (Var a)) (Var b))).
 Notation "'subborrow_u32' ( c , a , b )" := (Op (SubWithGetBorrow 32 (TWord 3) (TWord 3) (TWord 5) (TWord 5) (TWord 3)) (Pair (Pair (Var c) (Var a)) (Var b))).
 Notation "'subborrow_u32' ( c , a , b )" := (Op (SubWithGetBorrow 32 (TWord 3) (TWord 5) (TWord 3) (TWord 5) (TWord 3)) (Pair (Pair (Var c) (Var a)) (Var b))).
+Notation "'subborrow_u32' ( c , a , b )" := (Op (SubWithGetBorrow 32 (TWord 3) (TWord 3) (TWord 3) (TWord 5) (TWord 3)) (Pair (Pair (Var c) (Var a)) (Var b))).
 (*Notation "T0 out ; T1 c_out = '_subborrow_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 32 (TWord 3) (TWord 5) (TWord 5) (TWord 5) (TWord 3)) (Pair (Pair (Var c) (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 32 (TWord 3) (TWord 3) (TWord 5) (TWord 5) (TWord 3)) (Pair (Pair (Var c) (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 32 (TWord 3) (TWord 5) (TWord 3) (TWord 5) (TWord 3)) (Pair (Pair (Var c) (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_subborrow_u32' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 32 (TWord 3) (TWord 3) (TWord 3) (TWord 5) (TWord 3)) (Pair (Pair (Var c) (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 Notation "'subborrow_u64' ( c , a , b )" := (Op (SubWithGetBorrow 64 (TWord 0) (TWord 6) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair c a) b)).
 Notation "'subborrow_u64' ( c , a , b )" := (Op (SubWithGetBorrow 64 (TWord 0) (TWord 0) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair c a) b)).
 Notation "'subborrow_u64' ( c , a , b )" := (Op (SubWithGetBorrow 64 (TWord 0) (TWord 6) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair c a) b)).
+Notation "'subborrow_u64' ( c , a , b )" := (Op (SubWithGetBorrow 64 (TWord 0) (TWord 0) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair c a) b)).
 (*Notation "T0 out ; T1 c_out = '_subborrow_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 64 (TWord 0) (TWord 6) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair c a) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 64 (TWord 0) (TWord 0) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair c a) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 64 (TWord 0) (TWord 6) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair c a) b)) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_subborrow_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 64 (TWord 0) (TWord 0) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair c a) b)) (fun '((out, c_out)%core) => REST)).*)
 Notation "'subborrow_u64' ( c , a , b )" := (Op (SubWithGetBorrow 64 (TWord 3) (TWord 6) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair c a) b)).
 Notation "'subborrow_u64' ( c , a , b )" := (Op (SubWithGetBorrow 64 (TWord 3) (TWord 3) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair c a) b)).
 Notation "'subborrow_u64' ( c , a , b )" := (Op (SubWithGetBorrow 64 (TWord 3) (TWord 6) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair c a) b)).
+Notation "'subborrow_u64' ( c , a , b )" := (Op (SubWithGetBorrow 64 (TWord 3) (TWord 3) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair c a) b)).
 (*Notation "T0 out ; T1 c_out = '_subborrow_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 64 (TWord 3) (TWord 6) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair c a) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 64 (TWord 3) (TWord 3) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair c a) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 64 (TWord 3) (TWord 6) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair c a) b)) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_subborrow_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 64 (TWord 3) (TWord 3) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair c a) b)) (fun '((out, c_out)%core) => REST)).*)
 Notation "'subborrow_u64' ( c , a , b )" := (Op (SubWithGetBorrow 64 (TWord 0) (TWord 6) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair c a) (Var b))).
 Notation "'subborrow_u64' ( c , a , b )" := (Op (SubWithGetBorrow 64 (TWord 0) (TWord 0) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair c a) (Var b))).
 Notation "'subborrow_u64' ( c , a , b )" := (Op (SubWithGetBorrow 64 (TWord 0) (TWord 6) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair c a) (Var b))).
+Notation "'subborrow_u64' ( c , a , b )" := (Op (SubWithGetBorrow 64 (TWord 0) (TWord 0) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair c a) (Var b))).
 (*Notation "T0 out ; T1 c_out = '_subborrow_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 64 (TWord 0) (TWord 6) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair c a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 64 (TWord 0) (TWord 0) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair c a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 64 (TWord 0) (TWord 6) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair c a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_subborrow_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 64 (TWord 0) (TWord 0) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair c a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 Notation "'subborrow_u64' ( c , a , b )" := (Op (SubWithGetBorrow 64 (TWord 3) (TWord 6) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair c a) (Var b))).
 Notation "'subborrow_u64' ( c , a , b )" := (Op (SubWithGetBorrow 64 (TWord 3) (TWord 3) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair c a) (Var b))).
 Notation "'subborrow_u64' ( c , a , b )" := (Op (SubWithGetBorrow 64 (TWord 3) (TWord 6) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair c a) (Var b))).
+Notation "'subborrow_u64' ( c , a , b )" := (Op (SubWithGetBorrow 64 (TWord 3) (TWord 3) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair c a) (Var b))).
 (*Notation "T0 out ; T1 c_out = '_subborrow_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 64 (TWord 3) (TWord 6) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair c a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 64 (TWord 3) (TWord 3) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair c a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 64 (TWord 3) (TWord 6) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair c a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_subborrow_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 64 (TWord 3) (TWord 3) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair c a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 Notation "'subborrow_u64' ( c , a , b )" := (Op (SubWithGetBorrow 64 (TWord 0) (TWord 6) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair c (Var a)) b)).
 Notation "'subborrow_u64' ( c , a , b )" := (Op (SubWithGetBorrow 64 (TWord 0) (TWord 0) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair c (Var a)) b)).
 Notation "'subborrow_u64' ( c , a , b )" := (Op (SubWithGetBorrow 64 (TWord 0) (TWord 6) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair c (Var a)) b)).
+Notation "'subborrow_u64' ( c , a , b )" := (Op (SubWithGetBorrow 64 (TWord 0) (TWord 0) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair c (Var a)) b)).
 (*Notation "T0 out ; T1 c_out = '_subborrow_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 64 (TWord 0) (TWord 6) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair c (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 64 (TWord 0) (TWord 0) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair c (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 64 (TWord 0) (TWord 6) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair c (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_subborrow_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 64 (TWord 0) (TWord 0) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair c (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 Notation "'subborrow_u64' ( c , a , b )" := (Op (SubWithGetBorrow 64 (TWord 3) (TWord 6) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair c (Var a)) b)).
 Notation "'subborrow_u64' ( c , a , b )" := (Op (SubWithGetBorrow 64 (TWord 3) (TWord 3) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair c (Var a)) b)).
 Notation "'subborrow_u64' ( c , a , b )" := (Op (SubWithGetBorrow 64 (TWord 3) (TWord 6) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair c (Var a)) b)).
+Notation "'subborrow_u64' ( c , a , b )" := (Op (SubWithGetBorrow 64 (TWord 3) (TWord 3) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair c (Var a)) b)).
 (*Notation "T0 out ; T1 c_out = '_subborrow_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 64 (TWord 3) (TWord 6) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair c (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 64 (TWord 3) (TWord 3) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair c (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 64 (TWord 3) (TWord 6) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair c (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_subborrow_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 64 (TWord 3) (TWord 3) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair c (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 Notation "'subborrow_u64' ( c , a , b )" := (Op (SubWithGetBorrow 64 (TWord 0) (TWord 6) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair c (Var a)) (Var b))).
 Notation "'subborrow_u64' ( c , a , b )" := (Op (SubWithGetBorrow 64 (TWord 0) (TWord 0) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair c (Var a)) (Var b))).
 Notation "'subborrow_u64' ( c , a , b )" := (Op (SubWithGetBorrow 64 (TWord 0) (TWord 6) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair c (Var a)) (Var b))).
+Notation "'subborrow_u64' ( c , a , b )" := (Op (SubWithGetBorrow 64 (TWord 0) (TWord 0) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair c (Var a)) (Var b))).
 (*Notation "T0 out ; T1 c_out = '_subborrow_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 64 (TWord 0) (TWord 6) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair c (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 64 (TWord 0) (TWord 0) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair c (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 64 (TWord 0) (TWord 6) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair c (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_subborrow_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 64 (TWord 0) (TWord 0) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair c (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 Notation "'subborrow_u64' ( c , a , b )" := (Op (SubWithGetBorrow 64 (TWord 3) (TWord 6) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair c (Var a)) (Var b))).
 Notation "'subborrow_u64' ( c , a , b )" := (Op (SubWithGetBorrow 64 (TWord 3) (TWord 3) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair c (Var a)) (Var b))).
 Notation "'subborrow_u64' ( c , a , b )" := (Op (SubWithGetBorrow 64 (TWord 3) (TWord 6) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair c (Var a)) (Var b))).
+Notation "'subborrow_u64' ( c , a , b )" := (Op (SubWithGetBorrow 64 (TWord 3) (TWord 3) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair c (Var a)) (Var b))).
 (*Notation "T0 out ; T1 c_out = '_subborrow_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 64 (TWord 3) (TWord 6) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair c (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 64 (TWord 3) (TWord 3) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair c (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 64 (TWord 3) (TWord 6) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair c (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_subborrow_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 64 (TWord 3) (TWord 3) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair c (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 Notation "'subborrow_u64' ( c , a , b )" := (Op (SubWithGetBorrow 64 (TWord 0) (TWord 6) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair (Var c) a) b)).
 Notation "'subborrow_u64' ( c , a , b )" := (Op (SubWithGetBorrow 64 (TWord 0) (TWord 0) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair (Var c) a) b)).
 Notation "'subborrow_u64' ( c , a , b )" := (Op (SubWithGetBorrow 64 (TWord 0) (TWord 6) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair (Var c) a) b)).
+Notation "'subborrow_u64' ( c , a , b )" := (Op (SubWithGetBorrow 64 (TWord 0) (TWord 0) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair (Var c) a) b)).
 (*Notation "T0 out ; T1 c_out = '_subborrow_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 64 (TWord 0) (TWord 6) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair (Var c) a) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 64 (TWord 0) (TWord 0) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair (Var c) a) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 64 (TWord 0) (TWord 6) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair (Var c) a) b)) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_subborrow_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 64 (TWord 0) (TWord 0) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair (Var c) a) b)) (fun '((out, c_out)%core) => REST)).*)
 Notation "'subborrow_u64' ( c , a , b )" := (Op (SubWithGetBorrow 64 (TWord 3) (TWord 6) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair (Var c) a) b)).
 Notation "'subborrow_u64' ( c , a , b )" := (Op (SubWithGetBorrow 64 (TWord 3) (TWord 3) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair (Var c) a) b)).
 Notation "'subborrow_u64' ( c , a , b )" := (Op (SubWithGetBorrow 64 (TWord 3) (TWord 6) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair (Var c) a) b)).
+Notation "'subborrow_u64' ( c , a , b )" := (Op (SubWithGetBorrow 64 (TWord 3) (TWord 3) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair (Var c) a) b)).
 (*Notation "T0 out ; T1 c_out = '_subborrow_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 64 (TWord 3) (TWord 6) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair (Var c) a) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 64 (TWord 3) (TWord 3) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair (Var c) a) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 64 (TWord 3) (TWord 6) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair (Var c) a) b)) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_subborrow_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 64 (TWord 3) (TWord 3) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair (Var c) a) b)) (fun '((out, c_out)%core) => REST)).*)
 Notation "'subborrow_u64' ( c , a , b )" := (Op (SubWithGetBorrow 64 (TWord 0) (TWord 6) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair (Var c) a) (Var b))).
 Notation "'subborrow_u64' ( c , a , b )" := (Op (SubWithGetBorrow 64 (TWord 0) (TWord 0) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair (Var c) a) (Var b))).
 Notation "'subborrow_u64' ( c , a , b )" := (Op (SubWithGetBorrow 64 (TWord 0) (TWord 6) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair (Var c) a) (Var b))).
+Notation "'subborrow_u64' ( c , a , b )" := (Op (SubWithGetBorrow 64 (TWord 0) (TWord 0) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair (Var c) a) (Var b))).
 (*Notation "T0 out ; T1 c_out = '_subborrow_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 64 (TWord 0) (TWord 6) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair (Var c) a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 64 (TWord 0) (TWord 0) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair (Var c) a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 64 (TWord 0) (TWord 6) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair (Var c) a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_subborrow_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 64 (TWord 0) (TWord 0) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair (Var c) a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 Notation "'subborrow_u64' ( c , a , b )" := (Op (SubWithGetBorrow 64 (TWord 3) (TWord 6) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair (Var c) a) (Var b))).
 Notation "'subborrow_u64' ( c , a , b )" := (Op (SubWithGetBorrow 64 (TWord 3) (TWord 3) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair (Var c) a) (Var b))).
 Notation "'subborrow_u64' ( c , a , b )" := (Op (SubWithGetBorrow 64 (TWord 3) (TWord 6) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair (Var c) a) (Var b))).
+Notation "'subborrow_u64' ( c , a , b )" := (Op (SubWithGetBorrow 64 (TWord 3) (TWord 3) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair (Var c) a) (Var b))).
 (*Notation "T0 out ; T1 c_out = '_subborrow_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 64 (TWord 3) (TWord 6) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair (Var c) a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 64 (TWord 3) (TWord 3) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair (Var c) a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 64 (TWord 3) (TWord 6) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair (Var c) a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_subborrow_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 64 (TWord 3) (TWord 3) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair (Var c) a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 Notation "'subborrow_u64' ( c , a , b )" := (Op (SubWithGetBorrow 64 (TWord 0) (TWord 6) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair (Var c) (Var a)) b)).
 Notation "'subborrow_u64' ( c , a , b )" := (Op (SubWithGetBorrow 64 (TWord 0) (TWord 0) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair (Var c) (Var a)) b)).
 Notation "'subborrow_u64' ( c , a , b )" := (Op (SubWithGetBorrow 64 (TWord 0) (TWord 6) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair (Var c) (Var a)) b)).
+Notation "'subborrow_u64' ( c , a , b )" := (Op (SubWithGetBorrow 64 (TWord 0) (TWord 0) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair (Var c) (Var a)) b)).
 (*Notation "T0 out ; T1 c_out = '_subborrow_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 64 (TWord 0) (TWord 6) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair (Var c) (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 64 (TWord 0) (TWord 0) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair (Var c) (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 64 (TWord 0) (TWord 6) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair (Var c) (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_subborrow_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 64 (TWord 0) (TWord 0) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair (Var c) (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 Notation "'subborrow_u64' ( c , a , b )" := (Op (SubWithGetBorrow 64 (TWord 3) (TWord 6) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair (Var c) (Var a)) b)).
 Notation "'subborrow_u64' ( c , a , b )" := (Op (SubWithGetBorrow 64 (TWord 3) (TWord 3) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair (Var c) (Var a)) b)).
 Notation "'subborrow_u64' ( c , a , b )" := (Op (SubWithGetBorrow 64 (TWord 3) (TWord 6) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair (Var c) (Var a)) b)).
+Notation "'subborrow_u64' ( c , a , b )" := (Op (SubWithGetBorrow 64 (TWord 3) (TWord 3) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair (Var c) (Var a)) b)).
 (*Notation "T0 out ; T1 c_out = '_subborrow_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 64 (TWord 3) (TWord 6) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair (Var c) (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 64 (TWord 3) (TWord 3) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair (Var c) (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 64 (TWord 3) (TWord 6) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair (Var c) (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_subborrow_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 64 (TWord 3) (TWord 3) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair (Var c) (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 Notation "'subborrow_u64' ( c , a , b )" := (Op (SubWithGetBorrow 64 (TWord 0) (TWord 6) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair (Var c) (Var a)) (Var b))).
 Notation "'subborrow_u64' ( c , a , b )" := (Op (SubWithGetBorrow 64 (TWord 0) (TWord 0) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair (Var c) (Var a)) (Var b))).
 Notation "'subborrow_u64' ( c , a , b )" := (Op (SubWithGetBorrow 64 (TWord 0) (TWord 6) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair (Var c) (Var a)) (Var b))).
+Notation "'subborrow_u64' ( c , a , b )" := (Op (SubWithGetBorrow 64 (TWord 0) (TWord 0) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair (Var c) (Var a)) (Var b))).
 (*Notation "T0 out ; T1 c_out = '_subborrow_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 64 (TWord 0) (TWord 6) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair (Var c) (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 64 (TWord 0) (TWord 0) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair (Var c) (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 64 (TWord 0) (TWord 6) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair (Var c) (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_subborrow_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 64 (TWord 0) (TWord 0) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair (Var c) (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 Notation "'subborrow_u64' ( c , a , b )" := (Op (SubWithGetBorrow 64 (TWord 3) (TWord 6) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair (Var c) (Var a)) (Var b))).
 Notation "'subborrow_u64' ( c , a , b )" := (Op (SubWithGetBorrow 64 (TWord 3) (TWord 3) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair (Var c) (Var a)) (Var b))).
 Notation "'subborrow_u64' ( c , a , b )" := (Op (SubWithGetBorrow 64 (TWord 3) (TWord 6) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair (Var c) (Var a)) (Var b))).
+Notation "'subborrow_u64' ( c , a , b )" := (Op (SubWithGetBorrow 64 (TWord 3) (TWord 3) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair (Var c) (Var a)) (Var b))).
 (*Notation "T0 out ; T1 c_out = '_subborrow_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 64 (TWord 3) (TWord 6) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair (Var c) (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 64 (TWord 3) (TWord 3) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair (Var c) (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 64 (TWord 3) (TWord 6) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair (Var c) (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_subborrow_u64' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 64 (TWord 3) (TWord 3) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair (Var c) (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 Notation "'subborrow_u128' ( c , a , b )" := (Op (SubWithGetBorrow 128 (TWord 0) (TWord 7) (TWord 7) (TWord 7) (TWord 0)) (Pair (Pair c a) b)).
 Notation "'subborrow_u128' ( c , a , b )" := (Op (SubWithGetBorrow 128 (TWord 0) (TWord 0) (TWord 7) (TWord 7) (TWord 0)) (Pair (Pair c a) b)).
 Notation "'subborrow_u128' ( c , a , b )" := (Op (SubWithGetBorrow 128 (TWord 0) (TWord 7) (TWord 0) (TWord 7) (TWord 0)) (Pair (Pair c a) b)).
+Notation "'subborrow_u128' ( c , a , b )" := (Op (SubWithGetBorrow 128 (TWord 0) (TWord 0) (TWord 0) (TWord 7) (TWord 0)) (Pair (Pair c a) b)).
 (*Notation "T0 out ; T1 c_out = '_subborrow_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 128 (TWord 0) (TWord 7) (TWord 7) (TWord 7) (TWord 0)) (Pair (Pair c a) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 128 (TWord 0) (TWord 0) (TWord 7) (TWord 7) (TWord 0)) (Pair (Pair c a) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 128 (TWord 0) (TWord 7) (TWord 0) (TWord 7) (TWord 0)) (Pair (Pair c a) b)) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_subborrow_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 128 (TWord 0) (TWord 0) (TWord 0) (TWord 7) (TWord 0)) (Pair (Pair c a) b)) (fun '((out, c_out)%core) => REST)).*)
 Notation "'subborrow_u128' ( c , a , b )" := (Op (SubWithGetBorrow 128 (TWord 3) (TWord 7) (TWord 7) (TWord 7) (TWord 3)) (Pair (Pair c a) b)).
 Notation "'subborrow_u128' ( c , a , b )" := (Op (SubWithGetBorrow 128 (TWord 3) (TWord 3) (TWord 7) (TWord 7) (TWord 3)) (Pair (Pair c a) b)).
 Notation "'subborrow_u128' ( c , a , b )" := (Op (SubWithGetBorrow 128 (TWord 3) (TWord 7) (TWord 3) (TWord 7) (TWord 3)) (Pair (Pair c a) b)).
+Notation "'subborrow_u128' ( c , a , b )" := (Op (SubWithGetBorrow 128 (TWord 3) (TWord 3) (TWord 3) (TWord 7) (TWord 3)) (Pair (Pair c a) b)).
 (*Notation "T0 out ; T1 c_out = '_subborrow_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 128 (TWord 3) (TWord 7) (TWord 7) (TWord 7) (TWord 3)) (Pair (Pair c a) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 128 (TWord 3) (TWord 3) (TWord 7) (TWord 7) (TWord 3)) (Pair (Pair c a) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 128 (TWord 3) (TWord 7) (TWord 3) (TWord 7) (TWord 3)) (Pair (Pair c a) b)) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_subborrow_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 128 (TWord 3) (TWord 3) (TWord 3) (TWord 7) (TWord 3)) (Pair (Pair c a) b)) (fun '((out, c_out)%core) => REST)).*)
 Notation "'subborrow_u128' ( c , a , b )" := (Op (SubWithGetBorrow 128 (TWord 0) (TWord 7) (TWord 7) (TWord 7) (TWord 0)) (Pair (Pair c a) (Var b))).
 Notation "'subborrow_u128' ( c , a , b )" := (Op (SubWithGetBorrow 128 (TWord 0) (TWord 0) (TWord 7) (TWord 7) (TWord 0)) (Pair (Pair c a) (Var b))).
 Notation "'subborrow_u128' ( c , a , b )" := (Op (SubWithGetBorrow 128 (TWord 0) (TWord 7) (TWord 0) (TWord 7) (TWord 0)) (Pair (Pair c a) (Var b))).
+Notation "'subborrow_u128' ( c , a , b )" := (Op (SubWithGetBorrow 128 (TWord 0) (TWord 0) (TWord 0) (TWord 7) (TWord 0)) (Pair (Pair c a) (Var b))).
 (*Notation "T0 out ; T1 c_out = '_subborrow_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 128 (TWord 0) (TWord 7) (TWord 7) (TWord 7) (TWord 0)) (Pair (Pair c a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 128 (TWord 0) (TWord 0) (TWord 7) (TWord 7) (TWord 0)) (Pair (Pair c a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 128 (TWord 0) (TWord 7) (TWord 0) (TWord 7) (TWord 0)) (Pair (Pair c a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_subborrow_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 128 (TWord 0) (TWord 0) (TWord 0) (TWord 7) (TWord 0)) (Pair (Pair c a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 Notation "'subborrow_u128' ( c , a , b )" := (Op (SubWithGetBorrow 128 (TWord 3) (TWord 7) (TWord 7) (TWord 7) (TWord 3)) (Pair (Pair c a) (Var b))).
 Notation "'subborrow_u128' ( c , a , b )" := (Op (SubWithGetBorrow 128 (TWord 3) (TWord 3) (TWord 7) (TWord 7) (TWord 3)) (Pair (Pair c a) (Var b))).
 Notation "'subborrow_u128' ( c , a , b )" := (Op (SubWithGetBorrow 128 (TWord 3) (TWord 7) (TWord 3) (TWord 7) (TWord 3)) (Pair (Pair c a) (Var b))).
+Notation "'subborrow_u128' ( c , a , b )" := (Op (SubWithGetBorrow 128 (TWord 3) (TWord 3) (TWord 3) (TWord 7) (TWord 3)) (Pair (Pair c a) (Var b))).
 (*Notation "T0 out ; T1 c_out = '_subborrow_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 128 (TWord 3) (TWord 7) (TWord 7) (TWord 7) (TWord 3)) (Pair (Pair c a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 128 (TWord 3) (TWord 3) (TWord 7) (TWord 7) (TWord 3)) (Pair (Pair c a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 128 (TWord 3) (TWord 7) (TWord 3) (TWord 7) (TWord 3)) (Pair (Pair c a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_subborrow_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 128 (TWord 3) (TWord 3) (TWord 3) (TWord 7) (TWord 3)) (Pair (Pair c a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 Notation "'subborrow_u128' ( c , a , b )" := (Op (SubWithGetBorrow 128 (TWord 0) (TWord 7) (TWord 7) (TWord 7) (TWord 0)) (Pair (Pair c (Var a)) b)).
 Notation "'subborrow_u128' ( c , a , b )" := (Op (SubWithGetBorrow 128 (TWord 0) (TWord 0) (TWord 7) (TWord 7) (TWord 0)) (Pair (Pair c (Var a)) b)).
 Notation "'subborrow_u128' ( c , a , b )" := (Op (SubWithGetBorrow 128 (TWord 0) (TWord 7) (TWord 0) (TWord 7) (TWord 0)) (Pair (Pair c (Var a)) b)).
+Notation "'subborrow_u128' ( c , a , b )" := (Op (SubWithGetBorrow 128 (TWord 0) (TWord 0) (TWord 0) (TWord 7) (TWord 0)) (Pair (Pair c (Var a)) b)).
 (*Notation "T0 out ; T1 c_out = '_subborrow_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 128 (TWord 0) (TWord 7) (TWord 7) (TWord 7) (TWord 0)) (Pair (Pair c (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 128 (TWord 0) (TWord 0) (TWord 7) (TWord 7) (TWord 0)) (Pair (Pair c (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 128 (TWord 0) (TWord 7) (TWord 0) (TWord 7) (TWord 0)) (Pair (Pair c (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_subborrow_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 128 (TWord 0) (TWord 0) (TWord 0) (TWord 7) (TWord 0)) (Pair (Pair c (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 Notation "'subborrow_u128' ( c , a , b )" := (Op (SubWithGetBorrow 128 (TWord 3) (TWord 7) (TWord 7) (TWord 7) (TWord 3)) (Pair (Pair c (Var a)) b)).
 Notation "'subborrow_u128' ( c , a , b )" := (Op (SubWithGetBorrow 128 (TWord 3) (TWord 3) (TWord 7) (TWord 7) (TWord 3)) (Pair (Pair c (Var a)) b)).
 Notation "'subborrow_u128' ( c , a , b )" := (Op (SubWithGetBorrow 128 (TWord 3) (TWord 7) (TWord 3) (TWord 7) (TWord 3)) (Pair (Pair c (Var a)) b)).
+Notation "'subborrow_u128' ( c , a , b )" := (Op (SubWithGetBorrow 128 (TWord 3) (TWord 3) (TWord 3) (TWord 7) (TWord 3)) (Pair (Pair c (Var a)) b)).
 (*Notation "T0 out ; T1 c_out = '_subborrow_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 128 (TWord 3) (TWord 7) (TWord 7) (TWord 7) (TWord 3)) (Pair (Pair c (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 128 (TWord 3) (TWord 3) (TWord 7) (TWord 7) (TWord 3)) (Pair (Pair c (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 128 (TWord 3) (TWord 7) (TWord 3) (TWord 7) (TWord 3)) (Pair (Pair c (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_subborrow_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 128 (TWord 3) (TWord 3) (TWord 3) (TWord 7) (TWord 3)) (Pair (Pair c (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 Notation "'subborrow_u128' ( c , a , b )" := (Op (SubWithGetBorrow 128 (TWord 0) (TWord 7) (TWord 7) (TWord 7) (TWord 0)) (Pair (Pair c (Var a)) (Var b))).
 Notation "'subborrow_u128' ( c , a , b )" := (Op (SubWithGetBorrow 128 (TWord 0) (TWord 0) (TWord 7) (TWord 7) (TWord 0)) (Pair (Pair c (Var a)) (Var b))).
 Notation "'subborrow_u128' ( c , a , b )" := (Op (SubWithGetBorrow 128 (TWord 0) (TWord 7) (TWord 0) (TWord 7) (TWord 0)) (Pair (Pair c (Var a)) (Var b))).
+Notation "'subborrow_u128' ( c , a , b )" := (Op (SubWithGetBorrow 128 (TWord 0) (TWord 0) (TWord 0) (TWord 7) (TWord 0)) (Pair (Pair c (Var a)) (Var b))).
 (*Notation "T0 out ; T1 c_out = '_subborrow_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 128 (TWord 0) (TWord 7) (TWord 7) (TWord 7) (TWord 0)) (Pair (Pair c (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 128 (TWord 0) (TWord 0) (TWord 7) (TWord 7) (TWord 0)) (Pair (Pair c (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 128 (TWord 0) (TWord 7) (TWord 0) (TWord 7) (TWord 0)) (Pair (Pair c (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_subborrow_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 128 (TWord 0) (TWord 0) (TWord 0) (TWord 7) (TWord 0)) (Pair (Pair c (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 Notation "'subborrow_u128' ( c , a , b )" := (Op (SubWithGetBorrow 128 (TWord 3) (TWord 7) (TWord 7) (TWord 7) (TWord 3)) (Pair (Pair c (Var a)) (Var b))).
 Notation "'subborrow_u128' ( c , a , b )" := (Op (SubWithGetBorrow 128 (TWord 3) (TWord 3) (TWord 7) (TWord 7) (TWord 3)) (Pair (Pair c (Var a)) (Var b))).
 Notation "'subborrow_u128' ( c , a , b )" := (Op (SubWithGetBorrow 128 (TWord 3) (TWord 7) (TWord 3) (TWord 7) (TWord 3)) (Pair (Pair c (Var a)) (Var b))).
+Notation "'subborrow_u128' ( c , a , b )" := (Op (SubWithGetBorrow 128 (TWord 3) (TWord 3) (TWord 3) (TWord 7) (TWord 3)) (Pair (Pair c (Var a)) (Var b))).
 (*Notation "T0 out ; T1 c_out = '_subborrow_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 128 (TWord 3) (TWord 7) (TWord 7) (TWord 7) (TWord 3)) (Pair (Pair c (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 128 (TWord 3) (TWord 3) (TWord 7) (TWord 7) (TWord 3)) (Pair (Pair c (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 128 (TWord 3) (TWord 7) (TWord 3) (TWord 7) (TWord 3)) (Pair (Pair c (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_subborrow_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 128 (TWord 3) (TWord 3) (TWord 3) (TWord 7) (TWord 3)) (Pair (Pair c (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 Notation "'subborrow_u128' ( c , a , b )" := (Op (SubWithGetBorrow 128 (TWord 0) (TWord 7) (TWord 7) (TWord 7) (TWord 0)) (Pair (Pair (Var c) a) b)).
 Notation "'subborrow_u128' ( c , a , b )" := (Op (SubWithGetBorrow 128 (TWord 0) (TWord 0) (TWord 7) (TWord 7) (TWord 0)) (Pair (Pair (Var c) a) b)).
 Notation "'subborrow_u128' ( c , a , b )" := (Op (SubWithGetBorrow 128 (TWord 0) (TWord 7) (TWord 0) (TWord 7) (TWord 0)) (Pair (Pair (Var c) a) b)).
+Notation "'subborrow_u128' ( c , a , b )" := (Op (SubWithGetBorrow 128 (TWord 0) (TWord 0) (TWord 0) (TWord 7) (TWord 0)) (Pair (Pair (Var c) a) b)).
 (*Notation "T0 out ; T1 c_out = '_subborrow_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 128 (TWord 0) (TWord 7) (TWord 7) (TWord 7) (TWord 0)) (Pair (Pair (Var c) a) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 128 (TWord 0) (TWord 0) (TWord 7) (TWord 7) (TWord 0)) (Pair (Pair (Var c) a) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 128 (TWord 0) (TWord 7) (TWord 0) (TWord 7) (TWord 0)) (Pair (Pair (Var c) a) b)) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_subborrow_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 128 (TWord 0) (TWord 0) (TWord 0) (TWord 7) (TWord 0)) (Pair (Pair (Var c) a) b)) (fun '((out, c_out)%core) => REST)).*)
 Notation "'subborrow_u128' ( c , a , b )" := (Op (SubWithGetBorrow 128 (TWord 3) (TWord 7) (TWord 7) (TWord 7) (TWord 3)) (Pair (Pair (Var c) a) b)).
 Notation "'subborrow_u128' ( c , a , b )" := (Op (SubWithGetBorrow 128 (TWord 3) (TWord 3) (TWord 7) (TWord 7) (TWord 3)) (Pair (Pair (Var c) a) b)).
 Notation "'subborrow_u128' ( c , a , b )" := (Op (SubWithGetBorrow 128 (TWord 3) (TWord 7) (TWord 3) (TWord 7) (TWord 3)) (Pair (Pair (Var c) a) b)).
+Notation "'subborrow_u128' ( c , a , b )" := (Op (SubWithGetBorrow 128 (TWord 3) (TWord 3) (TWord 3) (TWord 7) (TWord 3)) (Pair (Pair (Var c) a) b)).
 (*Notation "T0 out ; T1 c_out = '_subborrow_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 128 (TWord 3) (TWord 7) (TWord 7) (TWord 7) (TWord 3)) (Pair (Pair (Var c) a) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 128 (TWord 3) (TWord 3) (TWord 7) (TWord 7) (TWord 3)) (Pair (Pair (Var c) a) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 128 (TWord 3) (TWord 7) (TWord 3) (TWord 7) (TWord 3)) (Pair (Pair (Var c) a) b)) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_subborrow_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 128 (TWord 3) (TWord 3) (TWord 3) (TWord 7) (TWord 3)) (Pair (Pair (Var c) a) b)) (fun '((out, c_out)%core) => REST)).*)
 Notation "'subborrow_u128' ( c , a , b )" := (Op (SubWithGetBorrow 128 (TWord 0) (TWord 7) (TWord 7) (TWord 7) (TWord 0)) (Pair (Pair (Var c) a) (Var b))).
 Notation "'subborrow_u128' ( c , a , b )" := (Op (SubWithGetBorrow 128 (TWord 0) (TWord 0) (TWord 7) (TWord 7) (TWord 0)) (Pair (Pair (Var c) a) (Var b))).
 Notation "'subborrow_u128' ( c , a , b )" := (Op (SubWithGetBorrow 128 (TWord 0) (TWord 7) (TWord 0) (TWord 7) (TWord 0)) (Pair (Pair (Var c) a) (Var b))).
+Notation "'subborrow_u128' ( c , a , b )" := (Op (SubWithGetBorrow 128 (TWord 0) (TWord 0) (TWord 0) (TWord 7) (TWord 0)) (Pair (Pair (Var c) a) (Var b))).
 (*Notation "T0 out ; T1 c_out = '_subborrow_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 128 (TWord 0) (TWord 7) (TWord 7) (TWord 7) (TWord 0)) (Pair (Pair (Var c) a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 128 (TWord 0) (TWord 0) (TWord 7) (TWord 7) (TWord 0)) (Pair (Pair (Var c) a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 128 (TWord 0) (TWord 7) (TWord 0) (TWord 7) (TWord 0)) (Pair (Pair (Var c) a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_subborrow_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 128 (TWord 0) (TWord 0) (TWord 0) (TWord 7) (TWord 0)) (Pair (Pair (Var c) a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 Notation "'subborrow_u128' ( c , a , b )" := (Op (SubWithGetBorrow 128 (TWord 3) (TWord 7) (TWord 7) (TWord 7) (TWord 3)) (Pair (Pair (Var c) a) (Var b))).
 Notation "'subborrow_u128' ( c , a , b )" := (Op (SubWithGetBorrow 128 (TWord 3) (TWord 3) (TWord 7) (TWord 7) (TWord 3)) (Pair (Pair (Var c) a) (Var b))).
 Notation "'subborrow_u128' ( c , a , b )" := (Op (SubWithGetBorrow 128 (TWord 3) (TWord 7) (TWord 3) (TWord 7) (TWord 3)) (Pair (Pair (Var c) a) (Var b))).
+Notation "'subborrow_u128' ( c , a , b )" := (Op (SubWithGetBorrow 128 (TWord 3) (TWord 3) (TWord 3) (TWord 7) (TWord 3)) (Pair (Pair (Var c) a) (Var b))).
 (*Notation "T0 out ; T1 c_out = '_subborrow_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 128 (TWord 3) (TWord 7) (TWord 7) (TWord 7) (TWord 3)) (Pair (Pair (Var c) a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 128 (TWord 3) (TWord 3) (TWord 7) (TWord 7) (TWord 3)) (Pair (Pair (Var c) a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 128 (TWord 3) (TWord 7) (TWord 3) (TWord 7) (TWord 3)) (Pair (Pair (Var c) a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_subborrow_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 128 (TWord 3) (TWord 3) (TWord 3) (TWord 7) (TWord 3)) (Pair (Pair (Var c) a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 Notation "'subborrow_u128' ( c , a , b )" := (Op (SubWithGetBorrow 128 (TWord 0) (TWord 7) (TWord 7) (TWord 7) (TWord 0)) (Pair (Pair (Var c) (Var a)) b)).
 Notation "'subborrow_u128' ( c , a , b )" := (Op (SubWithGetBorrow 128 (TWord 0) (TWord 0) (TWord 7) (TWord 7) (TWord 0)) (Pair (Pair (Var c) (Var a)) b)).
 Notation "'subborrow_u128' ( c , a , b )" := (Op (SubWithGetBorrow 128 (TWord 0) (TWord 7) (TWord 0) (TWord 7) (TWord 0)) (Pair (Pair (Var c) (Var a)) b)).
+Notation "'subborrow_u128' ( c , a , b )" := (Op (SubWithGetBorrow 128 (TWord 0) (TWord 0) (TWord 0) (TWord 7) (TWord 0)) (Pair (Pair (Var c) (Var a)) b)).
 (*Notation "T0 out ; T1 c_out = '_subborrow_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 128 (TWord 0) (TWord 7) (TWord 7) (TWord 7) (TWord 0)) (Pair (Pair (Var c) (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 128 (TWord 0) (TWord 0) (TWord 7) (TWord 7) (TWord 0)) (Pair (Pair (Var c) (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 128 (TWord 0) (TWord 7) (TWord 0) (TWord 7) (TWord 0)) (Pair (Pair (Var c) (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_subborrow_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 128 (TWord 0) (TWord 0) (TWord 0) (TWord 7) (TWord 0)) (Pair (Pair (Var c) (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 Notation "'subborrow_u128' ( c , a , b )" := (Op (SubWithGetBorrow 128 (TWord 3) (TWord 7) (TWord 7) (TWord 7) (TWord 3)) (Pair (Pair (Var c) (Var a)) b)).
 Notation "'subborrow_u128' ( c , a , b )" := (Op (SubWithGetBorrow 128 (TWord 3) (TWord 3) (TWord 7) (TWord 7) (TWord 3)) (Pair (Pair (Var c) (Var a)) b)).
 Notation "'subborrow_u128' ( c , a , b )" := (Op (SubWithGetBorrow 128 (TWord 3) (TWord 7) (TWord 3) (TWord 7) (TWord 3)) (Pair (Pair (Var c) (Var a)) b)).
+Notation "'subborrow_u128' ( c , a , b )" := (Op (SubWithGetBorrow 128 (TWord 3) (TWord 3) (TWord 3) (TWord 7) (TWord 3)) (Pair (Pair (Var c) (Var a)) b)).
 (*Notation "T0 out ; T1 c_out = '_subborrow_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 128 (TWord 3) (TWord 7) (TWord 7) (TWord 7) (TWord 3)) (Pair (Pair (Var c) (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 128 (TWord 3) (TWord 3) (TWord 7) (TWord 7) (TWord 3)) (Pair (Pair (Var c) (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 128 (TWord 3) (TWord 7) (TWord 3) (TWord 7) (TWord 3)) (Pair (Pair (Var c) (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_subborrow_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 128 (TWord 3) (TWord 3) (TWord 3) (TWord 7) (TWord 3)) (Pair (Pair (Var c) (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 Notation "'subborrow_u128' ( c , a , b )" := (Op (SubWithGetBorrow 128 (TWord 0) (TWord 7) (TWord 7) (TWord 7) (TWord 0)) (Pair (Pair (Var c) (Var a)) (Var b))).
 Notation "'subborrow_u128' ( c , a , b )" := (Op (SubWithGetBorrow 128 (TWord 0) (TWord 0) (TWord 7) (TWord 7) (TWord 0)) (Pair (Pair (Var c) (Var a)) (Var b))).
 Notation "'subborrow_u128' ( c , a , b )" := (Op (SubWithGetBorrow 128 (TWord 0) (TWord 7) (TWord 0) (TWord 7) (TWord 0)) (Pair (Pair (Var c) (Var a)) (Var b))).
+Notation "'subborrow_u128' ( c , a , b )" := (Op (SubWithGetBorrow 128 (TWord 0) (TWord 0) (TWord 0) (TWord 7) (TWord 0)) (Pair (Pair (Var c) (Var a)) (Var b))).
 (*Notation "T0 out ; T1 c_out = '_subborrow_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 128 (TWord 0) (TWord 7) (TWord 7) (TWord 7) (TWord 0)) (Pair (Pair (Var c) (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 128 (TWord 0) (TWord 0) (TWord 7) (TWord 7) (TWord 0)) (Pair (Pair (Var c) (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 128 (TWord 0) (TWord 7) (TWord 0) (TWord 7) (TWord 0)) (Pair (Pair (Var c) (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_subborrow_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 128 (TWord 0) (TWord 0) (TWord 0) (TWord 7) (TWord 0)) (Pair (Pair (Var c) (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 Notation "'subborrow_u128' ( c , a , b )" := (Op (SubWithGetBorrow 128 (TWord 3) (TWord 7) (TWord 7) (TWord 7) (TWord 3)) (Pair (Pair (Var c) (Var a)) (Var b))).
 Notation "'subborrow_u128' ( c , a , b )" := (Op (SubWithGetBorrow 128 (TWord 3) (TWord 3) (TWord 7) (TWord 7) (TWord 3)) (Pair (Pair (Var c) (Var a)) (Var b))).
 Notation "'subborrow_u128' ( c , a , b )" := (Op (SubWithGetBorrow 128 (TWord 3) (TWord 7) (TWord 3) (TWord 7) (TWord 3)) (Pair (Pair (Var c) (Var a)) (Var b))).
+Notation "'subborrow_u128' ( c , a , b )" := (Op (SubWithGetBorrow 128 (TWord 3) (TWord 3) (TWord 3) (TWord 7) (TWord 3)) (Pair (Pair (Var c) (Var a)) (Var b))).
 (*Notation "T0 out ; T1 c_out = '_subborrow_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 128 (TWord 3) (TWord 7) (TWord 7) (TWord 7) (TWord 3)) (Pair (Pair (Var c) (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 128 (TWord 3) (TWord 3) (TWord 7) (TWord 7) (TWord 3)) (Pair (Pair (Var c) (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 128 (TWord 3) (TWord 7) (TWord 3) (TWord 7) (TWord 3)) (Pair (Pair (Var c) (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_subborrow_u128' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 128 (TWord 3) (TWord 3) (TWord 3) (TWord 7) (TWord 3)) (Pair (Pair (Var c) (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 Notation "'subborrow_u51' ( c , a , b )" := (Op (SubWithGetBorrow 51 (TWord 0) (TWord 6) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair c a) b)).
 Notation "'subborrow_u51' ( c , a , b )" := (Op (SubWithGetBorrow 51 (TWord 0) (TWord 0) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair c a) b)).
 Notation "'subborrow_u51' ( c , a , b )" := (Op (SubWithGetBorrow 51 (TWord 0) (TWord 6) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair c a) b)).
+Notation "'subborrow_u51' ( c , a , b )" := (Op (SubWithGetBorrow 51 (TWord 0) (TWord 0) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair c a) b)).
 (*Notation "T0 out ; T1 c_out = '_subborrow_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 51 (TWord 0) (TWord 6) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair c a) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 51 (TWord 0) (TWord 0) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair c a) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 51 (TWord 0) (TWord 6) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair c a) b)) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_subborrow_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 51 (TWord 0) (TWord 0) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair c a) b)) (fun '((out, c_out)%core) => REST)).*)
 Notation "'subborrow_u51' ( c , a , b )" := (Op (SubWithGetBorrow 51 (TWord 3) (TWord 6) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair c a) b)).
 Notation "'subborrow_u51' ( c , a , b )" := (Op (SubWithGetBorrow 51 (TWord 3) (TWord 3) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair c a) b)).
 Notation "'subborrow_u51' ( c , a , b )" := (Op (SubWithGetBorrow 51 (TWord 3) (TWord 6) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair c a) b)).
+Notation "'subborrow_u51' ( c , a , b )" := (Op (SubWithGetBorrow 51 (TWord 3) (TWord 3) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair c a) b)).
 (*Notation "T0 out ; T1 c_out = '_subborrow_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 51 (TWord 3) (TWord 6) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair c a) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 51 (TWord 3) (TWord 3) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair c a) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 51 (TWord 3) (TWord 6) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair c a) b)) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_subborrow_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 51 (TWord 3) (TWord 3) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair c a) b)) (fun '((out, c_out)%core) => REST)).*)
 Notation "'subborrow_u51' ( c , a , b )" := (Op (SubWithGetBorrow 51 (TWord 0) (TWord 6) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair c a) (Var b))).
 Notation "'subborrow_u51' ( c , a , b )" := (Op (SubWithGetBorrow 51 (TWord 0) (TWord 0) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair c a) (Var b))).
 Notation "'subborrow_u51' ( c , a , b )" := (Op (SubWithGetBorrow 51 (TWord 0) (TWord 6) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair c a) (Var b))).
+Notation "'subborrow_u51' ( c , a , b )" := (Op (SubWithGetBorrow 51 (TWord 0) (TWord 0) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair c a) (Var b))).
 (*Notation "T0 out ; T1 c_out = '_subborrow_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 51 (TWord 0) (TWord 6) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair c a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 51 (TWord 0) (TWord 0) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair c a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 51 (TWord 0) (TWord 6) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair c a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_subborrow_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 51 (TWord 0) (TWord 0) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair c a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 Notation "'subborrow_u51' ( c , a , b )" := (Op (SubWithGetBorrow 51 (TWord 3) (TWord 6) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair c a) (Var b))).
 Notation "'subborrow_u51' ( c , a , b )" := (Op (SubWithGetBorrow 51 (TWord 3) (TWord 3) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair c a) (Var b))).
 Notation "'subborrow_u51' ( c , a , b )" := (Op (SubWithGetBorrow 51 (TWord 3) (TWord 6) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair c a) (Var b))).
+Notation "'subborrow_u51' ( c , a , b )" := (Op (SubWithGetBorrow 51 (TWord 3) (TWord 3) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair c a) (Var b))).
 (*Notation "T0 out ; T1 c_out = '_subborrow_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 51 (TWord 3) (TWord 6) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair c a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 51 (TWord 3) (TWord 3) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair c a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 51 (TWord 3) (TWord 6) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair c a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_subborrow_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 51 (TWord 3) (TWord 3) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair c a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 Notation "'subborrow_u51' ( c , a , b )" := (Op (SubWithGetBorrow 51 (TWord 0) (TWord 6) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair c (Var a)) b)).
 Notation "'subborrow_u51' ( c , a , b )" := (Op (SubWithGetBorrow 51 (TWord 0) (TWord 0) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair c (Var a)) b)).
 Notation "'subborrow_u51' ( c , a , b )" := (Op (SubWithGetBorrow 51 (TWord 0) (TWord 6) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair c (Var a)) b)).
+Notation "'subborrow_u51' ( c , a , b )" := (Op (SubWithGetBorrow 51 (TWord 0) (TWord 0) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair c (Var a)) b)).
 (*Notation "T0 out ; T1 c_out = '_subborrow_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 51 (TWord 0) (TWord 6) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair c (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 51 (TWord 0) (TWord 0) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair c (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 51 (TWord 0) (TWord 6) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair c (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_subborrow_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 51 (TWord 0) (TWord 0) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair c (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 Notation "'subborrow_u51' ( c , a , b )" := (Op (SubWithGetBorrow 51 (TWord 3) (TWord 6) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair c (Var a)) b)).
 Notation "'subborrow_u51' ( c , a , b )" := (Op (SubWithGetBorrow 51 (TWord 3) (TWord 3) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair c (Var a)) b)).
 Notation "'subborrow_u51' ( c , a , b )" := (Op (SubWithGetBorrow 51 (TWord 3) (TWord 6) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair c (Var a)) b)).
+Notation "'subborrow_u51' ( c , a , b )" := (Op (SubWithGetBorrow 51 (TWord 3) (TWord 3) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair c (Var a)) b)).
 (*Notation "T0 out ; T1 c_out = '_subborrow_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 51 (TWord 3) (TWord 6) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair c (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 51 (TWord 3) (TWord 3) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair c (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 51 (TWord 3) (TWord 6) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair c (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_subborrow_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 51 (TWord 3) (TWord 3) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair c (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 Notation "'subborrow_u51' ( c , a , b )" := (Op (SubWithGetBorrow 51 (TWord 0) (TWord 6) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair c (Var a)) (Var b))).
 Notation "'subborrow_u51' ( c , a , b )" := (Op (SubWithGetBorrow 51 (TWord 0) (TWord 0) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair c (Var a)) (Var b))).
 Notation "'subborrow_u51' ( c , a , b )" := (Op (SubWithGetBorrow 51 (TWord 0) (TWord 6) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair c (Var a)) (Var b))).
+Notation "'subborrow_u51' ( c , a , b )" := (Op (SubWithGetBorrow 51 (TWord 0) (TWord 0) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair c (Var a)) (Var b))).
 (*Notation "T0 out ; T1 c_out = '_subborrow_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 51 (TWord 0) (TWord 6) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair c (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 51 (TWord 0) (TWord 0) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair c (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 51 (TWord 0) (TWord 6) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair c (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_subborrow_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 51 (TWord 0) (TWord 0) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair c (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 Notation "'subborrow_u51' ( c , a , b )" := (Op (SubWithGetBorrow 51 (TWord 3) (TWord 6) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair c (Var a)) (Var b))).
 Notation "'subborrow_u51' ( c , a , b )" := (Op (SubWithGetBorrow 51 (TWord 3) (TWord 3) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair c (Var a)) (Var b))).
 Notation "'subborrow_u51' ( c , a , b )" := (Op (SubWithGetBorrow 51 (TWord 3) (TWord 6) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair c (Var a)) (Var b))).
+Notation "'subborrow_u51' ( c , a , b )" := (Op (SubWithGetBorrow 51 (TWord 3) (TWord 3) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair c (Var a)) (Var b))).
 (*Notation "T0 out ; T1 c_out = '_subborrow_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 51 (TWord 3) (TWord 6) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair c (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 51 (TWord 3) (TWord 3) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair c (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 51 (TWord 3) (TWord 6) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair c (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_subborrow_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 51 (TWord 3) (TWord 3) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair c (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 Notation "'subborrow_u51' ( c , a , b )" := (Op (SubWithGetBorrow 51 (TWord 0) (TWord 6) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair (Var c) a) b)).
 Notation "'subborrow_u51' ( c , a , b )" := (Op (SubWithGetBorrow 51 (TWord 0) (TWord 0) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair (Var c) a) b)).
 Notation "'subborrow_u51' ( c , a , b )" := (Op (SubWithGetBorrow 51 (TWord 0) (TWord 6) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair (Var c) a) b)).
+Notation "'subborrow_u51' ( c , a , b )" := (Op (SubWithGetBorrow 51 (TWord 0) (TWord 0) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair (Var c) a) b)).
 (*Notation "T0 out ; T1 c_out = '_subborrow_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 51 (TWord 0) (TWord 6) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair (Var c) a) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 51 (TWord 0) (TWord 0) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair (Var c) a) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 51 (TWord 0) (TWord 6) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair (Var c) a) b)) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_subborrow_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 51 (TWord 0) (TWord 0) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair (Var c) a) b)) (fun '((out, c_out)%core) => REST)).*)
 Notation "'subborrow_u51' ( c , a , b )" := (Op (SubWithGetBorrow 51 (TWord 3) (TWord 6) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair (Var c) a) b)).
 Notation "'subborrow_u51' ( c , a , b )" := (Op (SubWithGetBorrow 51 (TWord 3) (TWord 3) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair (Var c) a) b)).
 Notation "'subborrow_u51' ( c , a , b )" := (Op (SubWithGetBorrow 51 (TWord 3) (TWord 6) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair (Var c) a) b)).
+Notation "'subborrow_u51' ( c , a , b )" := (Op (SubWithGetBorrow 51 (TWord 3) (TWord 3) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair (Var c) a) b)).
 (*Notation "T0 out ; T1 c_out = '_subborrow_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 51 (TWord 3) (TWord 6) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair (Var c) a) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 51 (TWord 3) (TWord 3) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair (Var c) a) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 51 (TWord 3) (TWord 6) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair (Var c) a) b)) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_subborrow_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 51 (TWord 3) (TWord 3) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair (Var c) a) b)) (fun '((out, c_out)%core) => REST)).*)
 Notation "'subborrow_u51' ( c , a , b )" := (Op (SubWithGetBorrow 51 (TWord 0) (TWord 6) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair (Var c) a) (Var b))).
 Notation "'subborrow_u51' ( c , a , b )" := (Op (SubWithGetBorrow 51 (TWord 0) (TWord 0) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair (Var c) a) (Var b))).
 Notation "'subborrow_u51' ( c , a , b )" := (Op (SubWithGetBorrow 51 (TWord 0) (TWord 6) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair (Var c) a) (Var b))).
+Notation "'subborrow_u51' ( c , a , b )" := (Op (SubWithGetBorrow 51 (TWord 0) (TWord 0) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair (Var c) a) (Var b))).
 (*Notation "T0 out ; T1 c_out = '_subborrow_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 51 (TWord 0) (TWord 6) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair (Var c) a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 51 (TWord 0) (TWord 0) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair (Var c) a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 51 (TWord 0) (TWord 6) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair (Var c) a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_subborrow_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 51 (TWord 0) (TWord 0) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair (Var c) a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 Notation "'subborrow_u51' ( c , a , b )" := (Op (SubWithGetBorrow 51 (TWord 3) (TWord 6) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair (Var c) a) (Var b))).
 Notation "'subborrow_u51' ( c , a , b )" := (Op (SubWithGetBorrow 51 (TWord 3) (TWord 3) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair (Var c) a) (Var b))).
 Notation "'subborrow_u51' ( c , a , b )" := (Op (SubWithGetBorrow 51 (TWord 3) (TWord 6) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair (Var c) a) (Var b))).
+Notation "'subborrow_u51' ( c , a , b )" := (Op (SubWithGetBorrow 51 (TWord 3) (TWord 3) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair (Var c) a) (Var b))).
 (*Notation "T0 out ; T1 c_out = '_subborrow_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 51 (TWord 3) (TWord 6) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair (Var c) a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 51 (TWord 3) (TWord 3) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair (Var c) a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 51 (TWord 3) (TWord 6) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair (Var c) a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_subborrow_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 51 (TWord 3) (TWord 3) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair (Var c) a) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 Notation "'subborrow_u51' ( c , a , b )" := (Op (SubWithGetBorrow 51 (TWord 0) (TWord 6) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair (Var c) (Var a)) b)).
 Notation "'subborrow_u51' ( c , a , b )" := (Op (SubWithGetBorrow 51 (TWord 0) (TWord 0) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair (Var c) (Var a)) b)).
 Notation "'subborrow_u51' ( c , a , b )" := (Op (SubWithGetBorrow 51 (TWord 0) (TWord 6) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair (Var c) (Var a)) b)).
+Notation "'subborrow_u51' ( c , a , b )" := (Op (SubWithGetBorrow 51 (TWord 0) (TWord 0) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair (Var c) (Var a)) b)).
 (*Notation "T0 out ; T1 c_out = '_subborrow_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 51 (TWord 0) (TWord 6) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair (Var c) (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 51 (TWord 0) (TWord 0) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair (Var c) (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 51 (TWord 0) (TWord 6) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair (Var c) (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_subborrow_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 51 (TWord 0) (TWord 0) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair (Var c) (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 Notation "'subborrow_u51' ( c , a , b )" := (Op (SubWithGetBorrow 51 (TWord 3) (TWord 6) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair (Var c) (Var a)) b)).
 Notation "'subborrow_u51' ( c , a , b )" := (Op (SubWithGetBorrow 51 (TWord 3) (TWord 3) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair (Var c) (Var a)) b)).
 Notation "'subborrow_u51' ( c , a , b )" := (Op (SubWithGetBorrow 51 (TWord 3) (TWord 6) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair (Var c) (Var a)) b)).
+Notation "'subborrow_u51' ( c , a , b )" := (Op (SubWithGetBorrow 51 (TWord 3) (TWord 3) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair (Var c) (Var a)) b)).
 (*Notation "T0 out ; T1 c_out = '_subborrow_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 51 (TWord 3) (TWord 6) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair (Var c) (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 51 (TWord 3) (TWord 3) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair (Var c) (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 51 (TWord 3) (TWord 6) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair (Var c) (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_subborrow_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 51 (TWord 3) (TWord 3) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair (Var c) (Var a)) b)) (fun '((out, c_out)%core) => REST)).*)
 Notation "'subborrow_u51' ( c , a , b )" := (Op (SubWithGetBorrow 51 (TWord 0) (TWord 6) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair (Var c) (Var a)) (Var b))).
 Notation "'subborrow_u51' ( c , a , b )" := (Op (SubWithGetBorrow 51 (TWord 0) (TWord 0) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair (Var c) (Var a)) (Var b))).
 Notation "'subborrow_u51' ( c , a , b )" := (Op (SubWithGetBorrow 51 (TWord 0) (TWord 6) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair (Var c) (Var a)) (Var b))).
+Notation "'subborrow_u51' ( c , a , b )" := (Op (SubWithGetBorrow 51 (TWord 0) (TWord 0) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair (Var c) (Var a)) (Var b))).
 (*Notation "T0 out ; T1 c_out = '_subborrow_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 51 (TWord 0) (TWord 6) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair (Var c) (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 51 (TWord 0) (TWord 0) (TWord 6) (TWord 6) (TWord 0)) (Pair (Pair (Var c) (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 51 (TWord 0) (TWord 6) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair (Var c) (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_subborrow_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 51 (TWord 0) (TWord 0) (TWord 0) (TWord 6) (TWord 0)) (Pair (Pair (Var c) (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 Notation "'subborrow_u51' ( c , a , b )" := (Op (SubWithGetBorrow 51 (TWord 3) (TWord 6) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair (Var c) (Var a)) (Var b))).
 Notation "'subborrow_u51' ( c , a , b )" := (Op (SubWithGetBorrow 51 (TWord 3) (TWord 3) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair (Var c) (Var a)) (Var b))).
 Notation "'subborrow_u51' ( c , a , b )" := (Op (SubWithGetBorrow 51 (TWord 3) (TWord 6) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair (Var c) (Var a)) (Var b))).
+Notation "'subborrow_u51' ( c , a , b )" := (Op (SubWithGetBorrow 51 (TWord 3) (TWord 3) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair (Var c) (Var a)) (Var b))).
 (*Notation "T0 out ; T1 c_out = '_subborrow_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 51 (TWord 3) (TWord 6) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair (Var c) (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 51 (TWord 3) (TWord 3) (TWord 6) (TWord 6) (TWord 3)) (Pair (Pair (Var c) (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 (*Notation "T0 out ; T1 c_out = '_subborrow_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 51 (TWord 3) (TWord 6) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair (Var c) (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
+(*Notation "T0 out ; T1 c_out = '_subborrow_u51' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (SubWithGetBorrow 51 (TWord 3) (TWord 3) (TWord 3) (TWord 6) (TWord 3)) (Pair (Pair (Var c) (Var a)) (Var b))) (fun '((out, c_out)%core) => REST)).*)
 Notation "'mulx_u32' ( a , b )" := (Op (MulSplit 32 (TWord 5) (TWord 5) (TWord 5) (TWord 5)) (Pair a b)).
 (*Notation "T0 out ; T1 c_out = '_mulx_u32' ( a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (MulSplit 32 (TWord 5) (TWord 5) (TWord 5) (TWord 5)) (Pair a b)) (fun '((out, c_out)%core) => REST)).*)
 Notation "'mulx_u32' ( a , b )" := (Op (MulSplit 32 (TWord 5) (TWord 5) (TWord 5) (TWord 5)) (Pair a (Var b))).
-- 
cgit v1.2.3


From 4c0ee90c7d1dda0c7a3177fc64728385d48844ac Mon Sep 17 00:00:00 2001
From: Jason Gross <jgross@mit.edu>
Date: Thu, 29 Jun 2017 14:17:52 -0400
Subject: make display

---
 src/Specific/IntegrationTestMontgomeryP256_128Display.log   |  9 ++++-----
 .../IntegrationTestMontgomeryP256_128_AddDisplay.log        |  9 ++++-----
 .../IntegrationTestMontgomeryP256_128_OppDisplay.log        |  9 +++------
 .../IntegrationTestMontgomeryP256_128_SubDisplay.log        |  9 +++------
 .../NISTP256/AMD64/IntegrationTestMontgomeryP256Display.log | 13 ++++++-------
 .../AMD64/IntegrationTestMontgomeryP256_AddDisplay.log      | 13 ++++++-------
 .../AMD64/IntegrationTestMontgomeryP256_OppDisplay.log      | 13 +++++--------
 .../AMD64/IntegrationTestMontgomeryP256_SubDisplay.log      | 13 +++++--------
 8 files changed, 36 insertions(+), 52 deletions(-)

(limited to 'src')

diff --git a/src/Specific/IntegrationTestMontgomeryP256_128Display.log b/src/Specific/IntegrationTestMontgomeryP256_128Display.log
index ff714ff16..5a9182d47 100644
--- a/src/Specific/IntegrationTestMontgomeryP256_128Display.log
+++ b/src/Specific/IntegrationTestMontgomeryP256_128Display.log
@@ -32,10 +32,9 @@ Interp-η
  uint8_t x89 = x88 + x64;
  uint128_t x91, uint8_t x92 = subborrow_u128(0x0, x84, 0xffffffffffffffffffffffffL);
  uint128_t x94, uint8_t x95 = subborrow_u128(x92, x87, 0xffffffff000000010000000000000000L);
- ℤ x96 = Op (Syntax.Opp (Syntax.TWord 3) Syntax.TZ) (Return x95);
- uint128_t _, ℤ x99 = addcarryx_u128ℤ(0x0, x96, x89);
- uint128_t x100 = x99 == 0 ? x94 : x87;
- uint128_t x101 = x99 == 0 ? x91 : x84;
- return (x100, x101))
+ uint128_t _, uint8_t x98 = subborrow_u128(x95, x89, 0x0);
+ uint128_t x99 = x98 == 0 ? x94 : x87;
+ uint128_t x100 = x98 == 0 ? x91 : x84;
+ return (x99, x100))
 (x, x0)%core
      : word128 * word128 → word128 * word128 → ReturnType (uint128_t * uint128_t)
diff --git a/src/Specific/IntegrationTestMontgomeryP256_128_AddDisplay.log b/src/Specific/IntegrationTestMontgomeryP256_128_AddDisplay.log
index ea170fc85..3c1716a73 100644
--- a/src/Specific/IntegrationTestMontgomeryP256_128_AddDisplay.log
+++ b/src/Specific/IntegrationTestMontgomeryP256_128_AddDisplay.log
@@ -6,10 +6,9 @@ Interp-η
  uint128_t x12, uint8_t x13 = addcarryx_u128(x10, x4, x6);
  uint128_t x15, uint8_t x16 = subborrow_u128(0x0, x9, 0xffffffffffffffffffffffffL);
  uint128_t x18, uint8_t x19 = subborrow_u128(x16, x12, 0xffffffff000000010000000000000000L);
- ℤ x20 = Op (Syntax.Opp (Syntax.TWord 3) Syntax.TZ) (Return x19);
- uint128_t _, ℤ x23 = addcarryx_u128ℤ(0x0, x20, x13);
- uint128_t x24 = x23 == 0 ? x18 : x12;
- uint128_t x25 = x23 == 0 ? x15 : x9;
- return (x24, x25))
+ uint128_t _, uint8_t x22 = subborrow_u128(x19, x13, 0x0);
+ uint128_t x23 = x22 == 0 ? x18 : x12;
+ uint128_t x24 = x22 == 0 ? x15 : x9;
+ return (x23, x24))
 (x, x0)%core
      : word128 * word128 → word128 * word128 → ReturnType (uint128_t * uint128_t)
diff --git a/src/Specific/IntegrationTestMontgomeryP256_128_OppDisplay.log b/src/Specific/IntegrationTestMontgomeryP256_128_OppDisplay.log
index 4e8fe5a50..50c41e1af 100644
--- a/src/Specific/IntegrationTestMontgomeryP256_128_OppDisplay.log
+++ b/src/Specific/IntegrationTestMontgomeryP256_128_OppDisplay.log
@@ -6,12 +6,9 @@ Interp-η
  uint128_t x7, uint8_t x8 = subborrow_u128(x5, 0x0, x1);
  uint128_t x9 = (uint128_t) (x8 == 0 ? 0x0 : 0xffffffffffffffffffffffffffffffffL);
  uint128_t x10 = x9 & 0xffffffffffffffffffffffffL;
- uint128_t x12, uint8_t x13 = addcarryx_u128(0x0, x4, x10);
+ uint128_t x12, uint8_t x13 = subborrow_u128(0x0, x4, x10);
  uint128_t x14 = x9 & 0xffffffff000000010000000000000000L;
- uint256_t x15 = 0x100000000000000000000000000000000L * x8;
- ℤ x16 = Op (Syntax.Opp (Syntax.TWord 8) Syntax.TZ) (Return x15);
- uint128_t x18, ℤ _ = addcarryx_u128ℤ(x7, x16, x14);
- uint128_t x21, uint8_t _ = addcarryx_u128(0x0, x13, x18);
- (Return x21, Return x12))
+ uint128_t x16, uint8_t _ = subborrow_u128(x13, x7, x14);
+ (Return x16, Return x12))
 x
      : word128 * word128 → ReturnType (uint128_t * uint128_t)
diff --git a/src/Specific/IntegrationTestMontgomeryP256_128_SubDisplay.log b/src/Specific/IntegrationTestMontgomeryP256_128_SubDisplay.log
index 576f0c6be..07579501c 100644
--- a/src/Specific/IntegrationTestMontgomeryP256_128_SubDisplay.log
+++ b/src/Specific/IntegrationTestMontgomeryP256_128_SubDisplay.log
@@ -6,12 +6,9 @@ Interp-η
  uint128_t x12, uint8_t x13 = subborrow_u128(x10, x4, x6);
  uint128_t x14 = (uint128_t) (x13 == 0 ? 0x0 : 0xffffffffffffffffffffffffffffffffL);
  uint128_t x15 = x14 & 0xffffffffffffffffffffffffL;
- uint128_t x17, uint8_t x18 = addcarryx_u128(0x0, x9, x15);
+ uint128_t x17, uint8_t x18 = subborrow_u128(0x0, x9, x15);
  uint128_t x19 = x14 & 0xffffffff000000010000000000000000L;
- uint256_t x20 = 0x100000000000000000000000000000000L * x13;
- ℤ x21 = Op (Syntax.Opp (Syntax.TWord 8) Syntax.TZ) (Return x20);
- uint128_t x23, ℤ _ = addcarryx_u128ℤ(x12, x21, x19);
- uint128_t x26, uint8_t _ = addcarryx_u128(0x0, x18, x23);
- (Return x26, Return x17))
+ uint128_t x21, uint8_t _ = subborrow_u128(x18, x12, x19);
+ (Return x21, Return x17))
 (x, x0)%core
      : word128 * word128 → word128 * word128 → ReturnType (uint128_t * uint128_t)
diff --git a/src/Specific/NISTP256/AMD64/IntegrationTestMontgomeryP256Display.log b/src/Specific/NISTP256/AMD64/IntegrationTestMontgomeryP256Display.log
index 3c47f3fc9..1dc1b7ba3 100644
--- a/src/Specific/NISTP256/AMD64/IntegrationTestMontgomeryP256Display.log
+++ b/src/Specific/NISTP256/AMD64/IntegrationTestMontgomeryP256Display.log
@@ -104,12 +104,11 @@ Interp-η
  uint64_t x308, uint8_t x309 = subborrow_u64(x306, x295, 0xffffffff);
  uint64_t x311, uint8_t x312 = subborrow_u64(x309, x298, 0x0);
  uint64_t x314, uint8_t x315 = subborrow_u64(x312, x301, 0xffffffff00000001L);
- ℤ x316 = Op (Syntax.Opp (Syntax.TWord 3) Syntax.TZ) (Return x315);
- uint64_t _, ℤ x319 = addcarryx_u64ℤ(0x0, x316, x303);
- uint64_t x320 = x319 == 0 ? x314 : x301;
- uint64_t x321 = x319 == 0 ? x311 : x298;
- uint64_t x322 = x319 == 0 ? x308 : x295;
- uint64_t x323 = x319 == 0 ? x305 : x292;
- return (x320, x321, x322, x323))
+ uint64_t _, uint8_t x318 = subborrow_u64(x315, x303, 0x0);
+ uint64_t x319 = x318 == 0 ? x314 : x301;
+ uint64_t x320 = x318 == 0 ? x311 : x298;
+ uint64_t x321 = x318 == 0 ? x308 : x295;
+ uint64_t x322 = x318 == 0 ? x305 : x292;
+ return (x319, x320, x321, x322))
 (x, x0)%core
      : word64 * word64 * word64 * word64 → word64 * word64 * word64 * word64 → ReturnType (uint64_t * uint64_t * uint64_t * uint64_t)
diff --git a/src/Specific/NISTP256/AMD64/IntegrationTestMontgomeryP256_AddDisplay.log b/src/Specific/NISTP256/AMD64/IntegrationTestMontgomeryP256_AddDisplay.log
index 0f46e27f6..e6498cf83 100644
--- a/src/Specific/NISTP256/AMD64/IntegrationTestMontgomeryP256_AddDisplay.log
+++ b/src/Specific/NISTP256/AMD64/IntegrationTestMontgomeryP256_AddDisplay.log
@@ -10,12 +10,11 @@ Interp-η
  uint64_t x32, uint8_t x33 = subborrow_u64(x30, x20, 0xffffffff);
  uint64_t x35, uint8_t x36 = subborrow_u64(x33, x23, 0x0);
  uint64_t x38, uint8_t x39 = subborrow_u64(x36, x26, 0xffffffff00000001L);
- ℤ x40 = Op (Syntax.Opp (Syntax.TWord 3) Syntax.TZ) (Return x39);
- uint64_t _, ℤ x43 = addcarryx_u64ℤ(0x0, x40, x27);
- uint64_t x44 = x43 == 0 ? x38 : x26;
- uint64_t x45 = x43 == 0 ? x35 : x23;
- uint64_t x46 = x43 == 0 ? x32 : x20;
- uint64_t x47 = x43 == 0 ? x29 : x17;
- return (x44, x45, x46, x47))
+ uint64_t _, uint8_t x42 = subborrow_u64(x39, x27, 0x0);
+ uint64_t x43 = x42 == 0 ? x38 : x26;
+ uint64_t x44 = x42 == 0 ? x35 : x23;
+ uint64_t x45 = x42 == 0 ? x32 : x20;
+ uint64_t x46 = x42 == 0 ? x29 : x17;
+ return (x43, x44, x45, x46))
 (x, x0)%core
      : word64 * word64 * word64 * word64 → word64 * word64 * word64 * word64 → ReturnType (uint64_t * uint64_t * uint64_t * uint64_t)
diff --git a/src/Specific/NISTP256/AMD64/IntegrationTestMontgomeryP256_OppDisplay.log b/src/Specific/NISTP256/AMD64/IntegrationTestMontgomeryP256_OppDisplay.log
index 0b94a81ce..b76a34a56 100644
--- a/src/Specific/NISTP256/AMD64/IntegrationTestMontgomeryP256_OppDisplay.log
+++ b/src/Specific/NISTP256/AMD64/IntegrationTestMontgomeryP256_OppDisplay.log
@@ -8,15 +8,12 @@ Interp-η
  uint64_t x17, uint8_t x18 = subborrow_u64(x15, 0x0, x5);
  uint64_t x19 = (uint64_t) (x18 == 0 ? 0x0 : 0xffffffffffffffffL);
  uint64_t x20 = x19 & 0xffffffffffffffffL;
- uint64_t x22, uint8_t x23 = addcarryx_u64(0x0, x8, x20);
+ uint64_t x22, uint8_t x23 = subborrow_u64(0x0, x8, x20);
  uint64_t x24 = x19 & 0xffffffff;
- uint64_t x26, uint8_t x27 = addcarryx_u64(x23, x11, x24);
- uint64_t x29, uint8_t x30 = addcarryx_u64(x27, x14, 0x0);
+ uint64_t x26, uint8_t x27 = subborrow_u64(x23, x11, x24);
+ uint64_t x29, uint8_t x30 = subborrow_u64(x27, x14, 0x0);
  uint64_t x31 = x19 & 0xffffffff00000001L;
- uint128_t x32 = 0x10000000000000000L * x18;
- ℤ x33 = Op (Syntax.Opp (Syntax.TWord 7) Syntax.TZ) (Return x32);
- uint64_t x35, ℤ _ = addcarryx_u64ℤ(x17, x33, x31);
- uint64_t x38, uint8_t _ = addcarryx_u64(0x0, x30, x35);
- (Return x38, Return x29, Return x26, Return x22))
+ uint64_t x33, uint8_t _ = subborrow_u64(x30, x17, x31);
+ (Return x33, Return x29, Return x26, Return x22))
 x
      : word64 * word64 * word64 * word64 → ReturnType (uint64_t * uint64_t * uint64_t * uint64_t)
diff --git a/src/Specific/NISTP256/AMD64/IntegrationTestMontgomeryP256_SubDisplay.log b/src/Specific/NISTP256/AMD64/IntegrationTestMontgomeryP256_SubDisplay.log
index 9b301c678..de068350b 100644
--- a/src/Specific/NISTP256/AMD64/IntegrationTestMontgomeryP256_SubDisplay.log
+++ b/src/Specific/NISTP256/AMD64/IntegrationTestMontgomeryP256_SubDisplay.log
@@ -8,15 +8,12 @@ Interp-η
  uint64_t x26, uint8_t x27 = subborrow_u64(x24, x8, x14);
  uint64_t x28 = (uint64_t) (x27 == 0 ? 0x0 : 0xffffffffffffffffL);
  uint64_t x29 = x28 & 0xffffffffffffffffL;
- uint64_t x31, uint8_t x32 = addcarryx_u64(0x0, x17, x29);
+ uint64_t x31, uint8_t x32 = subborrow_u64(0x0, x17, x29);
  uint64_t x33 = x28 & 0xffffffff;
- uint64_t x35, uint8_t x36 = addcarryx_u64(x32, x20, x33);
- uint64_t x38, uint8_t x39 = addcarryx_u64(x36, x23, 0x0);
+ uint64_t x35, uint8_t x36 = subborrow_u64(x32, x20, x33);
+ uint64_t x38, uint8_t x39 = subborrow_u64(x36, x23, 0x0);
  uint64_t x40 = x28 & 0xffffffff00000001L;
- uint128_t x41 = 0x10000000000000000L * x27;
- ℤ x42 = Op (Syntax.Opp (Syntax.TWord 7) Syntax.TZ) (Return x41);
- uint64_t x44, ℤ _ = addcarryx_u64ℤ(x26, x42, x40);
- uint64_t x47, uint8_t _ = addcarryx_u64(0x0, x39, x44);
- (Return x47, Return x38, Return x35, Return x31))
+ uint64_t x42, uint8_t _ = subborrow_u64(x39, x26, x40);
+ (Return x42, Return x38, Return x35, Return x31))
 (x, x0)%core
      : word64 * word64 * word64 * word64 → word64 * word64 * word64 * word64 → ReturnType (uint64_t * uint64_t * uint64_t * uint64_t)
-- 
cgit v1.2.3


From e60833730f6f3f82b50485ba4405bc45f7fabc3d Mon Sep 17 00:00:00 2001
From: Jason Gross <jgross@mit.edu>
Date: Thu, 29 Jun 2017 14:41:55 -0400
Subject: Fix comment-in-string issues

---
 src/Compilers/Z/CNotations.v | 22 +++++++++++-----------
 1 file changed, 11 insertions(+), 11 deletions(-)

(limited to 'src')

diff --git a/src/Compilers/Z/CNotations.v b/src/Compilers/Z/CNotations.v
index 335d4ad4b..0c4838fdf 100644
--- a/src/Compilers/Z/CNotations.v
+++ b/src/Compilers/Z/CNotations.v
@@ -93,10 +93,10 @@ Notation "T x = A ; 'return' ( b0 , b1 , .. , b2 )" := (LetIn (tx:=T) A (fun x =
 Notation "T x = A ; 'return' ( b0 , b1 , .. , b2 )" := (LetIn (tx:=T) A (fun x => Pair .. (Pair (Var b0) (Var b1)) .. (Var b2))) : expr_scope.
 Notation "T0 x , T1 y = A ; b" := (LetIn (tx:=Prod T0 T1) A (fun '((x, y)%core) => b)) : expr_scope.
 Notation "T0 x , T1 y = A ; 'return' b" := (LetIn (tx:=Prod T0 T1) A (fun '((x, y)%core) => Var b)) : expr_scope.
-(*Notation "T0 x , T1 y = A ; 'return' ( b0 , b1 , .. , b2 )" := (LetIn (tx:=Prod T0 T1) A (fun '((x, y)%core) => (Pair .. (Pair b0%expr b1%expr) .. b2%expr))) : expr_scope.*) (* Error: Unsupported construction in recursive notations., https://coq.inria.fr/bugs/show_bug.cgi?id=5523 *)
-(*Notation "T0 x , T1 y = A ; 'return' ( b0 , b1 , .. , b2 )" := (LetIn (tx:=Prod T0 T1) A (fun '((x, y)%core) => (Pair .. (Pair (Var b0) (Var b1)) .. (Var b2)))) : expr_scope.*) (* Error: Unsupported construction in recursive notations., https://coq.inria.fr/bugs/show_bug.cgi?id=5523 *)
+(""" + r"""*Notation "T0 x , T1 y = A ; 'return' ( b0 , b1 , .. , b2 )" := (LetIn (tx:=Prod T0 T1) A (fun '((x, y)%core) => (Pair .. (Pair b0%expr b1%expr) .. b2%expr))) : expr_scope.*""" + r""") (""" + r"""* Error: Unsupported construction in recursive notations., https://coq.inria.fr/bugs/show_bug.cgi?id=5523 *""" + r""")
+(""" + r"""*Notation "T0 x , T1 y = A ; 'return' ( b0 , b1 , .. , b2 )" := (LetIn (tx:=Prod T0 T1) A (fun '((x, y)%core) => (Pair .. (Pair (Var b0) (Var b1)) .. (Var b2)))) : expr_scope.*""" + r""") (""" + r"""* Error: Unsupported construction in recursive notations., https://coq.inria.fr/bugs/show_bug.cgi?id=5523 *""" + r""")
 
-(* for now, handle with
+(""" + r"""* for now, handle with
 <<
 sed s':^\([^,]*\) \([^, ]*\)\(\s*\),\(.*\)\(addcarryx.*\))\([; ]*\)$:\1 \2\3;\4_\5, \&\2)\6:'
 sed s':^\([^,]*\) \([^, ]*\)\(\s*\),\(.*\)\(subborrow.*\))\([; ]*\)$:\1 \2\3;\4_\5, \&\2)\6:'
@@ -109,15 +109,15 @@ Reserved Notation "T0 out ; T1 c_out = '_addcarryx_u32' ( c_in , a , b , & out )
  (at level 200, REST at level 200, only printing format "T0  out ; '//' T1  c_out  =  '_addcarryx_u64' ( c_in ,  a ,  b ,  & out ) ; '//' REST").
 Reserved Notation "T0 out ; T1 c_out = '_addcarryx_u64' ( c_in , a , b , & out ) ; REST"
  (at level 200, REST at level 200, only printing format "T0  out ; '//' T1  c_out  =  '_addcarryx_u64' ( c_in ,  a ,  b ,  & out ) ; '//' REST").
->> *)
+>> *""" + r""")
 Reserved Notation "'addcarryx_u32' ( c , a , b )" (format "'addcarryx_u32' ( c ,  a ,  b )").
 Reserved Notation "'addcarryx_u64' ( c , a , b )" (format "'addcarryx_u64' ( c ,  a ,  b )").
 Reserved Notation "'addcarryx_u128' ( c , a , b )" (format "'addcarryx_u128' ( c ,  a ,  b )").
-Reserved Notation "'addcarryx_u51' ( c , a , b )" (format "'addcarryx_u51' ( c ,  a ,  b )"). (* temporary for testing *)
+Reserved Notation "'addcarryx_u51' ( c , a , b )" (format "'addcarryx_u51' ( c ,  a ,  b )"). (""" + r"""* temporary for testing *""" + r""")
 Reserved Notation "'subborrow_u32' ( c , a , b )" (format "'subborrow_u32' ( c ,  a ,  b )").
 Reserved Notation "'subborrow_u64' ( c , a , b )" (format "'subborrow_u64' ( c ,  a ,  b )").
 Reserved Notation "'subborrow_u128' ( c , a , b )" (format "'subborrow_u128' ( c ,  a ,  b )").
-Reserved Notation "'subborrow_u51' ( c , a , b )" (format "'subborrow_u51' ( c ,  a ,  b )"). (* temporary for testing *)
+Reserved Notation "'subborrow_u51' ( c , a , b )" (format "'subborrow_u51' ( c ,  a ,  b )"). (""" + r"""* temporary for testing *""" + r""")
 Reserved Notation "'mulx_u32' ( a , b )" (format "'mulx_u32' ( a ,  b )").
 Reserved Notation "'mulx_u64' ( a , b )" (format "'mulx_u64' ( a ,  b )").
 Reserved Notation "'mulx_u128' ( a , b )" (format "'mulx_u128' ( a ,  b )").
@@ -125,21 +125,21 @@ Reserved Notation "'mulx_u128' ( a , b )" (format "'mulx_u128' ( a ,  b )").
 Reserved Notation "'addcarryx_u32ℤ' ( c , a , b )" (format "'addcarryx_u32ℤ' ( c ,  a ,  b )").
 Reserved Notation "'addcarryx_u64ℤ' ( c , a , b )" (format "'addcarryx_u64ℤ' ( c ,  a ,  b )").
 Reserved Notation "'addcarryx_u128ℤ' ( c , a , b )" (format "'addcarryx_u128ℤ' ( c ,  a ,  b )").
-Reserved Notation "'addcarryx_u51ℤ' ( c , a , b )" (format "'addcarryx_u51ℤ' ( c ,  a ,  b )"). (* temporary for testing *)
+Reserved Notation "'addcarryx_u51ℤ' ( c , a , b )" (format "'addcarryx_u51ℤ' ( c ,  a ,  b )"). """ + r"""(* temporary for testing *""" + r""")
 Reserved Notation "'subborrow_u32ℤ' ( c , a , b )" (format "'subborrow_u32ℤ' ( c ,  a ,  b )").
 Reserved Notation "'subborrow_u64ℤ' ( c , a , b )" (format "'subborrow_u64ℤ' ( c ,  a ,  b )").
 Reserved Notation "'subborrow_u128ℤ' ( c , a , b )" (format "'subborrow_u128ℤ' ( c ,  a ,  b )").
-Reserved Notation "'subborrow_u51ℤ' ( c , a , b )" (format "'subborrow_u51ℤ' ( c ,  a ,  b )"). (* temporary for testing *)
+Reserved Notation "'subborrow_u51ℤ' ( c , a , b )" (format "'subborrow_u51ℤ' ( c ,  a ,  b )"). (""" + r"""* temporary for testing *""" + r""")
 Reserved Notation "'mulx_u32ℤ' ( a , b )" (format "'mulx_u32ℤ' ( a ,  b )").
 Reserved Notation "'mulx_u64ℤ' ( a , b )" (format "'mulx_u64ℤ' ( a ,  b )").
 Reserved Notation "'mulx_u128ℤ' ( a , b )" (format "'mulx_u128ℤ' ( a ,  b )").
 
-(* python:
+(""" + r"""* python:
 <<""")
 
 print(open(__file__).read())
 
-print(r">> *)")
+print('>> *' + ')')
 
 def log2_up(x):
     return int(math.ceil(math.log(x, 2)))
@@ -285,7 +285,7 @@ for opn, op in (('addcarryx', 'AddWithGetCarry'), ('subborrow', 'SubWithGetBorro
                     b = ('b' if not v2 else '(Var b)')
                     for lgwordsz_small in (0, 3):
                         for notation_string in ('Notation "\'%s_u%d\' ( c , a , b )" := (Op (%s %d (TWord %d) (TWord %d) (TWord %d) (TWord %d) (TWord %d)) (Pair (Pair %s %s) %s)).',
-                                                '(*Notation "T0 out ; T1 c_out = \'_%s_u%d\' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (%s %d (TWord %d) (TWord %d) (TWord %d) (TWord %d) (TWord %d)) (Pair (Pair %s %s) %s)) (fun \'((out, c_out)%%core) => REST)).*)'):
+                                                ('(' + '*Notation "T0 out ; T1 c_out = \'_%s_u%d\' ( c , a , b , & out ) ; REST" := (LetIn (tx:=Prod T0 T1) (Op (%s %d (TWord %d) (TWord %d) (TWord %d) (TWord %d) (TWord %d)) (Pair (Pair %s %s) %s)) (fun \'((out, c_out)%%core) => REST)).*' + ')')):
                             print(notation_string % (opn, wordsz, op, wordsz, lgwordsz_small, lgwordsz, lgwordsz, lgwordsz, lgwordsz_small, c, a, b))
                             print(notation_string % (opn, wordsz, op, wordsz, lgwordsz_small, lgwordsz_small, lgwordsz, lgwordsz, lgwordsz_small, c, a, b))
                             print(notation_string % (opn, wordsz, op, wordsz, lgwordsz_small, lgwordsz, lgwordsz_small, lgwordsz, lgwordsz_small, c, a, b))
-- 
cgit v1.2.3


From 90563fe2f8e09dec5fefcab82519f91dc784aba5 Mon Sep 17 00:00:00 2001
From: Jason Gross <jgross@mit.edu>
Date: Thu, 29 Jun 2017 14:45:30 -0400
Subject: Remove a [Check]

---
 src/Compilers/CommonSubexpressionEliminationInterp.v | 2 --
 1 file changed, 2 deletions(-)

(limited to 'src')

diff --git a/src/Compilers/CommonSubexpressionEliminationInterp.v b/src/Compilers/CommonSubexpressionEliminationInterp.v
index 0d7fa1e25..2152b5466 100644
--- a/src/Compilers/CommonSubexpressionEliminationInterp.v
+++ b/src/Compilers/CommonSubexpressionEliminationInterp.v
@@ -134,8 +134,6 @@ Section symbolic.
 
 
 
-Check @symbolize_exprf.
-
   Local Arguments lookupb : simpl never.
   Local Arguments extendb : simpl never.
   Lemma interpf_csef G t e1 e2
-- 
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