Move most notation level declarations into Util

This reveals and prevents notation clashes.

Notable breakage:
- `x {{ y }}` breaks `Context {forall x, {P x} + {~P x}}.`
  (@jadephilipoom)
- `x [[ y ]]` breaks `destruct x as [[a]|[b]].` (@jadephilipoom)
- `O :( A , B ): :?: L ::: R` breaks `((1):nat)` and `constr:(nat)`
  (@varomodt)

After    | File Name                                         | Before   || Change
------------------------------------------------------------------------------------
3m16.07s | Total                                             | 3m23.63s || -0m07.55s
------------------------------------------------------------------------------------
0m16.90s | ModularArithmetic/ModularBaseSystemProofs         | 0m19.02s || -0m02.12s
0m03.29s | ModularArithmetic/ModularBaseSystemOpt            | 0m05.30s || -0m02.00s
0m12.04s | Experiments/SpecEd25519                           | 0m13.89s || -0m01.85s
0m36.02s | CompleteEdwardsCurve/ExtendedCoordinates          | 0m36.12s || -0m00.09s
0m34.48s | Specific/GF25519                                  | 0m34.27s || +0m00.20s
0m15.62s | CompleteEdwardsCurve/CompleteEdwardsCurveTheorems | 0m15.76s || -0m00.14s
0m07.36s | Specific/GF1305                                   | 0m07.34s || +0m00.02s
0m06.64s | Algebra                                           | 0m06.14s || +0m00.50s
0m05.12s | WeierstrassCurve/Pre                              | 0m05.09s || +0m00.03s
0m04.58s | ModularArithmetic/Tutorial                        | 0m03.83s || +0m00.75s
0m04.46s | BaseSystemProofs                                  | 0m04.33s || +0m00.12s
0m04.26s | ModularArithmetic/Pow2BaseProofs                  | 0m05.16s || -0m00.90s
0m03.91s | CompleteEdwardsCurve/Pre                          | 0m04.62s || -0m00.71s
0m02.75s | Assembly/State                                    | 0m03.12s || -0m00.37s
0m02.55s | Experiments/EdDSARefinement                       | 0m01.85s || +0m00.69s
0m02.46s | Util/ZUtil                                        | 0m02.45s || +0m00.00s
0m01.86s | Assembly/Wordize                                  | 0m02.02s || -0m00.15s
0m01.68s | ModularArithmetic/ModularArithmeticTheorems       | 0m01.68s || +0m00.00s
0m01.67s | ModularArithmetic/PrimeFieldTheorems              | 0m01.96s || -0m00.29s
0m01.50s | Encoding/PointEncodingPre                         | 0m02.20s || -0m00.70s
0m01.46s | ModularArithmetic/BarrettReduction/Z              | 0m01.02s || +0m00.43s
0m01.26s | BaseSystem                                        | 0m01.21s || +0m00.05s
0m01.24s | Assembly/Pseudize                                 | 0m01.22s || +0m00.02s
0m01.20s | ModularArithmetic/ExtendedBaseVector              | 0m01.86s || -0m00.66s
0m01.04s | Util/IterAssocOp                                  | 0m00.74s || +0m00.30s
0m00.96s | ModularArithmetic/ExtPow2BaseMulProofs            | 0m00.67s || +0m00.28s
0m00.96s | Assembly/Pipeline                                 | 0m00.65s || +0m00.30s
0m00.93s | Experiments/DerivationsOptionRectLetInEncoding    | 0m00.98s || -0m00.04s
0m00.93s | ModularArithmetic/ModularBaseSystemField          | 0m00.95s || -0m00.01s
0m00.92s | Util/NumTheoryUtil                                | 0m01.19s || -0m00.26s
0m00.90s | ModularArithmetic/ModularBaseSystemListProofs     | 0m00.89s || +0m00.01s
0m00.82s | ModularArithmetic/PseudoMersenneBaseParamProofs   | 0m00.95s || -0m00.13s
0m00.81s | Assembly/QhasmEvalCommon                          | 0m00.86s || -0m00.04s
0m00.80s | Assembly/StringConversion                         | 0m00.60s || +0m00.20s
0m00.79s | Assembly/Qhasm                                    | 0m00.54s || +0m00.25s
0m00.73s | Assembly/Pseudo                                   | 0m00.98s || -0m00.25s
0m00.72s | Util/AdditionChainExponentiation                  | 0m00.92s || -0m00.20s
0m00.69s | Experiments/SpecificCurve25519                    | 0m00.72s || -0m00.03s
0m00.65s | Spec/ModularWordEncoding                          | 0m00.85s || -0m00.19s
0m00.65s | ModularArithmetic/ModularBaseSystemList           | 0m00.68s || -0m00.03s
0m00.65s | Assembly/PseudoConversion                         | 0m00.67s || -0m00.02s
0m00.64s | Encoding/ModularWordEncodingPre                   | 0m00.62s || +0m00.02s
0m00.64s | Spec/EdDSA                                        | 0m00.93s || -0m00.29s
0m00.64s | Testbit                                           | 0m00.94s || -0m00.29s
0m00.63s | Encoding/ModularWordEncodingTheorems              | 0m00.66s || -0m00.03s
0m00.62s | Assembly/AlmostQhasm                              | 0m00.49s || +0m00.13s
0m00.59s | ModularArithmetic/ModularBaseSystem               | 0m00.61s || -0m00.02s
0m00.49s | Spec/WeierstrassCurve                             | 0m00.43s || +0m00.06s
0m00.49s | Assembly/QhasmUtil                                | 0m00.51s || -0m00.02s
0m00.49s | ModularArithmetic/Pre                             | 0m00.47s || +0m00.02s
0m00.47s | Assembly/Vectorize                                | 0m00.51s || -0m00.04s
0m00.46s | Assembly/AlmostConversion                         | 0m00.44s || +0m00.02s
0m00.42s | ModularArithmetic/Pow2Base                        | 0m00.42s || +0m00.00s
0m00.41s | ModularArithmetic/PseudoMersenneBaseParams        | 0m00.45s || -0m00.04s
0m00.41s | Spec/ModularArithmetic                            | 0m00.41s || +0m00.00s
0m00.39s | Spec/CompleteEdwardsCurve                         | 0m00.41s || -0m00.01s
0m00.03s | Util/Notations                                    | 0m00.03s || +0m00.00s

2 files changed, 10 insertions, 10 deletions

diff --git a/src/CompleteEdwardsCurve/CompleteEdwardsCurveTheorems.v b/src/CompleteEdwardsCurve/CompleteEdwardsCurveTheorems.v
index dbfdb023e..716d72b3e 100644
--- a/src/CompleteEdwardsCurve/CompleteEdwardsCurveTheorems.v
+++ b/src/CompleteEdwardsCurve/CompleteEdwardsCurveTheorems.v
@@ -34,7 +34,7 @@ Module E.
                let x := fresh "x" p in
                let y := fresh "y" p in
                let pf := fresh "pf" p in
-               destruct p as [[x y] pf]
+               destruct p as [ [x y] pf]
              end.
 
     Local Obligation Tactic := intros; destruct_points; simpl; super_nsatz.
@@ -155,7 +155,7 @@ Module E.
     Program Definition ref_phi (P:Fpoint) : Kpoint := exist _ (
       let (x, y) := coordinates P in (phi x, phi y)) _.
     Next Obligation.
-      destruct P as [[? ?] ?]; simpl.
+      destruct P as [ [? ?] ?]; simpl.
       rewrite_strat bottomup hints field_homomorphism.
       eauto using is_homomorphism_phi_proper; assumption.
     Qed.
@@ -171,7 +171,7 @@ Module E.
              | |- _ => intro
              | |-  _ /\ _ => split
              | [H: _ /\ _ |- _ ] => destruct H
-             | [p: point |- _ ] => destruct p as [[??]?]
+             | [p: point |- _ ] => destruct p as [ [??]?]
              | |- context[point_phi] => setoid_rewrite point_phi_correct
              | |- _ => progress cbv [fst snd coordinates proj1_sig eq fieldwise fieldwise' add zero opp ref_phi] in *
              | |- Keq ?x ?x => reflexivity
diff --git a/src/CompleteEdwardsCurve/ExtendedCoordinates.v b/src/CompleteEdwardsCurve/ExtendedCoordinates.v
index ac3523889..6b28173e3 100644
--- a/src/CompleteEdwardsCurve/ExtendedCoordinates.v
+++ b/src/CompleteEdwardsCurve/ExtendedCoordinates.v
@@ -39,8 +39,8 @@ Module Extended.
              | |- Proper _ _ => intro
              | _ => progress intros
              | [ H: _ /\ _ |- _ ] => destruct H
-             | [ p:E.point |- _ ] => destruct p as [[??]?]
-             | [ p:point |- _ ] => destruct p as [[[[??]?]?]?]
+             | [ p:E.point |- _ ] => destruct p as [ [??] ? ]
+             | [ p:point |- _ ] => destruct p as [ [ [ [??] ? ] ? ] ? ]
              | _ => progress autounfold with bash in *
              | |- _ /\ _ => split
              | _ => solve [neq01]
@@ -98,7 +98,7 @@ Module Extended.
         let (x, y) := E.coordinates (E.add (to_twisted P) (to_twisted Q)) in
         (fieldwise (n:=2) Feq) (x, y) (X/Z, Y/Z).
       Proof.
-        destruct P as [[[[]?]?][HP []]]; destruct Q as [[[[]?]?][HQ []]].
+        destruct P as [ [ [ [ ] ? ] ? ] [ HP [ ] ] ]; destruct Q as [ [ [ [ ] ? ] ? ] [ HQ [ ] ] ].
         pose proof edwardsAddCompletePlus (a_nonzero:=E.nonzero_a)(a_square:=E.square_a)(d_nonsquare:=E.nonsquare_d)(char_gt_2:=E.char_gt_2) _ _ _ _ HP HQ.
         pose proof edwardsAddCompleteMinus (a_nonzero:=E.nonzero_a)(a_square:=E.square_a)(d_nonsquare:=E.nonsquare_d)(char_gt_2:=E.char_gt_2) _ _ _ _ HP HQ.
         bash.
@@ -110,7 +110,7 @@ Module Extended.
         intros.
         pose proof (add_coordinates_correct P Q) as Hrep.
         pose proof Pre.unifiedAdd'_onCurve(a_nonzero:=E.nonzero_a)(a_square:=E.square_a)(d_nonsquare:=E.nonsquare_d)(char_gt_2:=E.char_gt_2) (E.coordinates (to_twisted P)) (E.coordinates (to_twisted Q)) as Hon.
-        destruct P as [[[[]?]?][HP []]]; destruct Q as [[[[]?]?][HQ []]].
+        destruct P as [ [ [ [ ] ? ] ? ] [ HP [ ] ] ]; destruct Q as [ [ [ [ ] ? ] ? ] [ HQ [ ] ] ].
         pose proof edwardsAddCompletePlus (a_nonzero:=E.nonzero_a)(a_square:=E.square_a)(d_nonsquare:=E.nonsquare_d)(char_gt_2:=E.char_gt_2) _ _ _ _ HP HQ as Hnz1.
         pose proof edwardsAddCompleteMinus (a_nonzero:=E.nonzero_a)(a_square:=E.square_a)(d_nonsquare:=E.nonsquare_d)(char_gt_2:=E.char_gt_2) _ _ _ _ HP HQ as Hnz2.
         autounfold with bash in *; simpl in *.
@@ -122,7 +122,7 @@ Module Extended.
       Lemma to_twisted_add P Q : E.eq (to_twisted (add P Q)) (E.add (to_twisted P) (to_twisted Q)).
       Proof.
         pose proof (add_coordinates_correct P Q) as Hrep.
-        destruct P as [[[[]?]?][HP []]]; destruct Q as [[[[]?]?][HQ []]].
+        destruct P as [ [ [ [ ] ? ] ? ] [ HP [ ] ] ]; destruct Q as [ [ [ [ ] ? ] ? ] [ HQ [ ] ] ].
         autounfold with bash in *; simpl in *.
         destruct Hrep as [HA HB]. rewrite <-!HA, <-!HB; clear HA HB.
         split; reflexivity.
@@ -230,7 +230,7 @@ Module Extended.
     Program Definition ref_phi (P:Fpoint) : Kpoint := exist _ (
       let '(X, Y, Z, T) := coordinates P in (phi X, phi Y, phi Z, phi T)) _.
     Next Obligation.
-      destruct P as [[[[] ?] ?] [? [? ?]]]; unfold onCurve in *; simpl.
+      destruct P as [ [ [ [ ] ? ] ? ] [ ? [ ? ? ] ] ]; unfold onCurve in *; simpl.
       (rewrite_strat bottomup hints field_homomorphism); try assumption.
       eauto 10 using is_homomorphism_phi_proper, phi_nonzero.
     Qed.
@@ -246,7 +246,7 @@ Module Extended.
              | |- _ => intro
              | |-  _ /\ _ => split
              | [H: _ /\ _ |- _ ] => destruct H
-             | [p: point |- _ ] => destruct p as [[[[] ?] ?] [? [? ?]]]
+             | [p: point |- _ ] => destruct p as [ [ [ [ ] ? ] ? ] [ ? [ ? ? ] ] ]
              | |- context[point_phi] => setoid_rewrite point_phi_correct
              | |- _ => progress cbv [fst snd coordinates proj1_sig eq to_twisted E.eq E.coordinates fieldwise fieldwise' add add_coordinates ref_phi] in *
              | |- Keq ?x ?x => reflexivity