From 8ff2de8c01b3ba3563517627b1f5c9eb2c4bcb77 Mon Sep 17 00:00:00 2001
From: msozeau <msozeau@85f007b7-540e-0410-9357-904b9bb8a0f7>
Date: Wed, 14 Mar 2012 09:53:06 +0000
Subject: Final part of moving Program code inside the main code. Adapted
 add_definition/fixpoint and parsing of the "Program" prefix.

git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@15036 85f007b7-540e-0410-9357-904b9bb8a0f7
---
 theories/Program/Subset.v |  6 +++---
 theories/Program/Wf.v     | 12 ++++++------
 2 files changed, 9 insertions(+), 9 deletions(-)

(limited to 'theories/Program')

diff --git a/theories/Program/Subset.v b/theories/Program/Subset.v
index ca4002d7f..dda0ed68d 100644
--- a/theories/Program/Subset.v
+++ b/theories/Program/Subset.v
@@ -79,14 +79,14 @@ Qed.
 (* Somewhat trivial definition, but not unfolded automatically hence we can match on [match_eq ?A ?B ?x ?f]
    in tactics. *)
 
-Definition match_eq (A B : Type) (x : A) (fn : forall (y : A | y = x), B) : B :=
+Definition match_eq (A B : Type) (x : A) (fn : {y : A | y = x} -> B) : B :=
   fn (exist _ x eq_refl).
 
 (* This is what we want to be able to do: replace the originaly matched object by a new,
    propositionally equal one. If [fn] works on [x] it should work on any [y | y = x]. *)
 
-Lemma match_eq_rewrite : forall (A B : Type) (x : A) (fn : forall (y : A | y = x), B)
-  (y : A | y = x),
+Lemma match_eq_rewrite : forall (A B : Type) (x : A) (fn : {y : A | y = x} -> B)
+  (y : {y:A | y = x}),
   match_eq A B x fn = fn y.
 Proof.
   intros.
diff --git a/theories/Program/Wf.v b/theories/Program/Wf.v
index a823aedd3..ee0a7451b 100644
--- a/theories/Program/Wf.v
+++ b/theories/Program/Wf.v
@@ -35,11 +35,11 @@ Section Well_founded.
   Hypothesis
     F_ext :
     forall (x:A) (f g:forall y:{y:A | R y x}, P (`y)),
-      (forall (y : A | R y x), f y = g y) -> F_sub x f = F_sub x g.
+      (forall y:{y : A | R y x}, f y = g y) -> F_sub x f = F_sub x g.
 
   Lemma Fix_F_eq :
     forall (x:A) (r:Acc R x),
-      F_sub x (fun (y:A|R y x) => Fix_F_sub (`y) (Acc_inv r (proj2_sig y))) = Fix_F_sub x r.
+      F_sub x (fun y:{y:A | R y x} => Fix_F_sub (`y) (Acc_inv r (proj2_sig y))) = Fix_F_sub x r.
   Proof.
     destruct r using Acc_inv_dep; auto.
   Qed.
@@ -50,7 +50,7 @@ Section Well_founded.
     rewrite (proof_irrelevance (Acc R x) r s) ; auto.
   Qed.
 
-  Lemma Fix_eq : forall x:A, Fix_sub x = F_sub x (fun (y:A|R y x) => Fix_sub (proj1_sig y)).
+  Lemma Fix_eq : forall x:A, Fix_sub x = F_sub x (fun y:{ y:A | R y x} => Fix_sub (proj1_sig y)).
   Proof.
     intro x; unfold Fix_sub in |- *.
     rewrite <- (Fix_F_eq ).
@@ -62,7 +62,7 @@ Section Well_founded.
     forall x : A,
       Fix_sub x =
       let f_sub := F_sub in
-        f_sub x (fun (y : A | R y x) => Fix_sub (`y)).
+        f_sub x (fun y: {y : A | R y x} => Fix_sub (`y)).
     exact Fix_eq.
   Qed.
 
@@ -231,10 +231,10 @@ Module WfExtensionality.
   Program Lemma fix_sub_eq_ext :
     forall (A : Type) (R : A -> A -> Prop) (Rwf : well_founded R)
       (P : A -> Type)
-      (F_sub : forall x : A, (forall (y : A | R y x), P y) -> P x),
+      (F_sub : forall x : A, (forall y:{y : A | R y x}, P y) -> P x),
       forall x : A,
         Fix_sub A R Rwf P F_sub x =
-          F_sub x (fun (y : A | R y x) => Fix_sub A R Rwf P F_sub y).
+          F_sub x (fun y:{y : A | R y x} => Fix_sub A R Rwf P F_sub y).
   Proof.
     intros ; apply Fix_eq ; auto.
     intros.
-- 
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