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| author |  msozeau <msozeau@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2012-03-14 09:53:06 +0000 |
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| committer | msozeau <msozeau@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2012-03-14 09:53:06 +0000 |
| commit | 8ff2de8c01b3ba3563517627b1f5c9eb2c4bcb77 (patch) | |
| tree | 4f7e99ba36af1cf03d8c3315c371293ae46fe77c /theories/Program/Wf.v | |
| parent | 4d7b12f27a7cc520a319a9d4b652137c0a0cbb60 (diff) | |
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
Diffstat (limited to 'theories/Program/Wf.v')
| -rw-r--r-- | theories/Program/Wf.v | 12 |
1 files changed, 6 insertions, 6 deletions
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. |