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authorGravatar herbelin <herbelin@85f007b7-540e-0410-9357-904b9bb8a0f7>2002-04-17 11:30:23 +0000
committerGravatar herbelin <herbelin@85f007b7-540e-0410-9357-904b9bb8a0f7>2002-04-17 11:30:23 +0000
commitcc1be0bf512b421336e81099aa6906ca47e4257a (patch)
treec25fa8ed965729d7a85efa3b3292fdf7f442963d /theories/Logic/Eqdep_dec.v
parentebf9aa9f97ef0d49ed1b799c9213f78efad4fec7 (diff)
Uniformisation (Qed/Save et Implicits Arguments)
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@2650 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Logic/Eqdep_dec.v')
-rw-r--r--theories/Logic/Eqdep_dec.v18
1 files changed, 9 insertions, 9 deletions
diff --git a/theories/Logic/Eqdep_dec.v b/theories/Logic/Eqdep_dec.v
index 7daff9ba3..8f7e76d51 100644
--- a/theories/Logic/Eqdep_dec.v
+++ b/theories/Logic/Eqdep_dec.v
@@ -34,12 +34,12 @@ Set Implicit Arguments.
Lemma eq_eqT_bij: (A:Set)(x,y:A)(p:x=y)p==(eqT2eq (eq2eqT p)).
Intros.
Case p; Reflexivity.
-Save.
+Qed.
Lemma eqT_eq_bij: (A:Set)(x,y:A)(p:x==y)p==(eq2eqT (eqT2eq p)).
Intros.
Case p; Reflexivity.
-Save.
+Qed.
Section DecidableEqDep.
@@ -52,7 +52,7 @@ Section DecidableEqDep.
Remark trans_sym_eqT: (x,y:A)(u:x==y)(comp u u)==(refl_eqT ? y).
Intros.
Case u; Trivial.
-Save.
+Qed.
@@ -74,7 +74,7 @@ Case (eq_dec x y); Intros.
Reflexivity.
Case n; Trivial.
-Save.
+Qed.
Local nu_inv [y:A]: x==y->x==y := [v](comp (nu (refl_eqT ? x)) v).
@@ -84,7 +84,7 @@ Save.
Intros.
Case u; Unfold nu_inv.
Apply trans_sym_eqT.
-Save.
+Qed.
Theorem eq_proofs_unicity: (y:A)(p1,p2:x==y) p1==p2.
@@ -93,13 +93,13 @@ Elim nu_left_inv with u:=p1.
Elim nu_left_inv with u:=p2.
Elim nu_constant with y p1 p2.
Reflexivity.
-Save.
+Qed.
Theorem K_dec: (P:x==x->Prop)(P (refl_eqT ? x)) -> (p:x==x)(P p).
Intros.
Elim eq_proofs_unicity with x (refl_eqT ? x) p.
Trivial.
-Save.
+Qed.
(** The corollary *)
@@ -128,7 +128,7 @@ Case n; Trivial.
Case H.
Reflexivity.
-Save.
+Qed.
End DecidableEqDep.
@@ -146,4 +146,4 @@ Elim e; Left ; Reflexivity.
Right ; Red; Intro neq; Apply n; Elim neq; Reflexivity.
Trivial.
-Save.
+Qed.