diff options
| author | herbelin | 2011-08-08 23:04:24 +0000 |
|---|---|---|
| committer | herbelin | 2011-08-08 23:04:24 +0000 |
| commit | 022f78302514e071ca60c2e8719a1e2ec66eaed6 (patch) | |
| tree | 7942a37a69f7e591324daff14c20dea10f9c6bcb /theories/Logic | |
| parent | ea09770efde4a7bdd573407a408e54ec2b41b6ad (diff) | |
New proposition "rewrite Heq in H" for eq_rect (assuming that there is
a smaller risk that "rewrite" clashes with a name used for constr).
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@14390 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Logic')
| -rw-r--r-- | theories/Logic/EqdepFacts.v | 8 |
1 files changed, 4 insertions, 4 deletions
diff --git a/theories/Logic/EqdepFacts.v b/theories/Logic/EqdepFacts.v index 2646bb5ae2..8fbd79fa49 100644 --- a/theories/Logic/EqdepFacts.v +++ b/theories/Logic/EqdepFacts.v @@ -84,7 +84,7 @@ Section Dependent_Equality. equalities *) Inductive eq_dep1 (p:U) (x:P p) (q:U) (y:P q) : Prop := - eq_dep1_intro : forall h:q = p, x = rew h in y -> eq_dep1 p x q y. + eq_dep1_intro : forall h:q = p, x = rewrite h in y -> eq_dep1 p x q y. Lemma eq_dep1_dep : forall (p:U) (x:P p) (q:U) (y:P q), eq_dep1 p x q y -> eq_dep p x q y. @@ -164,7 +164,7 @@ Qed. Set Implicit Arguments. -Lemma eq_sigT_sig_eq : forall X P (x1 x2:X) H1 H2, existT P x1 H1 = existT P x2 H2 <-> {H:x1=x2 | rew H in H1 = H2}. +Lemma eq_sigT_sig_eq : forall X P (x1 x2:X) H1 H2, existT P x1 H1 = existT P x2 H2 <-> {H:x1=x2 | rewrite H in H1 = H2}. Proof. intros; split; intro H. - change x2 with (projT1 (existT P x2 H2)). @@ -186,7 +186,7 @@ Proof. Defined. Lemma eq_sigT_snd : - forall X P (x1 x2:X) H1 H2 (H:existT P x1 H1 = existT P x2 H2), rew (eq_sigT_fst H) in H1 = H2. + forall X P (x1 x2:X) H1 H2 (H:existT P x1 H1 = existT P x2 H2), rewrite (eq_sigT_fst H) in H1 = H2. Proof. intros. unfold eq_sigT_fst. @@ -206,7 +206,7 @@ Proof. Defined. Lemma eq_sig_snd : - forall X P (x1 x2:X) H1 H2 (H:exist P x1 H1 = exist P x2 H2), rew (eq_sig_fst H) in H1 = H2. + forall X P (x1 x2:X) H1 H2 (H:exist P x1 H1 = exist P x2 H2), rewrite (eq_sig_fst H) in H1 = H2. Proof. intros. unfold eq_sig_fst, eq_ind. |