diff options
| -rw-r--r-- | theories/Logic/EqdepFacts.v | 22 |
1 files changed, 22 insertions, 0 deletions
diff --git a/theories/Logic/EqdepFacts.v b/theories/Logic/EqdepFacts.v index 2f61e0e297..653f0b9b4e 100644 --- a/theories/Logic/EqdepFacts.v +++ b/theories/Logic/EqdepFacts.v @@ -440,3 +440,25 @@ End EqdepTheory. Arguments eq_dep U P p x q _ : clear implicits. Arguments eq_dep1 U P p x q y : clear implicits. + +(** Basic facts about eq_dep *) + +Lemma f_eq_dep : + forall U (P:U->Type) R p q x y (f:forall p, P p -> R p), + eq_dep x y -> eq_dep (f p x) (f q y). +Proof. +intros * []. reflexivity. +Qed. + +Lemma eq_dep_non_dep : + forall U P p q x y, @eq_dep U (fun _ => P) p x q y -> x = y. +Proof. +intros * []. reflexivity. +Qed. + +Lemma f_eq_dep_non_dep : + forall U (P:U->Type) R p q x y (f:forall p, P p -> R), + eq_dep x y -> f p x = f q y. +Proof. +intros * []. reflexivity. +Qed. |