diff options
Diffstat (limited to 'theories/Logic')
| -rw-r--r-- | theories/Logic/Eqdep_dec.v | 7 |
1 files changed, 7 insertions, 0 deletions
diff --git a/theories/Logic/Eqdep_dec.v b/theories/Logic/Eqdep_dec.v index e491a4d5c9..b45aa23fe8 100644 --- a/theories/Logic/Eqdep_dec.v +++ b/theories/Logic/Eqdep_dec.v @@ -158,6 +158,13 @@ Proof. apply (Streicher_K__eq_rect_eq A (K_dec_type eq_dec)). Qed. +(** We deduce the injectivity of dependent equality for decidable types *) +Theorem eq_dep_eq_dec : + forall A:Type, + (forall x y:A, {x = y} + {x <> y}) -> + forall (P:A->Type) (p:A) (x y:P p), eq_dep A P p x p y -> x = y. +Proof (fun A eq_dec => eq_rect_eq__eq_dep_eq A (eq_rect_eq_dec eq_dec)). + Unset Implicit Arguments. (************************************************************************) |