Proof fun A => K_dec_type (A:=A).

(** 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.