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

(* Specifications: *)
(** We deduce the [eq_rect_eq] axiom for (decidable) types *)
Theorem eq_rect_eq_dec :
forall A:Type,
(forall x y:A, {x = y} + {x <> y}) ->
forall (p:A) (Q:A -> Type) (x:Q p) (h:p = p), x = eq_rect p Q x p h.
(** 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.