Proof (@inj_right_pair_on A x (eq_dec x)).

(* Specifications: *)
(** We deduce axiom [K] for (decidable) types *)
Theorem K_dec_type (A:Type) (eq_dec:forall x y:A, {x = y} + {x <> y}) (x:A)
(P:x = x -> Prop) (H:P (eq_refl x)) (p:x = x) : P p.
Theorem K_dec_set :
forall A:Set,
(forall x y:A, {x = y} + {x <> y}) ->
forall (x:A) (P:x = x -> Prop), P (eq_refl x) -> forall p:x = x, P p.