Definition ifte (T : Set) (A B : Prop) (s : {A} + {B})
(th el : T) := if s then th else el.
Arguments ifte : default implicits.
intros.
elim s.
intro x.
split with x; reflexivity.
intro.
absurd (a = a); auto.
Qed.

Lemma Disequality_provable :
forall (A : Set) (a b : A),
a <> b -> forall s : {a = b} + {a <> b}, exists x : _, s = right _ x.