proposition: Lemma Y_if : forall (P : Prop) (hyp : P) (x y z : E), x = z -> Y P x y = z.
proof: Proof. ir. unfold Y in |- *. set (a := fun p : P => x). set (b := fun p : ~ P => y). transitivity (a hyp). ap by_cases_if. transitivity x. tv. am. Qed.
imports: tactics