proposition: Lemma pred_ext_5 : forall (P Q : forall (x1:A1) (x2:A2 x1) (x3:A3 x2) (x4:A4 x3) (x5:A5 x4), Prop), (forall x1 x2 x3 x4 x5, P x1 x2 x3 x4 x5 <-> Q x1 x2 x3 x4 x5) -> P = Q.
proof: Proof. Proof using. repeat (intros; apply fun_ext_dep). intros. apply~ prop_ext. Qed.
imports: TLC(LibTactics LibAxioms)