proposition: Lemma defined_lem : forall f x : E, axioms f -> defined f x -> inc (pair x (V x f)) f.
proof: Proof. ir. unfold axioms in H. unfold defined in H0. xd. unfold domain in H1. set (K := Image.ex H1) in *. nin K. nin H3. assert (ex (fun y : E => inc (pair x y) f)). eapply ex_intro with (pr2 x0). rewrite <- H4. rewrite H. am. am. set (K := choose_pr H5) in *. am. Qed.
imports: set_theory