proposition: Lemma mk_num_0 : mk_num IND_0 = 0.
proof: Proof. unfold mk_num. set (P := mk_num_pred IND_0). assert (h: exists n, P n). exists 0. reflexivity. generalize (ε_spec h). set (i := ε P). unfold P, mk_num_pred. intro e. apply dest_num_inj. simpl. symmetry. exact e. Qed.
imports: Coq.Logic.ClassicalEpsilon ClassicalFacts PropExtensionalityFacts