proposition: Lemma IND_0_def : IND_0 = (@ε ind (fun z : ind => (forall x1 : ind, forall x2 : ind, ((IND_SUC x1) = (IND_SUC x2)) = (x1 = x2)) /\ (forall x : ind, ~ ((IND_SUC x) = z)))).
proof: Proof. exact (eq_refl IND_0). Qed.
imports: coq theory_hol types