proposition: Lemma F_inj : injective F.
proof: Proof. intros n m Hnm. destruct (Nat.lt_total n m) as [H|[H|H] ]; trivial. - contradiction (F_inj' Hnm H). - symmetry in Hnm. contradiction (F_inj' Hnm H). Qed.
imports: Undecidability(Shared.Dec) Undecidability.Synthetic(ListEnumerabilityFacts) List PeanoNat ConstructiveEpsilon Lia