proposition: Lemma N_infty_extensionality (p q : N_infty) : N_equiv p q -> p = q.
proof: Proof. intros. destruct p, q. apply subset_eq_compat. apply functional_extensionality. auto. Qed.
imports: Coq(FunctionalExtensionality Lia PeanoNat ProofIrrelevance ProofIrrelevanceFacts) ZornsLemma(FiniteTypes FunctionProperties) Coq(RelationClasses)