proposition: Lemma nat_bounded_forall_edge_false (f : nat -> bool) (n : nat) : nat_bounded_forall f n = false -> (forall k, k < n -> nat_bounded_forall f k = true) -> f n = false.
proof: Proof. intros. induction n; simpl in *. { assumption. } rewrite Bool.andb_false_iff in H. destruct H; intuition. exfalso. specialize (H0 n). rewrite H0 in H; intuition. Qed.
imports: Coq(FunctionalExtensionality Lia PeanoNat ProofIrrelevance ProofIrrelevanceFacts) ZornsLemma(FiniteTypes FunctionProperties) Coq(RelationClasses)