proposition: Lemma first_index_error_None_correct {A} (P : A -> bool) (ls : list A) : first_index_error P ls = None <-> (forall elem, List.In elem ls -> P elem = false).
proof: Proof. induction ls; simpl; intros. { first_index_error_t. } { first_index_error_t. match goal with | [ H : first_index_error _ _ = Some _ |- _ ] => apply first_index_error_Some_correct in H end. first_index_error_t. } Qed.
imports: Fiat.Common.Coq__8_4__8_5__Compat Coq.ZArith.ZArith Coq.Lists.List Coq.Lists.SetoidList Coq.Bool.Bool Fiat.Common Fiat.Common.List.Operations Fiat.Common.Equality Fiat.Common.List.FlattenList Fiat.Common.LogicFacts