proposition: Lemma fold_right_map_andb_orb {T} x y f g (ls : list T) : fold_right andb x (map f ls) = true /\ fold_right orb y (map g ls) = true -> fold_right orb (andb x y) (map (fun k => andb (f k) (g k)) ls) = true.
proof: Proof. induction ls; simpl; intros; destruct_head_hnf bool; try tauto; repeat match goal with | [ H : _ |- _ ] => progress rewrite ?Bool.orb_true_iff, ?Bool.andb_true_iff in H | _ => progress rewrite ?Bool.orb_true_iff, ?Bool.andb_true_iff end; try tauto. Qed.
imports: Coq.Lists.List Coq.ZArith.ZArith Coq.Lists.SetoidList Coq.Setoids.Setoid Coq.Classes.RelationClasses Coq.Program.Program Coq.Classes.Morphisms Fiat.Common.Tactics.SplitInContext Fiat.Common.Tactics.Combinators Fiat.Common.Tactics.FreeIn Fiat.Common.Tactics.SetoidSubst Fiat.Common.Tactics.BreakMatch Fiat.Common.Tactics.Head Fiat.Common.Tactics.FoldIsTrue Fiat.Common.Tactics.SpecializeBy Fiat.Common.Tactics.DestructHyps Fiat.Common.Tactics.DestructSig Fiat.Common.Tactics.DestructHead Fiat.Common.Coq__8_4__8_5__Compat