proposition: Lemma DomainProdSubsetIntersect : forall {A : Set} (hn : list (A -> Prop)) (init : A -> Prop) (l : list bool) (x : A) (n : nat), SubsetIntersectFilter hn init l x -> match nth_error hn n, nth_error l n with | Some fg, Some b => if b then fg x else ~fg x | _, _ => True end.
proof: Proof. induction hn. - intros. destruct n; simpl; trivial. - intros. destruct n. + simpl. destruct l as [|b l]. trivial. destruct b; apply H. + simpl. destruct l as [|b l]. destruct (nth_error hn n); trivial. apply (IHhn init l). simpl in H. destruct b; apply H. Qed.
imports: QArith_base List ConstructiveReals ConstructiveRealsMorphisms ConstructiveAbs ConstructiveSum ConstructiveMinMax ConstructiveLimits ConstructivePartialFunctions CMTbase CMTIntegrableFunctions CMTIntegrableSets CMTFullSets CMTcast CMTprofile