proposition: Lemma ConstFilter_false : forall {A : Set} (hn : list (A -> Prop)) (x : A) (init : A -> Prop), init x -> Forall (fun h => ~h x) hn -> SubsetIntersectFilter hn init (ConstFilter false (length hn)) x.
proof: Proof. induction hn. - intros. exact H. - intros. inversion H0. split. 2: exact H3. exact (IHhn x init H H4). Qed.
imports: QArith_base List ConstructiveReals ConstructiveRealsMorphisms ConstructiveAbs ConstructiveSum ConstructiveMinMax ConstructiveLimits ConstructivePartialFunctions CMTbase CMTIntegrableFunctions CMTIntegrableSets CMTFullSets CMTcast CMTprofile