proposition: Lemma ApGlue : forall (X Y : RSetoid) (fl fr : StepF (X --> Y)) (o : OpenUnit) (b : StepF X), (glue o fl fr) <@> b = glue o (fl <@> (SplitL b o)) (fr <@> (SplitR b o)).
proof: Proof. intros X Y fl fr o b. unfold Ap. simpl (StepFunction.Map (@evalMorphism X Y) (glue o fl fr)). rewrite ApGlue. reflexivity. Qed.
imports: CoRN.algebra.RSetoid CoRN.metric2.StepFunction CoRN.model.structures.OpenUnit CoRN.tactics.CornTac CoRN.tactics.Qauto CoRN.model.ordfields.Qordfield CoRN.algebra.COrdFields