proposition: Lemma SplitR_resp_Xeq : forall (s1 s2:StepF X) a, s1 == s2 -> SplitR s1 a == SplitR s2 a.
proof: Proof. intros s1 s2 a H. pose (b:=OpenUnitDual a). apply StepF_eq_resp_Qeq with (Mirror (SplitL (Mirror s1) b)) (Mirror (SplitL (Mirror s2) b)); try (unfold Mirror, SplitR, SplitL, b;eapply StepF_Qeq_trans;[apply Mirror_resp_Qeq; apply StepF_Qeq_sym; apply MirrorSplitR_Qeq; reflexivity|apply MirrorMirror]). rewrite -> Mirror_eq_Mirror. apply SplitL_resp_Xeq. rewrite -> Mirror_eq_Mirror. assumption. 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