proposition: Lemma continuity_in_ext : forall D (f g : R -> R), (f == g)%F -> continuity_in D f -> continuity_in D g.
proof: Proof. intros D f g Heq Hf x ; eapply continuity_pt_in_ext, Hf ; eassumption. Qed.
imports: Rbase Ranalysis Rinterval Rfunctions Rfunction_def Ranalysis_def Ranalysis_def_simpl Rfunction_facts MyRIneq MyR_dist Lra Tactics