proposition: Lemma continuity_eq f g : f =1 g -> continuity f -> continuity g.
proof: Proof. move=> Hfg Hf x eps Heps. have [y [Hy1 Hy2]]:= Hf x eps Heps. by exists y; split=> // z; rewrite -!Hfg; exact: Hy2. Qed.
imports: Rdefinitions Raxioms RIneq Rbasic_fun Zwf Epsilon FunctionalExtensionality Ranalysis1 Rsqrt_def Rtrigo1 Reals mathcomp(all_ssreflect ssralg poly mxpoly ssrnum) HB(structures)