proposition: Lemma continuous_max (f g : T -> R^o) x : {for x, continuous f} -> {for x, continuous g} -> {for x, continuous (f \max g)}.
proof: Proof. move=> ctsf ctsg. under [_ \max _]eq_fun => ? do rewrite maxr_absE. apply: cvgM; [|exact: cvg_cst]; apply:cvgD; first exact: cvgD. by apply: cvg_norm; apply: cvgB. Qed.
imports: HB(structures) mathcomp(all_ssreflect ssralg ssrint ssrnum finmap matrix) mathcomp(rat interval zmodp vector fieldext falgebra) mathcomp(mathcomp_extra boolp classical_sets functions) mathcomp(cardinality set_interval Rstruct) ereal reals signed topology prodnormedzmodule