(** ** Composition *)
Section Comp.
Context {V : CompleteNormedModule R_AbsRing}.
(* Notation consistent version of the lemmas used in is_RInt_comp *)

Lemma continuous_ab_maj_consistent :
forall (f : R -> R) (a b : R),
a <= b ->
(forall c : R, a <= c <= b -> continuous f c) ->
exists Mx : R, (forall c : R, a <= c <= b -> f c <= f Mx) /\ a <= Mx <= b.