proposition: Lemma scale_affine (E : lmodType R_ringType) (t : R) : affine (fun x : E => t *: x).
proof: Proof. move=> p/= x y. by rewrite/conv/= scalerDr; congr GRing.add; rewrite 2!scalerA mulrC. Qed.
imports: mathcomp(all_ssreflect all_algebra vector reals ereal classical_sets boolp Rstruct) infotheo(convex Reals_ext) preliminaries Reals