proposition: Lemma R_convex_function_atN f a b t : concave_function_at f a b t -> convex_function_at (fun x => - f x)%coqR a b t.
proof: Proof. by rewrite /convex_function_at /leconv /= avgR_oppD leR_oppl oppRK. Qed.
imports: HB(structures) mathcomp(all_ssreflect ssralg fingroup perm matrix) mathcomp(mathcomp_extra boolp classical_sets Rstruct) mathcomp(ssrnum ereal) mathcomp(lra Rstruct reals) Reals ssrR Reals_ext Ranalysis_ext ssr_ext ssralg_ext logb realType_ext fdist