proposition: Lemma concave_function_at'P f a b t : concave_function_at' f a b t <-> concave_function_at f a b t.
proof: Proof. rewrite /concave_function_at'/concave_function_at/convex_function_at. by rewrite conv_leoppD leoppP. 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