fact: Definition convex_function (R : realType) (D : set R) (f : R -> R^o) := forall (t : {i01 R}), {in D &, forall (x y : R^o), (f (x <| t |> y) <= f x <| t |> f y)%R}.
imports: mathcomp(all_ssreflect ssralg ssrint ssrnum finmap) mathcomp(matrix interval zmodp vector fieldext falgebra) mathcomp(mathcomp_extra boolp classical_sets set_interval) mathcomp(functions cardinality) ereal reals signed topology prodnormedzmodule normedtype derive realfun itv HB(structures)