proposition: Lemma segment_is_convex (x y : T) : is_convex_set (segment x y).
proof: Proof. apply/asboolP => u v p [q _ <-] [r _ <-]. have [q' [p' [r' ->]]] := convACA' x y x y q p r. by rewrite convmm convmm; exists p'. 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