proposition: Lemma preimage_subset_convex_hull (f: {affine T -> U}) (Z: set U): hull (f @^-1` Z) `<=` f @^-1` (hull Z).
proof: Proof. move=>x [n [g [d [gZ ->]]]] /=. rewrite Convn_comp. exists n, (f \o g), d; split=>//. by move=>y [i _ <-]; apply gZ; exists i. 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