proposition: Lemma convA_pt_set p q x (Y Z : set A) : x <|p|>: (Y :<|q|>: Z) = (x <|[r_of p, q]|>: Y) :<|[s_of p, q]|>: Z.
proof: Proof. rewrite eqEsubset; split=> u; rewrite conv_pt_setE. - case=> yz [] y Yy; rewrite conv_pt_setE=> -[] z Zz <- <-. by rewrite convA; apply conv_in_conv_set=> //; apply conv_in_conv_pt_set. - case=> xy [] y Yy <-; rewrite conv_pt_setE; case=> z Zz <-. by rewrite -convA; apply conv_in_conv_pt_set=> //; apply conv_in_conv_set. Qed.
imports: HB(structures) Reals mathcomp(all_ssreflect ssralg ssrnum) mathcomp(mathcomp_extra boolp classical_sets Rstruct reals) mathcomp(finmap) Reals_ext realType_ext classical_sets_ext ssrR fdist fsdist convex