proposition: Lemma all_comm_mxP fs : reflect {in fs &, forall f g, f *m g = g *m f} (all_comm_mx fs).
proof: Proof. by apply: (iffP allrelP) => fsP ? ? ? ?; apply/eqP/fsP. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(fintype finfun bigop finset fingroup perm order) mathcomp(div prime binomial ssralg countalg finalg zmodp)