proposition: Lemma divz_mulAC d m n : (d %| m)%Z -> (m %/ d)%Z * n = (m * n %/ d)%Z.
proof: Proof. have [-> | d_nz] := eqVneq d 0; first by rewrite !divz0 mul0r. by move/divzK=> {2} <-; rewrite mulrAC mulzK. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq path) mathcomp(div choice fintype tuple finfun bigop prime order) mathcomp(ssralg poly ssrnum ssrint archimedean rat matrix) mathcomp(polydiv perm zmodp mxalgebra vector)