proposition: Lemma divzDl m n d : (d %| m)%Z -> ((m + n) %/ d)%Z = (m %/ d)%Z + (n %/ d)%Z.
proof: Proof. have [-> | d_nz] := eqVneq d 0; first by rewrite !divz0. by move/divzK=> {1}<-; rewrite divzMDl. 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)