proposition: Lemma modz_mod m d : ((m %% d)%Z = m %[mod d])%Z.
proof: Proof. rewrite -!(modz_abs _ d); case: {d}`|d|%N => [|d]; first by rewrite !modz0. by rewrite modz_small ?modz_ge0 ?ltz_mod. 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)