proposition: Lemma modnD m n d : 0 < d -> (m + n) %% d = m %% d + n %% d - (m %% d + n %% d >= d) * d.
proof: Proof. by move=> /(@edivnD m n); rewrite edivn_def => -[]. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq)