proposition: Lemma plus_commute : forall n1 m1, n1 + m1 = m1 + n1.
proof: Proof. elim=> [m1 | n1 IHn1 m1]. by elim: m1 => // m1 IHm1; rewrite -[0 + m1.+1]/(0 + m1).+1 IHm1. rewrite -[n1.+1 + m1]/(n1 + m1).+1 IHn1. by elim: m1 => // m1 IHm1; rewrite -[m1.+1 + n1]/(m1 + n1).+1 IHm1. Qed.
imports: mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat div)