proposition: Lemma leqif_add m1 n1 C1 m2 n2 C2 : m1 <= n1 ?= iff C1 -> m2 <= n2 ?= iff C2 -> m1 + m2 <= n1 + n2 ?= iff C1 && C2.
proof: Proof. rewrite -(mono_leqif (leq_add2r m2)) -(mono_leqif (leq_add2l n1) m2). exact: leqif_trans. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype) BinNat Ring