proposition: Lemma plus_comm: forall x y, x + y == y + x.
proof: Proof. Proof binop_comm Qplus QnonNeg.Qplus_nonneg Qplus_comm. Lemma plus_assoc: forall n m p, n + (m + p) == (n + m) + p. Proof. apply (binop_assoc Qplus QnonNeg.Qplus_nonneg Qplus_comm Qplus_assoc). intros. apply Qplus_le_compat; intuition. Qed.
imports: Coq.QArith.Qabs CoRN.model.ordfields.Qordfield CoRN.model.structures.Qpossec Coq.QArith.Qminmax Coq.setoid_ring.Ring Coq.Program.Program