proposition: Lemma RPlus_is_setoid_bin_fun: bin_fun_strext RCSetoid RCSetoid RCSetoid Rplus.
proof: Proof. unfold bin_fun_strext. intros x1 x2 y1 y2 H. elim (total_order_T x1 x2); intro H1. elim H1; clear H1; intro H2. left. apply: Rlt_not_eq; assumption. right. intro H0. apply H. rewrite H2. rewrite H0. reflexivity. left. apply: Rgt_not_eq; assumption. Qed.
imports: CoRN.algebra.CSetoids CoRN.algebra.CSemiGroups CoRN.algebra.CMonoids CoRN.algebra.CGroups CoRN.tactics.CornTac CoRN.algebra.CAbGroups CoRN.algebra.CRings CoRN.algebra.CFields CoRN.algebra.COrdFields CoRN.reals.CReals Coq.Reals.RIneq Coq.Reals.Rcomplete Coq.Reals.Rlimit Coq.Reals.Rbasic_fun Coq(Lra)