proposition: Lemma R_is_Ring : is_CRing RAbGroup (1%R) RMul_op.
proof: Proof. exists RMul_assoc. constructor. unfold is_rht_unit; intro x. apply Rmult_1_r. unfold is_lft_unit; intro x. apply Rmult_1_l. unfold commutes. apply Rmult_comm. unfold distributive; intros x y z. apply Rmult_plus_distr_l. apply R1_neq_R0. 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)