Definition posreal_one := mkposreal (1) (Rlt_0_1).Definition posreal_half := mkposreal (/ 2) pos_half_prf.(** * Compatibility *)

Notation prod_neq_R0 := Rmult_integral_contrapositive_currified (only parsing).Notation minus_Rgt := Rminus_gt (only parsing).Notation minus_Rge := Rminus_ge (only parsing).Notation plus_le_is_le := Rplus_le_reg_pos_r (only parsing).Notation plus_lt_is_lt := Rplus_lt_reg_pos_r (only parsing).Notation INR_lt_1 := lt_1_INR (only parsing).Notation lt_INR_0 := lt_0_INR (only parsing).Notation not_nm_INR := not_INR (only parsing).Notation INR_pos := pos_INR_nat_of_P (only parsing).Notation not_INR_O := INR_not_0 (only parsing).Notation not_O_INR := not_0_INR (only parsing).Notation not_O_IZR := not_0_IZR (only parsing).Notation le_O_IZR := le_0_IZR (only parsing).Notation lt_O_IZR := lt_0_IZR (only parsing).Notation tech_Rplus := Rplus_le_lt_0_neq_0 (only parsing).Notation tech_Rgt_minus := Rgt_minus_pos (only parsing).Notation le_epsilon := Rle_plus_epsilon (only parsing).Notation completeness_weak := upper_bound_thm (only parsing).Notation Req_EM_T := Req_dec_T (only parsing).Notation Rinv_r_simpl_r := Rmult_inv_m_id_r (only parsing).Notation Rinv_r_simpl_l := Rmult_inv_r_id_l (only parsing).Notation Rinv_r_simpl_m := Rmult_inv_r_id_m (only parsing).Notation Rplus_eq_R0 := Rplus_eq_0 (only parsing).

Lemma Rinv_involutive_depr : forall r, r <> 0 -> / / r = r.