Definition f_equal_R := (f_equal (A:=R)).

(* Specifications: *)
Lemma Rplus_eq_reg_l : forall r r1 r2, r + r1 = r + r2 -> r1 = r2.
Lemma Rplus_eq_reg_r : forall r r1 r2, r1 + r = r2 + r -> r1 = r2.
Lemma Rplus_0_r_uniq : forall r r1, r + r1 = r -> r1 = 0.
Lemma Rplus_0_l_uniq : forall r r1, r1 + r = r -> r1 = 0.
Lemma Ropp_eq_compat : forall r1 r2, r1 = r2 -> - r1 = - r2.
Lemma Ropp_0 : -0 = 0.
Lemma Ropp_eq_0_compat : forall r, r = 0 -> - r = 0.
Lemma Ropp_involutive : forall r, - - r = r.
Lemma Ropp_eq_reg : forall r1 r2, - r1 = - r2 -> r1 = r2.
Lemma Ropp_neq_0_compat : forall r, r <> 0 -> - r <> 0.
Lemma Ropp_plus_distr : forall r1 r2, - (r1 + r2) = - r1 + - r2.
Lemma Rmult_eq_compat_l : forall r r1 r2, r1 = r2 -> r * r1 = r * r2.
Lemma Rmult_eq_compat_r : forall r r1 r2, r1 = r2 -> r1 * r = r2 * r.
Lemma Rinv_r : forall r, r <> 0 -> r * / r = 1.
Lemma Rinv_l_sym : forall r, r <> 0 -> 1 = / r * r.
Lemma Rinv_r_sym : forall r, r <> 0 -> 1 = r * / r.