(** *** Cancellation *)

(* Specifications: *)
Lemma Rplus_lt_reg_l : forall r r1 r2, r + r1 < r + r2 -> r1 < r2.
Lemma Rplus_lt_reg_r : forall r r1 r2, r1 + r < r2 + r -> r1 < r2.
Lemma Rplus_le_reg_l : forall r r1 r2, r + r1 <= r + r2 -> r1 <= r2.
Lemma Rplus_le_reg_r : forall r r1 r2, r1 + r <= r2 + r -> r1 <= r2.
Lemma Rplus_gt_reg_l : forall r r1 r2, r + r1 > r + r2 -> r1 > r2.
Lemma Rplus_lt_reg_pos_r : forall r1 r2 r3, 0 <= r2 -> r1 + r2 < r3 -> r1 < r3.
Lemma Rplus_ge_reg_neg_r :
forall r1 r2 r3, 0 >= r2 -> r1 + r2 >= r3 -> r1 >= r3.
Lemma Rplus_gt_reg_neg_r : forall r1 r2 r3, 0 >= r2 -> r1 + r2 > r3 -> r1 > r3.
Lemma Rplus_le_lt_0_neq_0 : forall r1 r2, 0 <= r1 -> 0 < r2 -> r1 + r2 <> 0.
#[global]
Hint Immediate Rplus_le_lt_0_neq_0: real.