(** *** Comparison of addition with left operand *)

(* Specifications: *)
Lemma Rplus_pos_gt : forall r1 r2, r2 > 0 -> r1 + r2 > r1.
Lemma Rplus_nneg_ge : forall r1 r2, r2 >= 0 -> r1 + r2 >= r1.
Lemma Rplus_neg_lt : forall r1 r2, r2 < 0 -> r1 + r2 < r1.
Lemma Rplus_npos_le : forall r1 r2, r2 <= 0 -> r1 + r2 <= r1.
(** *** Sign of addition *)
Lemma Rplus_pos_pos : forall r1 r2, r1 > 0 -> r2 > 0 -> r1 + r2 > 0.
Lemma Rplus_nneg_nneg : forall r1 r2, r1 >= 0 -> r2 >= 0 -> r1 + r2 >= 0.
Lemma Rplus_npos_npos : forall r1 r2, r1 <= 0 -> r2 <= 0 -> r1 + r2 <= 0.
Lemma Rplus_pos_nneg : forall r1 r2, r1 > 0 -> r2 >= 0 -> r1 + r2 > 0.
Lemma Rplus_nneg_pos : forall r1 r2, r1 >= 0 -> r2 > 0 -> r1 + r2 > 0.
Lemma Rplus_neg_npos : forall r1 r2, r1 < 0 -> r2 <= 0 -> r1 + r2 < 0.
Lemma Rplus_npos_neg : forall r1 r2, r1 <= 0 -> r2 < 0 -> r1 + r2 < 0.
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(** ** Order and opposite                                *)
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(** *** Contravariant compatibility *)
Lemma Ropp_gt_lt_contravar : forall r1 r2, r1 > r2 -> - r1 < - r2.
#[global]
Hint Resolve Ropp_gt_lt_contravar : core.