Commit 01904806 authored by Robbert Krebbers's avatar Robbert Krebbers

Binary mononicity property for CMRA op.

parent ca8e04a3
......@@ -383,6 +383,7 @@ Proof.
Qed.
Lemma cmra_included_pcore x cx : pcore x = Some cx cx x.
Proof. exists x. by rewrite cmra_pcore_l. Qed.
Lemma cmra_monoN_l n x y z : x {n} y z x {n} z y.
Proof. by intros [z1 Hz1]; exists z1; rewrite Hz1 (assoc op). Qed.
Lemma cmra_mono_l x y z : x y z x z y.
......@@ -391,6 +392,10 @@ Lemma cmra_monoN_r n x y z : x ≼{n} y → x ⋅ z ≼{n} y ⋅ z.
Proof. by intros; rewrite -!(comm _ z); apply cmra_monoN_l. Qed.
Lemma cmra_mono_r x y z : x y x z y z.
Proof. by intros; rewrite -!(comm _ z); apply cmra_mono_l. Qed.
Lemma cmra_monoN n x1 x2 y1 y2 : x1 {n} y1 x2 {n} y2 x1 x2 {n} y1 y2.
Proof. intros; etrans; eauto using cmra_monoN_l, cmra_monoN_r. Qed.
Lemma cmra_mono x1 x2 y1 y2 : x1 y1 x2 y2 x1 x2 y1 y2.
Proof. intros; etrans; eauto using cmra_mono_l, cmra_mono_r. Qed.
Lemma cmra_included_dist_l n x1 x2 x1' :
x1 x2 x1' {n} x1 x2', x1' x2' x2' {n} x2.
......
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