From 81d719c9414454cfd2c1505ccb6b6fe92ffbd80f Mon Sep 17 00:00:00 2001 From: Robbert Krebbers <mail@robbertkrebbers.nl> Date: Thu, 9 Mar 2017 23:07:17 +0100 Subject: [PATCH] =?UTF-8?q?Mononicity=20of=20=E2=88=96.?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- theories/collections.v | 9 ++++++++- 1 file changed, 8 insertions(+), 1 deletion(-) diff --git a/theories/collections.v b/theories/collections.v index a37e1365..28a8f25b 100644 --- a/theories/collections.v +++ b/theories/collections.v @@ -346,7 +346,6 @@ Section simple_collection. Proof. set_solver. Qed. Lemma elem_of_union_r x X Y : x ∈ Y → x ∈ X ∪ Y. Proof. set_solver. Qed. - Lemma union_preserving_l X Y1 Y2 : Y1 ⊆ Y2 → X ∪ Y1 ⊆ X ∪ Y2. Proof. set_solver. Qed. Lemma union_preserving_r X1 X2 Y : X1 ⊆ X2 → X1 ∪ Y ⊆ X2 ∪ Y. @@ -613,6 +612,14 @@ Section collection. Lemma difference_disjoint X Y : X ⊥ Y → X ∖ Y ≡ X. Proof. set_solver. Qed. + Lemma difference_preserving X1 X2 Y1 Y2 : + X1 ⊆ X2 → Y2 ⊆ Y1 → X1 ∖ Y1 ⊆ X2 ∖ Y2. + Proof. set_solver. Qed. + Lemma difference_preserving_l X Y1 Y2 : Y2 ⊆ Y1 → X ∖ Y1 ⊆ X ∖ Y2. + Proof. set_solver. Qed. + Lemma difference_preserving_r X1 X2 Y : X1 ⊆ X2 → X1 ∖ Y ⊆ X2 ∖ Y. + Proof. set_solver. Qed. + (** Disjointness *) Lemma disjoint_intersection X Y : X ⊥ Y ↔ X ∩ Y ≡ ∅. Proof. set_solver. Qed. -- GitLab