Commit 81d719c9 authored by Robbert Krebbers's avatar Robbert Krebbers
Browse files

Mononicity of ∖.

parent 5c7064e1
......@@ -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.
......
Markdown is supported
0% or .
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment