From 7921671c2146147c79f6b34f187ebd342277f3e7 Mon Sep 17 00:00:00 2001 From: Robbert Krebbers <mail@robbertkrebbers.nl> Date: Mon, 26 Jul 2021 20:34:55 +0200 Subject: [PATCH] Add `singleton_subseteq_l` and `singleton_subseteq`. --- theories/sets.v | 5 +++++ 1 file changed, 5 insertions(+) diff --git a/theories/sets.v b/theories/sets.v index 3bfef576..6ac9a22e 100644 --- a/theories/sets.v +++ b/theories/sets.v @@ -471,6 +471,11 @@ Section semi_set. Lemma not_elem_of_singleton_2 x y : x ≠y → x ∉ ({[ y ]} : C). Proof. apply not_elem_of_singleton. Qed. + Lemma singleton_subseteq_l x X : {[ x ]} ⊆ X ↔ x ∈ X. + Proof. set_solver. Qed. + Lemma singleton_subseteq x y : {[ x ]} ⊆@{C} {[ y ]} ↔ x = y. + Proof. set_solver. Qed. + (** Disjointness *) Lemma elem_of_disjoint X Y : X ## Y ↔ ∀ x, x ∈ X → x ∈ Y → False. Proof. done. Qed. -- GitLab