From 67db2f248ac8250c6b2de6e4e25701f517ec265c Mon Sep 17 00:00:00 2001 From: Ralf Jung <jung@mpi-sws.org> Date: Fri, 7 Aug 2020 10:43:33 +0200 Subject: [PATCH] add directional versions of not_elem_of_singleton --- theories/sets.v | 4 ++++ 1 file changed, 4 insertions(+) diff --git a/theories/sets.v b/theories/sets.v index 2a97d742..749bd349 100644 --- a/theories/sets.v +++ b/theories/sets.v @@ -449,6 +449,10 @@ Section semi_set. Proof. set_solver. Qed. Lemma not_elem_of_singleton x y : x ∉ ({[ y ]} : C) ↔ x ≠y. Proof. by rewrite elem_of_singleton. Qed. + Lemma not_elem_of_singleton_1 x y : x ∉ ({[ y ]} : C) → x ≠y. + Proof. apply not_elem_of_singleton. Qed. + Lemma not_elem_of_singleton_2 x y : x ≠y → x ∉ ({[ y ]} : C). + Proof. apply not_elem_of_singleton. Qed. (** Disjointness *) Lemma elem_of_disjoint X Y : X ## Y ↔ ∀ x, x ∈ X → x ∈ Y → False. -- GitLab