Commit dbbda8cb authored by Robbert Krebbers's avatar Robbert Krebbers
Browse files

Prove that lockset ⊆ dom memory.

parent 7f9c5994
...@@ -815,6 +815,10 @@ Section prod_relation. ...@@ -815,6 +815,10 @@ Section prod_relation.
End prod_relation. End prod_relation.
(** ** Other *) (** ** Other *)
Lemma and_wlog_l (P Q : Prop) : (Q P) Q (P Q).
Proof. tauto. Qed.
Lemma and_wlog_r (P Q : Prop) : P (P Q) (P Q).
Proof. tauto. Qed.
Instance: A B (x : B), Commutative (=) (λ _ _ : A, x). Instance: A B (x : B), Commutative (=) (λ _ _ : A, x).
Proof. red. trivial. Qed. Proof. red. trivial. Qed.
Instance: A (x : A), Associative (=) (λ _ _ : A, x). Instance: A (x : A), Associative (=) (λ _ _ : A, x).
......
...@@ -35,6 +35,10 @@ Section simple_collection. ...@@ -35,6 +35,10 @@ Section simple_collection.
Qed. Qed.
Lemma collection_positive_l_alt X Y : X X Y . Lemma collection_positive_l_alt X Y : X X Y .
Proof. eauto using collection_positive_l. Qed. Proof. eauto using collection_positive_l. Qed.
Lemma elem_of_singleton_1 x y : x {[y]} x = y.
Proof. by rewrite elem_of_singleton. Qed.
Lemma elem_of_singleton_2 x y : x = y x {[y]}.
Proof. by rewrite elem_of_singleton. Qed.
Lemma elem_of_subseteq_singleton x X : x X {[ x ]} X. Lemma elem_of_subseteq_singleton x X : x X {[ x ]} X.
Proof. Proof.
split. split.
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...@@ -264,7 +264,11 @@ Arguments Z.modulo _ _ : simpl never. ...@@ -264,7 +264,11 @@ Arguments Z.modulo _ _ : simpl never.
Arguments Z.quot _ _ : simpl never. Arguments Z.quot _ _ : simpl never.
Arguments Z.rem _ _ : simpl never. Arguments Z.rem _ _ : simpl never.
Lemma Z_mod_pos a b : 0 < b 0 a `mod` b. Lemma Z_to_nat_neq_0_pos x : Z.to_nat x 0%nat 0 < x.
Proof. by destruct x. Qed.
Lemma Z_to_nat_neq_0_nonneg x : Z.to_nat x 0%nat 0 x.
Proof. by destruct x. Qed.
Lemma Z_mod_pos x y : 0 < y 0 x `mod` y.
Proof. apply Z.mod_pos_bound. Qed. Proof. apply Z.mod_pos_bound. Qed.
Hint Resolve Z.lt_le_incl : zpos. Hint Resolve Z.lt_le_incl : zpos.
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