Commit 498fe5f9 by Robbert Krebbers

### Bit of clean up.

parent 1cbda487
Pipeline #13181 passed with stage
in 7 minutes and 44 seconds
 ... ... @@ -1032,7 +1032,7 @@ Proof. Qed. (** ** The filter operation *) Section map_Filter. Section map_filter. Context {A} (P : K * A → Prop) `{!∀ x, Decision (P x)}. Implicit Types m : M A. ... ... @@ -1085,7 +1085,7 @@ Section map_Filter. Lemma map_filter_empty : filter P (∅ : M A) = ∅. Proof. apply map_fold_empty. Qed. End map_Filter. End map_filter. (** ** Properties of the [map_Forall] predicate *) Section map_Forall. ... ... @@ -1521,19 +1521,16 @@ Proof. Qed. Global Instance: IdemP (=@{M A}) (∪). Proof. intros A ?. by apply union_with_idemp. Qed. Lemma lookup_union {A} (m1 m2 : M A) i : (m1 ∪ m2) !! i = union_with (λ x _, Some x) (m1 !! i) (m2 !! i). Proof. apply lookup_union_with. Qed. Lemma lookup_union_Some_raw {A} (m1 m2 : M A) i x : (m1 ∪ m2) !! i = Some x ↔ m1 !! i = Some x ∨ (m1 !! i = None ∧ m2 !! i = Some x). Proof. unfold union, map_union, union_with, map_union_with. rewrite (lookup_merge _). destruct (m1 !! i), (m2 !! i); compute; intuition congruence. Qed. Proof. rewrite lookup_union. destruct (m1 !! i), (m2 !! i); naive_solver. Qed. Lemma lookup_union_None {A} (m1 m2 : M A) i : (m1 ∪ m2) !! i = None ↔ m1 !! i = None ∧ m2 !! i = None. Proof. unfold union, map_union, union_with, map_union_with. rewrite (lookup_merge _). destruct (m1 !! i), (m2 !! i); compute; intuition congruence. Qed. Proof. rewrite lookup_union. destruct (m1 !! i), (m2 !! i); naive_solver. Qed. Lemma map_positive_l {A} (m1 m2 : M A) : m1 ∪ m2 = ∅ → m1 = ∅. Proof. intros Hm. apply map_empty. intros i. apply (f_equal (!! i)) in Hm. ... ...
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