Merge branch 'robbert/map_filter' into 'master'

More lemmas for `filter` w.r.t. maps

See merge request !96

CHANGELOG.md

 This file lists "large-ish" changes to the std++ Coq library, but not every
 API-breaking change is listed.
 
+## std++ master
+
+- Rename `dom_map_filter` into `dom_map_filter_subseteq` and repurpose
+  `dom_map_filter` for the version with the equality. This follows the naming
+  convention for similar lemmas.
+
 ## std++ 1.2.1 (released 2019-08-29)
 
 This release of std++ received contributions by Dan Frumin, Michael Sammler,

theories/fin_map_dom.v

@@ -19,7 +19,14 @@ Class FinMapDom K M D `{∀ A, Dom (M A) D, FMap M,
 Section fin_map_dom.
 Context `{FinMapDom K M D}.
 
-Lemma dom_map_filter {A} (P : K * A → Prop) `{!∀ x, Decision (P x)} (m : M A):
+Lemma dom_map_filter {A} (P : K * A → Prop) `{!∀ x, Decision (P x)} (m : M A) X :
+  (∀ i, i ∈ X ↔ ∃ x, m !! i = Some x ∧ P (i, x)) →
+  dom D (filter P m) ≡ X.
+Proof.
+  intros HX i. rewrite elem_of_dom, HX.
+  unfold is_Some. by setoid_rewrite map_filter_lookup_Some.
+Qed.
+Lemma dom_map_filter_subseteq {A} (P : K * A → Prop) `{!∀ x, Decision (P x)} (m : M A):
   dom D (filter P m) ⊆ dom D m.
 Proof.
   intros ?. rewrite 2!elem_of_dom.
@@ -132,6 +139,10 @@ Global Instance dom_proper_L `{!Equiv A, !LeibnizEquiv D} :
 Proof. intros ???. unfold_leibniz. by apply dom_proper. Qed.
 
 Context `{!LeibnizEquiv D}.
+Lemma dom_map_filter_L {A} (P : K * A → Prop) `{!∀ x, Decision (P x)} (m : M A) X :
+  (∀ i, i ∈ X ↔ ∃ x, m !! i = Some x ∧ P (i, x)) →
+  dom D (filter P m) = X.
+Proof. unfold_leibniz. apply dom_map_filter. Qed.
 Lemma dom_empty_L {A} : dom D (@empty (M A) _) = ∅.
 Proof. unfold_leibniz; apply dom_empty. Qed.
 Lemma dom_empty_inv_L {A} (m : M A) : dom D m = ∅ → m = ∅.

theories/fin_maps.v

@@ -1507,6 +1507,12 @@ Proof.
 Qed.
 Lemma map_disjoint_delete_r {A} (m1 m2 : M A) i : m1 ##ₘ m2 → m1 ##ₘ delete i m2.
 Proof. symmetry. by apply map_disjoint_delete_l. Qed.
+Lemma map_disjoint_filter {A} (P : K * A → Prop) `{!∀ x, Decision (P x)} (m : M A) :
+  filter P m ##ₘ filter (λ v, ¬ P v) m.
+Proof.
+  apply map_disjoint_spec. intros i x y.
+  rewrite !map_filter_lookup_Some. naive_solver.
+Qed.
 
 (** ** Properties of the [union_with] operation *)
 Section union_with.
@@ -1783,6 +1789,13 @@ Proof.
   naive_solver eauto using map_Forall_union_11,
     map_Forall_union_12, map_Forall_union_2.
 Qed.
+Lemma map_union_filter {A} (P : K * A → Prop) `{!∀ x, Decision (P x)} (m : M A) :
+  filter P m ∪ filter (λ v, ¬ P v) m = m.
+Proof.
+  apply map_eq; intros i. apply option_eq; intros x.
+  rewrite lookup_union_Some, !map_filter_lookup_Some by apply map_disjoint_filter.
+  destruct (decide (P (i,x))); naive_solver.
+Qed.
 
 (** ** Properties of the [union_list] operation *)
 Lemma map_disjoint_union_list_l {A} (ms : list (M A)) (m : M A) :