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Remove `map` infix in lemmas about `dom` and `filter`.

Merged Robbert Krebbers requested to merge robbert/dom_filter into master
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@@ -21,14 +21,14 @@ Lemma lookup_lookup_total_dom `{!Inhabited A} (m : M A) i :
i dom D m m !! i = Some (m !!! i).
Proof. rewrite elem_of_dom. apply lookup_lookup_total. Qed.
Lemma dom_map_filter {A} (P : K * A Prop) `{!∀ x, Decision (P x)} (m : M A) X :
Lemma dom_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):
Lemma dom_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.
@@ -156,10 +156,10 @@ Proof. intros ???. unfold_leibniz. by apply dom_proper. Qed.
Section leibniz.
Context `{!LeibnizEquiv D}.
Lemma dom_map_filter_L {A} (P : K * A Prop) `{!∀ x, Decision (P x)} (m : M A) X :
Lemma dom_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.
Proof. unfold_leibniz. apply dom_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 = ∅.
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