Commit 16da535d authored by Robbert Krebbers's avatar Robbert Krebbers

Equality lemma for `dom D (filter P m)`.

parent 8e97f83a
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,
......
......@@ -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 = .
......
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