Commit e18f9a7d authored by Robbert Krebbers's avatar Robbert Krebbers
Browse files

Lemmas for `map_kmap` and disjointness and subsets.

parent cfdafacf
......@@ -2666,6 +2666,20 @@ Section map_kmap.
Lemma map_kmap_fmap {A B} (g : A B) (m : M1 A) :
map_kmap f (g <$> m) = g <$> (map_kmap f m).
Proof. by rewrite !map_fmap_alt, map_kmap_omap. Qed.
Lemma map_disjoint_kmap {A} (m1 m2 : M1 A) :
map_kmap f m1 ## map_kmap f m2 m1 ## m2.
Proof.
rewrite !map_disjoint_spec. setoid_rewrite lookup_map_kmap_Some. naive_solver.
Qed.
Lemma map_disjoint_subseteq {A} (m1 m2 : M1 A) :
map_kmap f m1 map_kmap f m2 m1 m2.
Proof.
rewrite !map_subseteq_spec. setoid_rewrite lookup_map_kmap_Some. naive_solver.
Qed.
Lemma map_disjoint_subset {A} (m1 m2 : M1 A) :
map_kmap f m1 map_kmap f m2 m1 m2.
Proof. unfold strict. by rewrite !map_disjoint_subseteq. Qed.
End map_kmap.
(** * Tactics *)
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