Commit 41df24bf authored by Michael Sammler's avatar Michael Sammler
Browse files

Add list_to_map_app

parent 59911631
......@@ -2227,7 +2227,14 @@ Lemma foldr_delete_union {A} (m1 m2 : M A) is :
foldr delete (m1 m2) is = foldr delete m1 is foldr delete m2 is.
Proof. apply foldr_delete_union_with. Qed.
(** ** Properties on disjointness of conversion to lists *)
(** ** Properties on conversion to lists that depend on [∪] and [##ₘ] *)
Lemma list_to_map_app {A} (l1 l2 : list (K * A)):
list_to_map (l1 ++ l2) =@{M A} list_to_map l1 list_to_map l2.
Proof.
induction l1 as [|[??] ? IH]; simpl.
{ by rewrite (left_id _ _). }
by rewrite IH, insert_union_l.
Qed.
Lemma map_disjoint_list_to_map_l {A} (m : M A) ixs :
list_to_map ixs ## m Forall (λ ix, m !! ix.1 = None) ixs.
Proof.
......
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