Section alistFacts.
(* Generic facts about alists. To eventually move to ExtLib. *)
Arguments alist_find {_ _ _ _}.
Definition alist_In {K R RD V} k m v := @alist_find K R RD V k m = Some v.
Arguments alist_add {_ _ _ _}.
Arguments alist_find {_ _ _ _}.
Arguments alist_remove {_ _ _ _}.
Context {K V: Type}.
Context {RR : @RelDec K (@eq K)}.
Context {RRC : @RelDec_Correct K (@eq K) RR}.

(* A removed key is not contained in the resulting map *)
Lemma not_In_remove:
forall (m : alist K V) (k : K) (v: V),
~ alist_In k (alist_remove k m) v.