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}.

(* alist_find fails iff no value is associated to the key in the map *)
Lemma alist_find_None:
forall k (m: alist K V),
(forall v, ~ In (k,v) m) <-> alist_find k m = None.