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}.

Lemma alist_find_remove_none:
forall (m : list (K*V)) (k1 k2 : K), k2 <> k1 -> alist_find k1 (alist_remove k2 m) = None -> alist_find k1 m = None.