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}.

(* Adding a value to a key does not alter other keys *)
Lemma In_In_add_ineq:
forall k v k' v' (m: alist K V),
k <> k' ->
alist_In k m v ->
alist_In k (alist_add k' v' m) v.