Section MapFacts.
Variables (K V : Type).
Context {map : Type}.
Context {M : Map K V map}.
Context {MOk: MapOk eq M}.
Context {Kdec: @RelDec K eq}.
Context {KdecOk: RelDec_Correct Kdec}.

(* Should move to extlib *)
Lemma lookup_remove_neq:
forall k k' s, k <> k' -> lookup k (remove k' s) = lookup k s.