Section FinMapKeyType.
Variables (K V : choiceType).
Implicit Types (f g : {fmap K -> V}).
Definition codomf f : {fset V} := [fset f k | k : domf f].

Lemma codomf_rem_exists f (A : {fset K})  :
codomf f.[\ A] = [fset v in codomf f
| [exists k : domf f, (val k \notin A) && (f k == v)]].