Section Cat.
Variables (K : choiceType) (V : Type).
Implicit Types (f g : {fmap K -> V}).
Definition catf (f g : {fmap K -> V}) :=
[fmap k : (domf f `\` domf g) `|` domf g=>
match fsetULVR (valP k) with
| inl kfDg => f.[fsubsetP (fsubsetDl _ _) _ kfDg]
| inr kg => g.[kg]
end].
Local Notation "f + g" := (catf f g) : fset_scope.

Lemma catf_setl f g k (v : V) :
f.[k <- v] + g = if k \in g then f + g else (f + g).[k <- v].