Definition fincl A B (AsubB : A `<=` B) (a : A) : B :=
[` (fsubsetP AsubB) _ (valP a)].
Definition fsub B A : {set B} := [set x : B | val x \in A].

Lemma fsetUidPl A B : reflect (A `|` B = A) (B `<=` A).
Hint Resolve fsub_inj.