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 fsetDSS A B C D : A `<=` C -> D `<=` B -> A `\` B `<=` C `\` D.
Hint Resolve fsubsetIl fsubsetIr fsubsetDl fsubD1set.