(* end semLiftGen4SizeMonotonic *)
Program Instance liftGen4Monotonic {A B C D E}
(f : A -> B -> C -> D -> E)
(g1 : G A) (g2 : G B) (g3 : G C) (g4 : G D)
`{ SizeMonotonic _ g1} `{ SizeMonotonic _ g2}
`{ SizeMonotonic _ g3} `{ SizeMonotonic _ g4}
: SizeMonotonic (liftGen4 f g1 g2 g3 g4).
Next Obligation.
rewrite ! semLiftGen4Size.
move => t /= [a1 [a2 [a3 [a4 [Ha1 [Ha2 [Ha3 [Ha4 H5]]]]]]]]; subst.
eexists. eexists. eexists. eexists.
repeat (split; try reflexivity); by eapply monotonic; eauto.
Qed.

Lemma semVectorOfSize {A : Type} (k : nat) (g : G A) n :
semGenSize (vectorOf k g) n <-->
[set l | length l = k /\ l \subset (semGenSize g n)].