Program Instance listOfMonotonic {A} (g : G A)
`{SizeMonotonic _ g } : SizeMonotonic (listOf g).
Next Obligation.
rewrite ! semListOfSize.
move => l [H1 H2]; split => //. by eapply leq_trans; eauto.
move => a /H2 Ha. by eapply monotonic; eauto.
Qed.

Lemma nth_imset T (def : T) l : nth def l @: [set n | n < length l] <--> l.