(***** subtyping and contractiveness -- should split this into a separate file ******)

Lemma allp_imp2_later_e2 {B}{A}{NA: NatDed A}{IA: Indir A}{RA: RecIndir A}:
forall (P Q: B -> A) (y: B) ,
(ALL x:B, |> P x <=> |> Q x) |-- |> Q y >=> |> P y.