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

Lemma subp_imp {A} {NA: NatDed A}{IA: Indir A}{RA: RecIndir A}  : forall G (P P' Q Q' : A),
G |-- P' >=> P ->
G |-- Q >=> Q' ->
G |-- (P --> Q) >=> (P' --> Q').