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

Lemma subp_andp {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').