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

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