Axiom
  typest_writing :
    forall t t' : type,
    typest t t' -> capst (getcap t') Write -> typest (getobj t') (getobj t).Axiom
  typest_reading :
    forall t t' : type,
    typest t t' -> capst (getcap t') Read -> typest (getobj t) (getobj t').Axiom
  typest_tail :
    forall t t' : type, typest t t' -> capst (getcap t) (getcap t').

Theorem subs_typing : forall (G : env) (P : proc), typing G P -> forall p q : PP, typest (G p) (G q) -> typing G (subs_par_proc P (pname p) q).