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 type_with_other_subs : forall (G : env) (P : proc) (p q : PP) (x : VV) (t : type), fresh p P -> fresh q P -> typing (addenv G p t) (subs_var_proc P (pname p) x) -> typing (addenv G q t) (subs_var_proc P (pname q) x).