Definition inPhantom := Phantom Prop.Definition onPhantom T P (x : T) := Phantom Prop (P x).Definition bijective_in aT rT (d : mem_pred aT) (f : aT -> rT) :=
  exists2 g, prop_in1 d (inPhantom (cancel f g))
           & prop_on1 d (Phantom _ (cancel g)) (onPhantom (cancel g) f).Definition bijective_on aT rT (cd : mem_pred rT) (f : aT -> rT) :=
  exists2 g, prop_on1 cd (Phantom _ (cancel f)) (onPhantom (cancel f) g)
           & prop_in1 cd (inPhantom (cancel g f)).

Lemma subon1 (Phf : ph (allQ1 f)) (Ph : ph (allQ1 f)) : prop_on1 d2' Phf Ph -> prop_on1 d2 Phf Ph.