Section AllAnd.
Variables (T : Type) (P1 P2 P3 P4 P5 : T -> Prop).
Local Notation a P := (forall x, P x).
End RelationProperties.

Lemma subon_bij (D2' : pred T2) :
{subset D2 <= D2'} -> {on D2', bijective f} -> {on D2, bijective f}.