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

Lemma sub_in2 T d d' (P : T -> T -> Prop) :
sub_mem d d' -> forall Ph : ph {all2 P}, prop_in2 d' Ph -> prop_in2 d Ph.