Definition pred_oapp T (D : {pred T}) : pred (option T) :=
  [pred x | oapp (mem D) false x].

Lemma sub_in21 T T3 d d' d3 d3' (P : T -> T -> T3 -> Prop) : sub_mem d d' -> sub_mem d3 d3' -> forall Ph : ph {all3 P}, prop_in21 d' d3' Ph -> prop_in21 d d3 Ph.