Definition RndPerm(n : nat) :=
  shuffle _ (allNatsLt n).

Theorem addInAllLocations_pred : forall (A B : Set) (R : A -> B -> Prop) (a : list A) (b : list B), list_pred R a b -> forall a1 a2, R a1 a2 -> list_pred (list_pred R) (addInAllLocations a1 a) (addInAllLocations a2 b).