reserve x for object;
reserve n for Nat;
reserve D for non empty set;
reserve p,q for PartialPredicate of D;
reserve D for set;
reserve p,q for PartialPredicate of D;
reserve f,g for BinominativeFunction of D;

theorem
  x in dom(PP_prediction(f,p)) implies
   x in dom(p*f) & ((p*f).x = TRUE or (p*f).x = FALSE)
  proof
    assume x in dom(PP_prediction(f,p));
    then x in dom(p*f) by D1;
    hence thesis by PARTPR_1:3;
  end;
