reserve x for object;
reserve D for set;
reserve p for PartialPredicate of D;
reserve D for non empty set;
reserve p,q,r for PartialPredicate of D;

theorem Th10:
  x in dom PP_or(p,q) & PP_or(p,q).x = TRUE implies
   x in dom p & p.x = TRUE or x in dom q & q.x = TRUE
  proof
    assume x in dom PP_or(p,q);
    then x in dom p & p.x = TRUE or x in dom q & q.x = TRUE
    or x in dom p & p.x = FALSE & x in dom q & q.x = FALSE by Th8;
    hence thesis by Th9;
  end;
