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 Th24:
  x in dom p & x in dom q & PP_and(p,q).x = FALSE implies
   p.x = FALSE or q.x = FALSE
  proof
    assume that
A1: x in dom p and
A2: x in dom q and
A3: PP_and(p,q).x = FALSE;
    p.x <> TRUE or q.x <> TRUE by A1,A2,A3,Th18;
    hence p.x = FALSE or q.x = FALSE by A1,A2,Th3;
  end;
