reserve x for object;
reserve D for set;
reserve p for PartialPredicate of D;

theorem Th4:
  x in dom p & PP_not(p).x = FALSE implies p.x = TRUE
  proof
    assume that
A1: x in dom p and
A2: PP_not(p).x = FALSE;
    assume p.x <> TRUE;
    then p.x = FALSE by A1,Th3;
    hence thesis by A1,A2,Def2;
  end;
