
theorem
  <*FALSE*> + <*FALSE*> = <*FALSE*>
proof
  add_ovfl(<*FALSE*>,<*FALSE*>) <> TRUE by Th13;
  then add_ovfl(<*FALSE*>,<*FALSE*>) = FALSE by XBOOLEAN:def 3;
  then <*FALSE*>,<*FALSE*> are_summable by BINARITH:def 7;
  then Absval(<*FALSE*> + <*FALSE*>) = Absval <*FALSE*> + Absval <*FALSE*> by
BINARITH:22
    .= Absval <*FALSE*> + 0 by BINARITH:15
    .= Absval <*FALSE*>;
  hence thesis by Th2;
end;
