
theorem
  <*TRUE*> + <*TRUE*> = <*FALSE*>
proof
A1: add_ovfl(<*TRUE*>,<*TRUE*>) = TRUE by Th13;
  Absval(<*TRUE*> + <*TRUE*>) = Absval(<*TRUE*> + <*TRUE*>) + 2 - 2
    .= Absval(<*TRUE*> + <*TRUE*>) + 2 to_power 1 - 2 by POWER:25
    .= Absval(<*TRUE*> + <*TRUE*>) + IFEQ(add_ovfl(<*TRUE*>,<*TRUE*>), FALSE
  ,0,2 to_power (1)) - 2 by A1,FUNCOP_1:def 8
    .= Absval <*TRUE*> + Absval <*TRUE*> - 2 by BINARITH:21
    .= Absval <*TRUE*> + 1 - 2 by BINARITH:16
    .= 1 + 1 - 2 by BINARITH:16
    .= Absval <*FALSE*> by BINARITH:15;
  hence thesis by Th2;
end;
