
theorem Th1:
  for x being Element of BOOLEAN holds inv1.<*x*> = 'not' x & inv1.
  <*x*> = nand2.<*x,x*> & inv1.<*0*> = 1 & inv1.<*1*> = 0
proof
  let x be Element of BOOLEAN;
  thus inv1.<*x*> = 'not' x by Def1;
  thus inv1.<*x*> = 'not' ( x '&' x ) by Def1
    .= nand2.<*x,x*> by TWOSCOMP:def 4;
  thus inv1.<*0*> = 'not' FALSE by Def1
    .= 1;
  thus inv1.<*1*> = 'not' TRUE by Def1
    .= 0;
end;
