
theorem
  for x,y,z being Element of BOOLEAN holds inv1.<* xor2.<* xor2c.<*x,y*>
  , z*> *> = xor2c.<* xor2c.<*x,y*>, z*>
proof
  let x,y,z be Element of BOOLEAN;
  thus inv1.<* xor2.<* xor2c.<*x,y*>, z*> *> = inv1.<* xor2.<* x 'xor' 'not' y
  , z *> *> by Def4
    .= inv1.<* ( x 'xor' 'not' y ) 'xor' z *> by FACIRC_1:def 4
    .= 'not' ( ( x 'xor' 'not' y ) 'xor' z ) by Def1
    .= ( x 'xor' 'not' y ) 'xor' 'not' z by XBOOLEAN:74
    .= xor2c.<* x 'xor' 'not' y, z *> by Def4
    .= xor2c.<* xor2c.<*x,y*>, z *> by Def4;
end;
