
theorem
  for x,y,z being Element of BOOLEAN holds inv1.<* xor2c.<* xor2b.<*x,y
  *>, z*> *> = xor2.<* xor2.<*x,y*>, z*>
proof
  let x,y,z be Element of BOOLEAN;
  thus inv1.<* xor2c.<* xor2b.<*x,y*>, z*> *> = inv1.<* xor2c.<* 'not' x 'xor'
  'not' y, z *> *> by TWOSCOMP:def 15
    .= inv1.<* ( 'not' x 'xor' 'not' y ) 'xor' 'not' z *> by Def4
    .= 'not' ( ( 'not' x 'xor' 'not' y ) 'xor' 'not' z ) by Def1
    .= ( x 'xor' y ) 'xor' z by XBOOLEAN:74
    .= xor2.<* x 'xor' y, z *> by FACIRC_1:def 4
    .= xor2.<* xor2.<*x,y*>, z *> by FACIRC_1:def 4;
end;
