reserve m,n,s for non zero Element of NAT;

theorem Th3:
  for u1 be Element of n-tuples_on BOOLEAN holds Op-XOR(u1,u1) = ZeroB n
proof
  let u1 be Element of n-tuples_on BOOLEAN;
A1: len Op-XOR(u1,u1) = n by Lm1;
A2: len ZeroB n = n by Lm1;
  now let i be Nat;
    assume 1 <= i & i <= len Op-XOR(u1,u1); then
A3: i in Seg n by A1;
    thus (Op-XOR(u1,u1)).i = u1.i 'xor' u1.i by DESCIP_1:def 4,A3
    .= FALSE by XBOOLEAN:147
    .= (ZeroB n).i;
  end;
  hence thesis by Lm1,A2,FINSEQ_1:14;
end;
