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

theorem Th2:
  for u1 be Element of n-tuples_on BOOLEAN holds Op-XOR(u1,ZeroB n) = u1
proof
  let u1 be Element of n-tuples_on BOOLEAN;
A1: len Op-XOR(u1,ZeroB n) = n by Lm1;
A2: len u1 = n by Lm1;
  now let i be Nat;
    assume 1 <= i & i <= len Op-XOR(u1,ZeroB n);
    then
A3: i in Seg n by A1;
    thus (Op-XOR(u1,ZeroB n)).i
    = u1.i 'xor' (ZeroB n).i by DESCIP_1:def 4,A3
    .= u1.i 'xor' FALSE
    .= u1.i;
  end;
  hence thesis by Lm1,A2,FINSEQ_1:14;
end;
