reserve n for non zero Nat,
  j,k,l,m for Nat,
  g,h,i for Integer;

theorem Th30:
  for l,m be Nat st l mod 2 to_power n = m mod 2 to_power n holds
  n-BinarySequence(l) = n-BinarySequence(m)
proof
  let l,m be Nat such that
A1: l mod 2 to_power n = m mod 2 to_power n;
  |.m.| = m by ABSVALUE:def 1;
  then
A2: 2sComplement(n,m) = n-BinarySequence(m) by Def2;
  |.l.| = l by ABSVALUE:def 1;
  then 2sComplement(n,l) = n-BinarySequence(l) by Def2;
  hence thesis by A1,A2,Lm5;
end;
