reserve a,b,p,k,l,m,n,s,h,i,j,t,i1,i2 for natural Number;

theorem
  for m,n be Integer holds (m mod n) mod n = m mod n
proof
  let m,n be Integer;
  m mod n = (m + 0) mod n .= ((m mod n) + (0 mod n)) mod n by Th66
  .= ((m mod n) + 0) mod n by INT_1:73;
  hence thesis;
end;
