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

theorem
  for i being Integer, n being Nat holds (i*n) mod n = 0
proof
  let i be Integer, n be Nat;
  (i*n) mod n = ((i mod n) * (n mod n)) mod n by Th67
    .= ((i mod n) * 0) mod n by Th25
    .= 0 mod n;
  hence thesis by Th26;
end;
