theorem Th22:
  for gi, gj, a be Element of GF(p) st
  gi = i mod p & gj = j mod p & i = j + 1 holds
  gi*a - gj*a = a
  proof
    let gi, gj, a be Element of GF(p) such that
    A1: gi = i mod p & gj = j mod p & i = j + 1;
    reconsider g1 = 1 mod p as Element of GF(p) by EC_PF_1:14;
    A2: g1 = (i-j) mod p by A1;
    p > 1 by INT_2:def 4;
    then g1 = 1 by NAT_D:63
    .= 1.GF(p) by EC_PF_1:12;
    then gi*a - gj*a = (1.GF(p))*a by A1,A2,Th21;
    hence thesis;
  end;
