theorem Th18:
  for gi, gj, gij, a be Element of GF(p) st
  gi = i mod p & gj = j mod p & gij = (i+j) mod p holds
  gi*a + gj*a = gij*a
  proof
    let gi, gj, gij, a be Element of GF(p) such that
A1: gi = i mod p & gj = j mod p & gij = (i+j) mod p;
    (gi + gj) * a = gij*a by A1,EC_PF_1:15;
    hence thesis by VECTSP_1:def 7;
  end;
