reserve x for set;
reserve i,j for Integer;
reserve n,n1,n2,n3 for Nat;
reserve p for Prime;
reserve a,b,c,d for Element of GF(p);
reserve K for Ring;
reserve a1,a2,a3,a4,a5,a6 for Element of K;

theorem
  for p be Prime, n be Nat, g2, g3 be Element of GF(p) st p > 3 &
  g3 = 3 mod p holds g3 <> 0.GF(p) & g3 |^n <> 0.GF(p)
  proof
    let p be Prime, n be Nat, g2, g3 be Element of GF(p) such that
    A1: p > 3;
    assume A2: g3 = 3 mod p;
    A3: g3 <> 0 by A1,A2,NAT_D:63;
    hence g3 <> 0.GF(p) by EC_PF_1:11;
    g3 |^n <> 0 by A3,EC_PF_1:25;
    hence g3 |^n <> 0.GF(p) by EC_PF_1:11;
  end;
