 reserve G, A for Group;
 reserve phi for Homomorphism of A,AutGroup(G);
 reserve G, A for Group;
 reserve phi for Homomorphism of A,AutGroup(G);
reserve G1,G2 for Group;

theorem Th82: :: TH82
  for g being Element of INT.Group 2
  st g = 1
  holds g * g = 1_(INT.Group 2)
proof
  let g be Element of INT.Group 2;
  assume A1: g = 1;
  g in the carrier of INT.Group 2;
  then A2: 1 in Segm 2 by A1,Th76;
  thus g * g = (addint 2).(g,g) by Th75
            .= (1 + 1) mod 2 by A1, A2, GR_CY_1:def 4
            .= (2 * 1) mod 2
            .= 0 by NAT_D:13
            .= 1_(INT.Group 2) by GR_CY_1:14;
end;
