 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 ThMultTableINTGroup2: :: TH84
  for x,y being Element of INT.Group 2
  holds (x = 0 implies x*y = y)
  & (y = 0 implies x*y = x)
  & (x = 1 & y = 1 implies x*y = 1_(INT.Group 2))
proof
  let x,y be Element of INT.Group 2;
  thus x = 0 implies x*y = y
  proof
    assume x = 0;
    then x = 1_(INT.Group 2) by GR_CY_1:14;
    hence x*y = y by GROUP_1:def 4;
  end;
  thus y = 0 implies x*y = x
  proof
    assume y = 0;
    then y = 1_(INT.Group 2) by GR_CY_1:14;
    hence x*y = x by GROUP_1:def 4;
  end;
  assume x = 1 & y = 1;
  hence thesis by Th82;
end;
