 reserve I for non empty set;
 reserve i for Element of I;
 reserve F for Group-Family of I;
 reserve G for Group;
reserve S for Subgroup-Family of F;
reserve f for Homomorphism-Family of G, F;

theorem ThNorm:
  for N being normal Subgroup of G
  for a,b being Element of G
  st a in N holds a |^ b in N
proof
  let N be normal Subgroup of G;
  let a,b be Element of G;
  assume a in N;
  then a |^ b in N |^ b by GROUP_3:58;
  then a |^ b in the multMagma of N by GROUP_3:def 13;
  hence a |^ b in N;
end;
