reserve x,y for set,
  k,n for Nat,
  i for Integer,
  G for Group,
  a,b,c ,d,e for Element of G,
  A,B,C,D for Subset of G,
  H,H1,H2,H3,H4 for Subgroup of G ,
  N1,N2 for normal Subgroup of G,
  F,F1,F2 for FinSequence of the carrier of G,
  I,I1,I2 for FinSequence of INT;

theorem Th3:
  for N being strict normal Subgroup of G holds a in N implies a |^ b in N
proof
  let N be strict normal Subgroup of G;
  assume a in N;
  then a |^ b in N |^ b by GROUP_3:58;
  hence thesis by GROUP_3:def 13;
end;
