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 Th69:
  [.N1,N2.] = [.N2,N1.]
proof
  [.N1,N2.] is Subgroup of [.N2,N1.] & [.N2,N1.] is Subgroup of [.N1,N2.]
  by Lm2;
  hence thesis by GROUP_2:55;
end;
