reserve x,y,X,Y for set,
  k,l,n for Nat,
  i,i1,i2,i3,j for Integer,
  G for Group,
  a,b,c,d for Element of G,
  A,B,C for Subset of G,
  H,H1,H2, H3 for Subgroup of G,
  h for Element of H,
  F,F1,F2 for FinSequence of the carrier of G,
  I,I1,I2 for FinSequence of INT;

theorem
  for N1,N2 being strict normal Subgroup of G holds N1 "\/" N2 is normal
  Subgroup of G
proof
  let N1,N2 be strict normal Subgroup of G;
  (ex N being strict normal Subgroup of G st the carrier of N = carr N1 *
  carr N2 )& the carrier of N1 "\/" N2 = N1 * N2 by Th53,GROUP_3:126;
  hence thesis by GROUP_2:59;
end;
