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 Th7:
  for N1,N2 being strict normal Subgroup of G holds x in N1 "\/" N2
  iff ex a,b st x = a * b & a in N1 & b in N2
proof
  let N1,N2 be strict normal Subgroup of G;
  N1 * N2 = N2 * N1 by GROUP_3:125;
  hence thesis by Th5;
end;
