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 Th17:
  [.a,b.] = (b * a)" * (a * b)
proof
  thus [.a,b.] = (a" * b") * (a * b) by Th16
    .= (b * a)" * (a * b) by GROUP_1:17;
end;
