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 Th20:
  [.a,a.] = 1_G
proof
  thus [.a,a.] = (a * a)" * (a * a) by Th17
    .= 1_G by GROUP_1:def 5;
end;
