reserve x,y for set,
  G for Group,
  A,B,H,H1,H2 for Subgroup of G,
  a,b,c for Element of G,
  F,F1 for FinSequence of the carrier of G,
  I,I1 for FinSequence of INT,
  i,j for Element of NAT;

theorem
   [.a,b,c|^ a.]  * [.c,a,b|^ c.]  * [.b,c,a|^ b.] = 1_G
proof
  [.a,b,c|^ a.] = [.b,a",c.]|^ a & [.c,a,b|^ c.] = [.a,c",b.]|^ c &
  [.b,c,a|^ b.] = [.c,b",a.]|^b by Th7;
  hence thesis by GROUP_5:46;
end;
