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 Th7:
  [.a,b",c.] |^ b  = [.b,a,c|^ b.]
proof
  [.a,b",c.] |^ b = [.[.a,b".]|^ b,c|^ b.] by Th5;
  hence thesis by Th6;
end;
