reserve n for Element of NAT;
reserve i for Integer;
reserve G,H,I for Group;
reserve A,B for Subgroup of G;
reserve N for normal Subgroup of G;
reserve a,a1,a2,a3,b,b1 for Element of G;
reserve c,d for Element of H;
reserve f for Function of the carrier of G, the carrier of H;
reserve x,y,y1,y2,z for set;
reserve A1,A2 for Subset of G;

theorem Th4:
  a * b * a" = b |^ a" & a * (b * a") = b |^ a"
proof
  thus a * b * a" = a"" * b * a" .= b |^ a" by GROUP_3:def 2;
  hence thesis by GROUP_1:def 3;
end;
