reserve x,y,y1,y2 for set;
reserve G for Group;
reserve a,b,c,d,g,h for Element of G;
reserve A,B,C,D for Subset of G;
reserve H,H1,H2,H3 for Subgroup of G;
reserve n for Nat;
reserve i for Integer;

theorem Th69:
  for G being Group, a being Element of G holds (Omega).G |^ a = (Omega).G
proof
  let G be Group, a be Element of G;
  let h be Element of G;
  (h |^ a") |^ a = h |^ (a" * a) by Th24
    .= h |^ 1_G by GROUP_1:def 5
    .= h by Th19;
  hence thesis by Th58,STRUCT_0:def 5;
end;
