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
  for G being strict trivial Group holds (1).G = G
proof
  let G be strict trivial Group;
  card G = 1 by Th11;
  then card G = card (1).G by GROUP_2:69;
  hence thesis by GROUP_2:73;
end;
