reserve F,G for Group;
reserve G1 for Subgroup of G;
reserve Gc for cyclic Group;
reserve H for Subgroup of Gc;
reserve f for Homomorphism of G,Gc;
reserve a,b for Element of G;
reserve g for Element of Gc;
reserve a1 for Element of G1;
reserve k,m,n,p,s for Element of NAT;
reserve i0,i,i1,i2 for Integer;
reserve j,j1 for Element of INT.Group;
reserve x,y,t for set;

theorem Th2:
  a in gr {a}
proof
  ex i st a=a|^i
  proof
    reconsider i=1 as Integer;
    take i;
    thus thesis by GROUP_1:26;
  end;
  hence thesis by GR_CY_1:5;
end;
