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
  Gc=gr{g} implies for G,f holds g in Image f implies f is onto
proof
  assume
A1: Gc=gr {g};
  let G,f;
  assume g in Image f;
  then Image f = Gc by A1,Th13;
  hence thesis by GROUP_6:57;
end;
