theorem
  F is associative & F is having_a_unity & e = the_unity_wrt F &
  F is having_an_inverseOp & G is_distributive_wrt F implies
    G[;](e,T) = i|->e
proof
  assume
A1: F is associative & F is having_a_unity & e = the_unity_wrt F & F is
  having_an_inverseOp & G is_distributive_wrt F;
  per cases;
  suppose
A2: i = 0;
    then G[;](e,T) = <*>D by Lm2;
    hence thesis by A2;
  end;
  suppose
    i <> 0;
    then reconsider C = Seg i as non empty set;
    T is Function of C,D by Lm4;
    hence thesis by A1,Th75;
  end;
end;
