theorem
  Hom(T,x,x) = id the Sorts of T
  proof
    set h = Hom(T,x,x);
    for s,x holds h.s.(x-term) = x-term
    proof
      let s1,x11;
      per cases;
      suppose s1 = s & x11 = x;
        hence h.s1.(x11-term) = x11-term by HOM;
      end;
      suppose s1 <> s or x11 <> x;
        hence thesis by HOM;
      end;
    end;
    hence thesis by Th52;
  end;
