theorem
  (t1 mod t2) value_at(C,u) = (t1 value_at(C,u)) mod (t2 value_at(C,u))
  proof
    thus (t1 mod t2) value_at(C,u) = (t1-(t1 div t2)*t2) value_at(C,u)
    .= (t1 value_at(C,u))-(((t1 div t2)*t2) value_at(C,u)) by Th56
    .= (t1 value_at(C,u))-(((t1 div t2) value_at(C,u))*(t2 value_at(C,u)))
    by Th57
    .= (t1 value_at(C,u)) mod (t2 value_at(C,u)) by Th58;
  end;
