theorem Th44:
  (t1 mod t2) value_at(C,s) = (t1 value_at(C,s)) mod (t2 value_at(C,s))
  proof
    thus (t1 mod t2) value_at(C,s) = (t1-(t1 div t2)*t2) value_at(C,s)
    .= (t1 value_at(C,s))-(((t1 div t2)*t2) value_at(C,s)) by Th41
    .= (t1 value_at(C,s))-(((t1 div t2) value_at(C,s))*(t2 value_at(C,s)))
    by Th42
    .= (t1 value_at(C,s)) mod (t2 value_at(C,s)) by Th43;
  end;
