Finite approximation of a lazy list

A finite list prefix followed by bottom records only the constructors known so far. The chain $\perp ,x_1:\perp ,x_1:x_2:\perp ,\dots$ approximates an infinite lazy list. A Scott continuous map is determined on the limit by its values on these approximations. This justifies extending an identity proved on finite partial lists to definable operations on infinite lists; equality merely on finite terminating lists does not provide the same premise.