Verb-to-INFL movement (advanced)

I. We have seen that:
(a) Auxiliaries have and be behave in many respects like modal auxiliaries and periphrastic do. Each of these elements can:

(i) be negated directly
(ii) undergo inversion in questions
(iii) form question tags

(b) There is evidence that modal auxiliaries and periphrastic do are base-generated under INFL and auxiliary have and be are base-generated under V.

II. We can capture the similarities and differences between these two groups of elements by claiming that auxiliary have and be:
(a) must move from V to INFL under certain conditions, namely when:

(i) INFL is [+Tense] and
(ii) no modal auxiliary or periphrastic do has been base-generated under INFL

(NOTE: if there is more than one have or be available (in such VPs as have been working), the highest of these moves.)
(b) receive tense and agreement inflection as a result of this movement:

John could be/* could is reading a book.
John is/* be reading a book.

John is reading a book.

III. This movement also accounts for the appearance of auxiliary have and be to the left or the right of negation, depending upon whether INFL is filled by a modal auxiliary or not.

John should not have stolen money.
John should not be stealing money.
(auxiliary have and be cannot move into INFL)
John has not stolen any money.
John is not stealing any money.
(auxiliary have and be have moved into INFL)