Prove the following about Algorithm 9.14: a) The IN's and OUT's never shrink. b) If variable x is put in m[B] or 0UTp9], then there is a path from the beginning or end of block B, respectively, along...

Prove the following about Algorithm 9.14:

a) The IN's and OUT's never shrink.

b) If variable x is put in m[B] or 0UTp9], then there is a path from the beginning or end of block B, respectively, along which x might be used.


c) If variable x is not put in IN[JB] or OUTp9], then there is no path from the beginning or end of block B, respectively, along which x might be used.