On 16/01/13 19:49, Yuntao Peng wrote:
> Now there is a goals I want to prove [...]

> Thanks to the listTheory is base on real, so I can not use its theorem.

I’m not sure what you mean by this last sentence.  Certainly, the theory of
lists (listTheory) is not tied to real numbers at all.

Also, assuming you don’t use MAP2 as Ramana suggested, you might also prefer to
write your definitions like

val list_ADD_def = Define`
  (list_ADD [] _ = []) /\
  (list_ADD _ [] = []) /\
  (list_ADD ((c1:complex)::t1) (c2::t2) = (c1 + c2) :: list_ADD t1 t2)
`

Best,
Michael

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