[isabelle] a question of formalization of parameterized-word (bit-vector)



Dear experts:
   Now I meet a problem of formalization of a parameterized bit-vector.
Here a parameterized bit-vector. means that the width of the bit vector is
a parmeterize, for instance a variable in a program (hardware design) is a
word of some length k. I want to prove that some property P on the varaible
is correct for any k.

   I notice that the examples usually are on a fixed-length word such as 32
word, 8 word. For instance, a lemma
lemma "0b110 AND 0b101 = (0b100 :: 5 word)" by simp

I want to have a lemma such as
lemma  lemmaTest: "0b110 AND 0b101 = (0b100 :: k word)" by simp, where k is
any natural number which is greater than or equal to 3.

But obviously  lemmaTest is not allowed in Isabelle.

How to formalize such a lemma? Or I can be shown some examples which
formalize the  parameterized-word problems.

regards!



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