# [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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