feat: BitVec.toFin/ToInt BitVec.ushiftRight #6238
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Unsigned shift right by at least one bit makes the value of the bitvector less than or equal to `2^(w-1)`,
makes the interpretation of the bitvector `Int` and `Nat` agree.
In the case when `n = 0`, then the shift right value equals the integer interpretation.
```lean
theorem toInt_ushiftRight_eq_ite {x : BitVec w} {n : Nat} :
(x >>> n).toInt = if n = 0 then x.toInt else x.toNat >>> n
```
---
```lean
theorem toFin_uShiftRight {x : BitVec w} {n : Nat} :
(x >>> n).toFin = x.toFin / (Fin.ofNat' (2^w) (2^n))
```
Co-authored-by: Harun Khan <[email protected]>
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Co-authored-by: Tobias Grosser <[email protected]>
Co-authored-by: Tobias Grosser <[email protected]>
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This PR adds theorems characterizing the value of the unsigned shift right of a bitvector in terms of its 2s complement interpretation as an integer.
Unsigned shift right by at least one bit makes the value of the bitvector less than or equal to
2^(w-1),makes the interpretation of the bitvector
IntandNatagree.In the case when
n = 0, then the shift right value equals the integer interpretation.