Lean 4 fork for HoTT-compatible kernel extensions (Path types, transport, HITs). Maintained against upstream leanprover/lean4.
77211029da
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 `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 <harun19@stanford.edu>
Co-authored-by: Tobias Grosser <github@grosser.es>
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