Lean 4 fork for HoTT-compatible kernel extensions (Path types, transport, HITs). Maintained against upstream leanprover/lean4.
7692343720
This PR adds `toNat` theorems for `BitVec.signExtend.`
Sign extending to a larger bitwidth depends on the msb. If the msb is
false, then the result equals the original value. If the msb is true,
then we add a value of `(2^v - 2^w)`, which arises from the sign
extension.
```lean
theorem toNat_signExtend (x : BitVec w) {v : Nat} :
(x.signExtend v).toNat = (x.setWidth v).toNat + if x.msb then 2^v - 2^w else 0
```
Co-authored-by: Harun Khan <harun19@stanford.edu>
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