feat: BitVec.shiftLeft in terms of extractLsb' #6743
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This PR supports rewriting `ushiftRight` in terms of `extractLsb'`. This is the companion PR to #6743 which adds the similar lemmas about `shiftLeft`. ```lean theorem ushiftRight_eq_zero {x : BitVec w} {n : Nat} (hn : w ≤ n) : x >>> n = 0#w theorem ushiftRight_eq_extractLsb'_of_lt {x : BitVec w} {n : Nat} (hn : n < w) : x >>> n = ((0#n) ++ (x.extractLsb' n (w - n))).cast (by omega) ```
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that normalize left shidts Also, update the theorem names in the PR message to match their current names. |
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This PR adds rewrites from Bitwuzla that normalize left shifts
in terms of extracting bits and concatenating zeroes.
If the shift amount is larger than the bitwidth, then the resulting bitvector is zero.
```lean
theorem shiftLeft_eq {x : BitVec w} {n : Nat} (hn : w ≤ n) : x <<< n = 0#w
theorem shiftLeft_eq_concat_of_lt {x : BitVec w} {n : Nat} (hn : n < w) :
x <<< n = ((x.extractLsb' 0 (w-n)).append (BitVec.zero n)).cast (by omega)
```
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This PR adds rewrites that normalizes left shifts by extracting bits and concatenating zeroes. If the shift amount is larger than the bit-width, then the resulting bitvector is zero.