feat: add Bitvec.(toInt, toFin)_twoPow
#7225
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luisacicolini
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Bitvec.(toInt, toFin)_twoPow
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luisacicolini
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Feb 26, 2025
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thank you @tobiasgrosser for this cute proof! looks good to me :)
Co-authored-by: Luisa Cicolini <[email protected]>
Co-authored-by: Luisa Cicolini <[email protected]> Co-authored-by: Siddharth <[email protected]>
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bollu
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Feb 26, 2025
| apply Nat.mod_eq_of_lt | ||
| apply Nat.pow_lt_pow_of_lt (by omega) (by omega) | ||
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| theorem toNat_twoPow_eq_if {i w : Nat} : (twoPow w i).toNat = if i < w then 2^i else 0 := by |
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I would like for us to contemplate, in a subsequent PR, whether this should be the simp normal form of toNat_twoPow.
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I looked into this, but this breaks a couple of proofs in non-trivial ways, as several proofs use % 2 ^ ? instead of an if statement to express that the RHS can be zero. I am happy to investigate this further, but given that this is not a clear-cut, we should investigate this more broadly and likely in a future PR.
luisacicolini
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Feb 26, 2025
Co-authored-by: Luisa Cicolini <[email protected]>
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This PR contains
BitVec.(toInt, toFin)_twoPowtheorems, completing the API forBitVec.*_twoPow. It also expands thetoNat_twoPowAPI withtoNat_twoPow_of_le,toNat_twoPow_of_lt, as well astoNat_twoPow_eq_ifand movesmsb_twoPowup, as it is used in thetoInt_msbproof.