feat: add BitVec.(getElem_umod_of_lt, getElem_umod, getLsbD_umod, getMsbD_umod)
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luisacicolini
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and support BitVec.le_zero_eq_zero`BitVec.(getElem_umod_of_lt, getElem_umod, getLsbD_umod, getMsbD_umod) and support BitVec.le_zero_eq_zero
luisacicolini
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Jan 27, 2025
luisacicolini
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tobiasgrosser
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Jan 28, 2025
…tMsbD_umod)` and support `BitVec.le_zero_eq_zero` This PR adds theorems `BitVec.(getElem_umod_of_lt, getElem_umod, getLsbD_umod, getMsbD_umod)` and support theorem `BitVec.le_zero_eq_zero`. For the defiition of these theorems we rely on `divRec`, excluding the case where `d=0#w`, which is treated separately because there is no infrastructure to reason about this case within `divRec`. In particular, our implementation follows the mathlib standard [where division by 0 yields 0](https://github.com/leanprover/lean4/blob/c7c1e091c9f07ae6f8e8ff7246eb7650e2740dcb/src/Init/Data/BitVec/Basic.lean#L217), while in [SMTLIB this yields `allOnes`](https://github.com/leanprover/lean4/blob/c7c1e091c9f07ae6f8e8ff7246eb7650e2740dcb/src/Init/Data/BitVec/Basic.lean#L237). Co-authored by @bollu.
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luisacicolini
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BitVec.(getElem_umod_of_lt, getElem_umod, getLsbD_umod, getMsbD_umod) and support BitVec.le_zero_eq_zeroBitVec.(getElem_umod_of_lt, getElem_umod, getLsbD_umod, getMsbD_umod)
bollu
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Jan 29, 2025
bollu
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bollu
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Jan 29, 2025
bollu
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Jan 30, 2025
bollu
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Jan 30, 2025
Co-authored-by: Siddharth <[email protected]>
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alexkeizer
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src/Init/Data/BitVec/Bitblast.lean
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| · have := (BitVec.not_le (x := d) (y := 0#w)).mp | ||
| simp only [le_zero_iff] at this | ||
| rw [← BitVec.umod_eq_divRec (by simp [hd, this])] | ||
| simp [hd] |
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Why don't we reuse getElem_umod_of_(lt/pos) here? That lemmas seems to describe exactly this case, no?
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so it's actually interesting, using that theorem in the proof seems to only make the proof longer. I guess we don't need getElem_umod_of_pos in the first place.
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This PR adds theorems
BitVec.(getElem_umod_of_lt, getElem_umod, getLsbD_umod, getMsbD_umod). For the defiition of these theorems we rely ondivRec, excluding the case whered=0#w, which is treated separately because there is no infrastructure to reason about this case withindivRec. In particular, our implementation follows the mathlib standard where division by 0 yields 0, while in SMTLIB this yieldsallOnes.Co-authored by @bollu.