feat: BitVec.[toFin|getMsbD]_setWidth and [getMsbD|msb]_signExtend #6338
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This patch adds BitVec.[toFin|getMsbD]_setWidth and [getMsb|msb]_signExtend as well as ofInt_toInt and toInt_cast.
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Co-authored-by: Siddharth <[email protected]>
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| @@ -645,6 +652,20 @@ theorem getElem?_setWidth (m : Nat) (x : BitVec n) (i : Nat) : | |||
| getLsbD (setWidth m x) i = (decide (i < m) && getLsbD x i) := by | |||
| simp [getLsbD, toNat_setWidth, Nat.testBit_mod_two_pow] | |||
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| theorem getMsbD_setWidth {m : Nat} {x : BitVec n} {i : Nat} : | |||
| getMsbD (setWidth m x) i = (decide (m - n ≤ i) && getMsbD x (i + n - m)) := by | |||
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No objection on this PR, but increasingly I am skeptical that decide inequality && boolean is really what we want on the RHS of all these lemmas. It probably should just be if inequality then boolean else false. Without a mixed linear arithmetic + SAT solver, this is doing us no favours, and the if style makes it much easier to use split to get the inequalities in usable form (e.g. for omega).
Something to consider; it would be a big refactor.
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This PR adds
BitVec.[toFin|getMsbD]_setWidthand[getMsb|msb]_signExtendas well asofInt_toInt.Also correct renamed the misnamed theorem for
signExtend_eq_setWidth_of_msb_false.