feat: add Bitvec.(toInt, toFin)_twoPow
#7225
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luisacicolini
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Bitvec.(toInt, toFin)_twoPow
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| have hy : (2 ^ i % 2 ^ (w + 1)) = 2 ^ i := by rw [Nat.mod_eq_of_lt (by rw [Nat.pow_lt_pow_iff_right (by omega)]; omega)] | ||
| have hj : 2 * 2 ^ i = 2 ^ (i + 1) := by rw [Nat.pow_add, Nat.mul_comm] |
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| have hy : (2 ^ i % 2 ^ (w + 1)) = 2 ^ i := by rw [Nat.mod_eq_of_lt (by rw [Nat.pow_lt_pow_iff_right (by omega)]; omega)] | |
| have hj : 2 * 2 ^ i = 2 ^ (i + 1) := by rw [Nat.pow_add, Nat.mul_comm] | |
| have hy : 2 ^ i % 2 ^ (w + 1) = 2 ^ i := by rw [Nat.mod_eq_of_lt (by rw [Nat.pow_lt_pow_iff_right (by omega)]; omega)] | |
| have hj : 2 * 2 ^ i = 2 ^ (i + 1) := by rw [Nat.pow_add, Nat.mul_comm] |
I wonder if these two lemma above should not be named simp lemmas.
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In fact, the entire second half of the proof would be a lot nicer, if we can make avoid the casts in the middle and just make this all simp away. I am wondering if there is a set of simp lemmas which could help here?
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| by_cases i + 1 = (w + 1) | ||
| · simp [show i = w by omega]; omega |
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| by_cases i + 1 = (w + 1) | |
| · simp [show i = w by omega]; omega | |
| by_cases i + 1 = w + 1 | |
| · simp [show i = w by omega]; omega |
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This PR contains
BitVec.(toInt, toFin)_twoPowtheorems, completing the API forBitVec.*_twoPow.