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feat: add BitVec.toInt_[pos|neg]_iff (#5083)

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Co-authored-by: Kim Morrison <scott@tqft.net>
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Tobias Grosser 2024-08-26 10:44:58 +01:00 • committed by GitHub
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src/Init/Data/BitVec/Lemmas.lean
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@ -303,6 +303,14 @@ theorem toInt_ofNat {n : Nat} (x : Nat) :
@[simp] theorem ofInt_natCast (w n : Nat) :
BitVec.ofInt w (n : Int) = BitVec.ofNat w n := rfl
theorem toInt_neg_iff {w : Nat} {x : BitVec w} :
BitVec.toInt x < 0 ↔ 2 ^ w ≤ 2 * x.toNat := by
simp [toInt_eq_toNat_cond]; omega
theorem toInt_pos_iff {w : Nat} {x : BitVec w} :
0 ≤ BitVec.toInt x ↔ 2 * x.toNat < 2 ^ w := by
simp [toInt_eq_toNat_cond]; omega
/-! ### zeroExtend and truncate -/
theorem truncate_eq_zeroExtend {v : Nat} {x : BitVec w} :