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feat(Data/BitVec): add lemmas about pow on BitVec #1608

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feat(Data/BitVec): add lemmas about pow on BitVec #1608

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feat(Data/BitVec): add lemmas about `pow` on `BitVec`
eric-wieser Jan 7, 2026
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Update Lemmas.lean
eric-wieser Jan 7, 2026
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7 changes: 7 additions & 0 deletions Batteries/Data/BitVec/Lemmas.lean
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Expand Up @@ -15,6 +15,13 @@ public import Batteries.Data.Int

namespace BitVec

@[simp]
theorem toNat_pow (b : BitVec w) (n : Nat) : (b ^ n).toNat = (b.toNat ^ n) % (2 ^ w) := by
induction n <;> simp_all [Lean.Grind.Semiring.pow_succ]

theorem ofNat_pow (n : Nat) (x d : Nat) : BitVec.ofNat n (x ^ d) = BitVec.ofNat n x ^ d := by
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@fgdorais fgdorais Jan 18, 2026

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I wish BitVec functions were more consistent using w for bit width.

Suggested change
theorem ofNat_pow (n : Nat) (x d : Nat) : BitVec.ofNat n (x ^ d) = BitVec.ofNat n x ^ d := by
theorem ofNat_pow (w x d : Nat) : BitVec.ofNat w (x ^ d) = BitVec.ofNat w x ^ d := by

Why isn't this simp?

rw [← toNat_inj, toNat_ofNat, toNat_pow, toNat_ofNat, Nat.pow_mod]

@[simp] theorem toNat_ofFnLEAux (m : Nat) (f : Fin n → Bool) :
(ofFnLEAux m f).toNat = Nat.ofBits f % 2 ^ m := by
simp only [ofFnLEAux]
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