feat: Decidable instance for Nat.isPowerOfTwo
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This PR provides a `Decidable` instance for `Nat.isPowerOfTwo` based on the identity `(n ≠ 0) ∧ (n &&& (n - 1)) = 0`. To do this it includes theorems about `Nat.testBit` to show that the `n.log2`th bit is set in `n` and `n - 1` for non powers of two. Bitwise lemmas are needed to reason about the `&&&` so the file `Init.Data.Nat.Power2` is renamed to `Init.Data.Nat.Power2.Basic` and `Init.Data.Nat.Power2.Lemmas` introduced that depends on `Init.Data.Nat.Bitwise.Lemmas` to prevent circular includes.
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kim-em
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Jan 9, 2026
kim-em
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Jan 9, 2026
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This PR provides a
Decidableinstance forNat.isPowerOfTwobased on the formula(n ≠ 0) ∧ (n &&& (n - 1)) = 0.To do this it includes theorems about
Nat.testBitto show that then.log2th bit is set innandn - 1for non powers of two.Bitwise lemmas are needed to reason about the
&&&so the fileInit.Data.Nat.Power2is renamed toInit.Data.Nat.Power2.BasicandInit.Data.Nat.Power2.Lemmasintroduced that depends onInit.Data.Nat.Bitwise.Lemmasto prevent circular includes.