ab26eaf647
This PR is part 2 of the `implicit_reducible` refactoring (part 1: #12567). **Background.** When Lean checks definitional equality of function applications `f a₁ ... aₙ =?= f b₁ ... bₙ`, it compares arguments `aᵢ =?= bᵢ` at a transparency level determined by the binder type. Previously, only instance-implicit (`[C]`) arguments received a transparency bump to `.instances`. With `backward.isDefEq.implicitBump` enabled, ALL implicit arguments (`{x}`, `⦃x⦄`, and `[x]`) are bumped to `.instances`, so that definitions marked `[implicit_reducible]` unfold when comparing implicit arguments. This is important because implicit arguments often carry type information (e.g., `P (i + 0)` vs `P i`) where the mismatch is in non-proof positions (Sort arguments to `cast`) — proof irrelevance does not help here, so the relevant definitions must actually unfold. **`[implicit_reducible]`** (renamed from `[instance_reducible]` in part 1) marks definitions that should unfold at `TransparencyMode.instances` — between `[reducible]` (unfolds at `.reducible` and above) and the default `[semireducible]` (unfolds only at `.default` and above). This is the right level for core arithmetic operations that appear in type indices. ## Changes - **Enable `backward.isDefEq.implicitBump` by default** and set it in `stage0/src/stdlib_flags.h` so stage0 also compiles with it - **Mark `Nat.add`, `Nat.mul`, `Nat.sub`, `Array.size` as `[implicit_reducible]`** so they unfold when comparing implicit arguments at `.instances` transparency - **Remove redundant unification hints** (`n + 0 =?= n`, `n - 0 =?= n`, `n * 0 =?= 0`) that are now handled by `[implicit_reducible]` - **Rename all remaining `[instance_reducible]` attribute usages** to `[implicit_reducible]` across the codebase (the old name remains as an alias) - **Remove 28 `set_option backward.isDefEq.respectTransparency false in`** workarounds that are no longer needed 🤖 Generated with [Claude Code](https://claude.com/claude-code) Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com> --------- Co-authored-by: Claude Opus 4.6 <noreply@anthropic.com>
23 lines
550 B
Text
23 lines
550 B
Text
mutual
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def isEven : Nat → Bool
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| 0 => true
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| n+1 => isOdd n
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decreasing_by apply Nat.lt_succ_self
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def isOdd : Nat → Bool
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| 0 => false
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| n+1 => isEven n
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decreasing_by apply Nat.lt_succ_self
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end
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theorem isEven_double (x : Nat) : isEven (2 * x) = true := by
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induction x with
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| zero => simp [isEven]
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| succ x ih =>
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unfold isEven
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trace_state
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unfold isOdd
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trace_state
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exact ih
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theorem isEven_succ_succ (x : Nat) : isEven (x + 2) = isEven x := by
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conv => lhs; unfold isEven; simp; unfold isOdd; simp
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