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>
This PR renames `instance_reducible` to `implicit_reducible` and adds a
new
`backward.isDefEq.implicitBump` option to prepare for treating all
implicit
arguments uniformly during definitional equality checking.
## Changes
**Rename `instance_reducible` → `implicit_reducible`:**
- Rename `ReducibilityStatus.instanceReducible` constructor to
`implicitReducible`
- Register new `[implicit_reducible]` attribute, keep
`[instance_reducible]` as alias
- Rename `isInstanceReducible` → `isImplicitReducible` (with deprecated
aliases)
- Update all references across src/ and tests/
The rename reflects that this reducibility level is used not just for
instances
but for any definition that needs unfolding during implicit argument
resolution
(e.g., `Nat.add`, `Array.size`).
**Add `backward.isDefEq.implicitBump` option:**
- When `true` (+ `respectTransparency`), bumps transparency to
`.instances` for
ALL implicit arguments in `isDefEqArgs`, not just instance-implicit ones
- Defaults to `false` for staging compatibility — will be flipped to
`true` after
stage0 update
- Adds `// update me!` to `stage0/src/stdlib_flags.h` to trigger CI
stage0 update
## Follow-up (after stage0 update)
- Flip `backward.isDefEq.implicitBump` default to `true`
- Fix resulting test/module failures
🤖 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>
