# simplify_theorems

Simplify theorem proofs by removing unnecessary tactics and cleaning up code.

## Input Parameters

`content` · str · required · Lean source code

The Lean source code to be processed by this tool.

`names` · list[str] · Theorem names to process

Optional list of theorem names to process. If not specified, all theorems are processed. Requesting a name not found in the code returns an error. When `theorems_only` is `false`, these select over all declarations (not just theorems).

`indices` · list[int] · Theorem indices to process

Optional list of theorem indices to process (0-based). Supports negative indices: `-1` is the last theorem, `-2` is second-to-last, etc. If not specified, all theorems are processed. When `theorems_only` is `false`, these select over all declarations (not just theorems).

`theorems_only` · bool · default: `True` · Process theorems/lemmas only

If `true` (default), only `theorem`/`lemma` declarations are processed. Set to `false` to process all declaration kinds (`def`/`instance`/`abbrev`/`opaque`/etc). When `false`, `names` and `indices` select over all declarations rather than just theorems.

`simplifications` · list[str] · List of simplifications to apply

If not specified, all simplifications are applied. See below for available simplifications.

`ignore_imports` · bool · default: `True` · Ignore import mismatches

Controls import statement handling:

- `true` (default): Ignore the imports in `content` and substitute the environment's default header. This uses the pre-built cached environment, so it is fast. The substituted code is returned in the `content` field.
- `false`: Process the imports in `content` exactly as written. This is significantly slower (the cached environment cannot be reused) and may produce inconsistent or incorrect results if a required dependency such as `Mathlib.Tactic` is missing. A warning is returned in these cases. See the troubleshooting page for more details.

`environment` · str · required · Lean environment or version

The Lean environment to use for evaluation. Each environment includes a specific Lean version and pre-built dependencies (typically Mathlib).

Available environments: `lean-4.28.0`, `lean-4.27.0`, `lean-4.26.0`, etc.

`timeout_seconds` · float · default: `120` · Max execution time in seconds

Maximum execution time in seconds. Requests exceeding this limit return a timeout error. Note that end-to-end request latency may exceed this timeout due to queue time and other overhead. Additionally, all non-admin requests are subject to an absolute maximum timeout of 900 seconds (15 minutes).

## Output Fields

`lean_messages` · dict · Messages from Lean compiler

Messages from the Lean compiler with `errors`, `warnings`, and `infos` lists. Errors here indicate invalid Lean code (syntax errors, type errors, etc.); an empty `errors` list means the code compiles.

`tool_messages` · dict · Messages from simplify_theorems tool

Messages from the simplify_theorems tool with `errors`, `warnings`, and `infos` lists. Errors here indicate tool-specific issues (not Lean compilation errors).

`content` · string · Lean code with simplified theorem proofs

May be shorter and cleaner than input.

`timings` · dict · Execution timing breakdown

Timing information in milliseconds for various stages of processing.

`simplification_stats` · dict · Count of each simplification type applied

Maps simplification names to counts (e.g., `{"remove_unused_tactics": 3}`).

## Available Simplifications

`remove_unused_tactics`

Removes tactics that don't contribute to the proof.

`remove_unused_haves`

Removes unused `have` statements.

`rename_unused_vars`

Cleans up unused variable names.

## Python API

```python
# Simplify all theorems with all simplifications
result = await axle.simplify_theorems(content=lean_code, environment="lean-4.28.0")

# Simplify specific theorems
result = await axle.simplify_theorems(
    content=lean_code,
    environment="lean-4.28.0",
    names=["complex_theorem"],
)

# Apply only specific simplifications
result = await axle.simplify_theorems(
    content=lean_code,
    environment="lean-4.28.0",
    simplifications=["remove_unused_tactics"],
)

print(result.content)
print(result.simplification_stats)
```

## CLI

**Usage:**`axle simplify-theorems CONTENT [OPTIONS]`

```bash
# Simplify all theorems
axle simplify-theorems complex.lean --environment lean-4.31.0
# Simplify specific theorems
axle simplify-theorems complex.lean --names main_theorem,helper --environment lean-4.31.0
# Apply only specific simplifications
axle simplify-theorems complex.lean --simplifications remove_unused_tactics --environment lean-4.31.0
# Pipeline usage
cat complex.lean | axle simplify-theorems - --environment lean-4.31.0 | axle check - --environment lean-4.31.0
```

## HTTP API

```
curl -s -X POST https://axle.axiommath.ai/api/v1/simplify_theorems \
    -d '{"content": "import Mathlib\ntheorem foo : 1 = 1 := by rfl <;> rfl", "environment": "lean-4.28.0", "names": ["foo"]}' | jq
```

## Example Response

```
{
  "lean_messages": {
    "errors": [],
    "warnings": [],
    "infos": []
  },
  "tool_messages": {
    "errors": [],
    "warnings": [],
    "infos": ["simplify_theorems completed in 1 iterations"]
  },
  "content": "import Mathlib\n\ntheorem foo : 1 = 1 := by rfl",
  "timings": {
    "total_ms": 97,
    "parse_ms": 92
  },
  "simplification_stats": {
    "remove_unused_tactics": 1,
    "rename_unused_vars": 0,
    "remove_unused_haves": 0
  }
}
```