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lean_minimal_hypotheses

Read-onlyIdempotent

Tests each explicit hypothesis of a Lean theorem to determine if it is load-bearing or unused, by re-elaborating the proof without it. Skips implicit and instance binders.

Instructions

For each explicit (h : T) hypothesis of a theorem, drop it and re-elaborate a scratch copy of the file. Reports which hypotheses are load-bearing and which are actually unused. Skips implicit {x : α} and instance [inst : C] binders (those are usually inferable / always load-bearing). Does not rewrite the proof body — a body that names h will fail to elaborate without the binder, which is the truthful answer (load-bearing).

Variants are checked in parallel on scratch documents; the file is never edited.

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
file_pathYesAbsolute path to Lean file
theorem_nameYesTheorem name. Either bare (e.g. `add_comm`) or fully qualified (e.g. `Namespace.add_comm`); only the trailing segment is used for source matching.
inactivity_timeoutNoPer-hypothesis elaboration timeout (seconds)

Output Schema

TableJSON Schema
NameRequiredDescriptionDefault
fileYesRelative file path
verdictsNoOne verdict per explicit (h : T) binder, in source order
theorem_nameYesTheorem analyzed
skipped_implicitNoCount of implicit {x : α} / instance [inst] binders not probed
Behavior5/5

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

Annotations already declare readOnlyHint=true and idempotentHint=true. The description adds significant behavioral context: that it creates scratch copies, works in parallel, does not edit the file, and that naming a hypothesis will cause elaboration failure if dropped. This is valuable beyond annotations.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness5/5

Is the description appropriately sized, front-loaded, and free of redundancy?

The description is two short paragraphs, front-loaded with the core action. Each sentence provides necessary detail (skipping certain binders, behavior of named hypothesis, parallel/scratch nature). No fluff; every sentence earns its place.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness5/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

Given the tool's complexity (hypothesis testing, parallel elaboration), the description fully explains the mechanism, scope, and non-destructive nature. The presence of an output schema means output format details are not needed in the description. The tool is well-specified for an AI agent.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters4/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Since schema description coverage is 100% (all parameters described in schema), the baseline is 3. The description adds the per-hypothesis timeout context for the inactivity_timeout parameter, slightly increasing clarity. No param info is missing, but the description does not elaborate on file_path or theorem_name beyond the schema.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose5/5

Does the description clearly state what the tool does and how it differs from similar tools?

The description clearly states that the tool drops each explicit hypothesis of a theorem and re-elaborates to determine which are load-bearing. It distinguishes itself by skipping implicit and instance binders, and explicitly says it does not rewrite the proof body. This precise verb+resource description differentiates it from siblings.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines4/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

The description explains what the tool does and what it skips (implicit/instance binders), but does not explicitly provide when-to-use or when-not-to-use guidance relative to sibling tools. The context is clear enough for an agent to infer usage, but lacks explicit exclusions or alternative suggestions.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.

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