AMSLinter.lean`

Explanation legend Lean4 Domain Explanation Language (L4DEL)

L4DEL explanations are a separate layer. They do not change the Lean source. Intuition is explanatory prose; numbered items are a reading path; sources link the wording back to evidence.

L4DEL: Lean4 Domain Explanation Language

Annotation provenance. This overlay contains 10 curated AI-written annotations and 7190 mechanical source-derived annotations. They have not been human-reviewed as explanations; treat them as unverified and not mathematical authority. Retained generation history: The 71 original curated annotations were produced in a Claude Sonnet 5.5 session at medium effort; Claude Opus 5.5 is recorded in that session as the advisor model, not the direct author. The bulk source-derived expansion was generated mechanically from pinned source comments by tooling developed in a GPT-5.6 Sol session at ultra reasoning; GPT-5.6 Sol did not originate the quoted source prose. On 2026-10-17 the mechanically generated source-comment annotations of the Formal Conjectures, Carleson, FLT, PFR, CompFiles, Mathematics in Lean and Theorem Proving in Lean overlays were regenerated by the same generator after three corrections made in a Claude Sonnet 5.5 session: titles no longer cut a sentence inside mathematics or end on a dangling word, workflow markers are removed from the quoted prose, and declaration names follow the scanner's namespace resolution. The boilerplate step line was dropped, and comments that were only a row of dashes no longer yield annotations. No new prose was written and no human review is claimed.

Credit: The upstream authors and contributors retain credit for the project and mathematics. lean4-explainer only renders their pinned source and adds the separately disclosed explanation layer.

Project sources: Pinned project documentation, Formal Conjectures paper, arXiv v1

12 declarations, 0 contain sorry, 0 declared as axioms

Imports (1)

FormalConjecturesUtil.Linters.AMSLinter

def AMSLinter.foo line 29 source
no axioms what this means
Statement uses: Nat
Proof uses: OfNat.ofNat
1 instances, coercions and auxiliary constants left out.
theorem AMSLinter.test_theorem A highly non-trivial theorem line 38 source
Source documentation
A highly non-trivial theorem

no axioms what this means
Statement uses: Eq, Nat, HAdd.hAdd, OfNat.ofNat
Proof uses: Eq.refl
6 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem test_theorem : 1 + 1 = 2 := by
…
```
theorem AMSLinter.test_theorem_with_hypothesis A highly non-trivial theorem with a helpful hypothesis line 48 source
Source documentation
A highly non-trivial theorem with a helpful hypothesis

no axioms what this means
Statement uses: True, Eq, Nat, HAdd.hAdd, OfNat.ofNat
Proof uses: Eq.refl
6 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem test_theorem_with_hypothesis (_ : True) : 1 + 1 = 2 := by
…
```
theorem AMSLinter.test_theorem_with_hypotheses A highly non-trivial theorem with two helpful hypotheses line 58 source
Source documentation
A highly non-trivial theorem with two helpful hypotheses

no axioms what this means
Statement uses: True, False, Eq, Nat, HAdd.hAdd, OfNat.ofNat
Proof uses: Eq.refl
6 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem test_theorem_with_hypotheses (_ : True) (_ : False): 1 + 1 = 2 := by
…
```
lemma AMSLinter.test_lemma line 68 source
no axioms what this means
Statement uses: Eq, Nat, HAdd.hAdd, OfNat.ofNat
Proof uses: Eq.refl
6 instances, coercions and auxiliary constants left out.

Tactic trace: 2 steps
Open to load the checked before-and-after goal states.
example AMSLinter.(example at line 77) line 77 source
theorem AMSLinter.test_theorem_with_docstring A highly non-trivial theorem with a helpful hypothesis line 88 source
Source documentation
A highly non-trivial theorem with a helpful hypothesis

no axioms what this means
Statement uses: Eq, Nat, HAdd.hAdd, OfNat.ofNat
Proof uses: Eq.refl
6 instances, coercions and auxiliary constants left out.

Tactic trace: 2 steps
Open to load the checked before-and-after goal states.
```
theorem test_theorem_with_docstring : 1 + 1 = 2 := by
…
```
example AMSLinter.(example at line 94) line 94 source
Source documentation
A highly non-trivial theorem with a helpful hypothesis
```
example: 1 + 1 = 2 := by
…
```
theorem AMSLinter.test_1 line 100 source
no axioms what this means
Statement uses: Eq, Nat, HAdd.hAdd, OfNat.ofNat
Proof uses: Eq.refl
6 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
theorem AMSLinter.test_3 line 106 source
no axioms what this means
Statement uses: Eq, Nat, HAdd.hAdd, OfNat.ofNat
Proof uses: Eq.refl
6 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
theorem AMSLinter.test_out_of_order line 116 source
no axioms what this means
Statement uses: Eq, Nat, HAdd.hAdd, OfNat.ofNat
Proof uses: Eq.refl
6 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
theorem AMSLinter.test_dup line 126 source
no axioms what this means
Statement uses: Eq, Nat, HAdd.hAdd, OfNat.ofNat
Proof uses: Eq.refl
6 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.