S02_Overview.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 9 curated AI-written annotations and 7 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 Mathematics in Lean documentation, Pinned Mathematics in Lean textbook

9 declarations, 1 contain sorry, 0 declared as axioms

Imports (1)

MIL.Common

Imported by 1 file

MIL.lean

def f line 8 source
no axioms what this means
Statement uses: Nat
Proof uses: HAdd.hAdd, OfNat.ofNat
3 instances, coercions and auxiliary constants left out.
def FermatLastTheorem line 16 source
standard axioms: propext what this means
Proof uses: Nat, And, GT.gt, OfNat.ofNat, Ne, HMul.hMul, HAdd.hAdd, HPow.hPow
9 instances, coercions and auxiliary constants left out.
theorem easy These are proofs of propositions line 22 source
Source comment
These are proofs of propositions.

no axioms what this means
Statement uses: Eq, Nat, HAdd.hAdd, OfNat.ofNat
Proof uses: rfl
6 instances, coercions and auxiliary constants left out.
```
theorem easy : 2 + 2 = 4 :=
…
```
theorem hard sorry line 27 source
depends on sorry what this means
Statement uses: FermatLastTheorem
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous, OfNat.ofNat, Nat
1 instances, coercions and auxiliary constants left out.

Tactic trace: 12 steps
Open to load the checked before-and-after goal states.

example (example at line 33) line 33 source

Source comment

Here are some proofs.

example : ∀ m n : Nat, Even n → Even (m * n) := fun m n ⟨k, (hk : n = k + k)⟩ ↦
…

example (example at line 37) line 37 source
example (example at line 40) line 40 source
example (example at line 50) line 50 source
example (example at line 53) line 53 source