PathCover.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

2 declarations, 0 contain sorry, 0 declared as axioms

Imports (3)

Imported by 1 file

FormalConjecturesForMathlib.lean

def SimpleGraph.IsPathCover A family of paths covering all vertices without overlaps line 29 source
Source documentation
A family of paths covering all vertices without overlaps.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Fintype, DecidableEq, SimpleGraph, Finset
Proof uses: And, Membership.mem, Ne, Disjoint, LE.le, Finset.univ, Finset.biUnion, id, Exists, SimpleGraph.Walk, SimpleGraph.Walk.IsPath, Eq, List.toFinset, SimpleGraph.Walk.support
6 instances, coercions and auxiliary constants left out.
```
def IsPathCover (G : SimpleGraph α) (P : Finset (Finset α)) : Prop :=
…
```
def SimpleGraph.pathCoverNumber Minimum size of a path cover of G line 35 source
Source documentation
Minimum size of a path cover of G.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Fintype, DecidableEq, SimpleGraph, Nat
Proof uses: InfSet.sInf, Set.ofPred, Exists, Finset, And, Eq, Finset.card, SimpleGraph.IsPathCover
1 instances, coercions and auxiliary constants left out.
```
noncomputable def pathCoverNumber (G : SimpleGraph α) : ℕ :=
…
```