3d.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 (2)

Imported by 1 file

FormalConjecturesForMathlib.lean

instance Module.orientedEuclideanSpaceFinThree The standard basis gives us a preferred orientation in ℝ³ line 32 source
Source documentation
The standard basis gives us a preferred orientation in ℝ³.
Note: when upstreaming this to Mathlib (and generalizing to Fin n) one must be careful to avoid an instance diamond with IsEmpty.Orientation. Presumably this can be avoided by assuming [NeZero n].

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Module.Oriented, Real, EuclideanSpace, Fin, OfNat.ofNat, Nat, ENNReal
Proof uses: Module.Oriented.mk, Module.Basis.orientation, PiLp.basisFun
44 instances, coercions and auxiliary constants left out.
```
noncomputable instance Module.orientedEuclideanSpaceFinThree : Module.Oriented ℝ ℝ³ (Fin 3) :=
…
```
instance fact_finrank_euclideanSpace_fin_three Three dimensional euclidean space is three-dimensional line 36 source
Source documentation
Three dimensional euclidean space is three-dimensional.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Fact, Eq, Nat, Module.finrank, Real, EuclideanSpace, Fin, OfNat.ofNat, ENNReal
Proof uses: Fact.mk, finrank_euclideanSpace_fin
35 instances, coercions and auxiliary constants left out.
```
instance fact_finrank_euclideanSpace_fin_three : Fact (Module.finrank ℝ ℝ³ = 3) :=
…
```