Basic.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 981 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, Pinned Carleson blueprint

1 declarations, 0 contain sorry, 0 declared as axioms

Imports (1)

Carleson.ToMathlib.MeasureTheory.Function.LorentzSeminorm.TriangleInequality

Imported by 1 file

Carleson.lean

def MeasureTheory.Lorentz TODO: basic results line 18 source
Source documentation
TODO: basic results

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: ENNReal, MeasurableSpace, MeasureTheory.Measure, MeasureTheory.SigmaFinite, TopologicalSpace, ESeminormedAddMonoid, ContinuousAdd, AddSubmonoid, MeasureTheory.AEEqFun
Proof uses: AddSubmonoid.mk, AddSubsemigroup.mk, Set.ofPred, LT.lt, MeasureTheory.eLorentzNorm, Top.top, Membership.mem, Set
22 instances, coercions and auxiliary constants left out.

Tactic trace: 2 steps
Open to load the checked before-and-after goal states.
```
def Lorentz {α ε : Type*} (p q : ℝ≥0∞) {m0 : MeasurableSpace α} (μ : Measure α) [SigmaFinite μ]
  [TopologicalSpace ε] [ESeminormedAddMonoid ε] [ContinuousAdd ε] :
    AddSubmonoid (α →ₘ[μ] ε) where
…
```