Archimedean.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 8 curated AI-written annotations and 1204 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 FLT blueprint introduction

1 declarations, 0 contain sorry, 0 declared as axioms

Archimedean

Material destined for Mathlib.

Imports (1)

Mathlib.Algebra.Order.Archimedean.Real.Basic

Imported by 2 files

lemma Int.eq_floor The file this was destined for (Mathlib.Data.Real.Archimedean) no longer exists -- it was moved to Mathlib.Algebra.Order.Archimedean.Real.Basic line 19 source
Source comment
The file this was destined for (Mathlib.Data.Real.Archimedean) no longer exists -- it was moved to Mathlib.Algebra.Order.Archimedean.Real.Basic

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Real, Int, LE.le, OfNat.ofNat, HSub.hSub, LT.lt, Eq, Int.floor
Proof uses: Eq.mpr, id, congrArg, propext, eq_comm, And, HAdd.hAdd, Int.floor_eq_iff
42 instances, coercions and auxiliary constants left out.

Tactic trace: 2 steps
Open to load the checked before-and-after goal states.
```
lemma Int.eq_floor {a : ℝ} {b : ℤ} (h1 : 0 ≤ a - b) (h2 : a - b < 1) : b = ⌊a⌋ := by
…
```