Fp.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

5 declarations, 0 contain sorry, 0 declared as axioms

Notation for finite field vector spaces

This file defines the notation 𝔽 p n for the vector space Fin n → ZMod p over the finite field of order p, and provides standard abbreviations for small primes.

Imports (1)

Mathlib.Data.ZMod.Basic

Imported by 1 file

FormalConjecturesForMathlib.lean

abbrev 𝔽 𝔽 p n is the vector space (Z/pZ)^n line 31 source
Source documentation
𝔽 p n is the vector space (Z/pZ)^n. When p is prime, this is $\mathbb{F}_p^n$.

no axioms what this means
Statement uses: Nat
Proof uses: Fin, ZMod
```
abbrev 𝔽 (p n : ℕ) := Fin n → ZMod p
```
abbrev 𝔽₂ 𝔽₂ n is the vector space $\mathbb{F}_2^n$ line 34 source
Source documentation
𝔽₂ n is the vector space $\mathbb{F}_2^n$.

no axioms what this means
Statement uses: Nat
Proof uses: 𝔽, OfNat.ofNat
1 instances, coercions and auxiliary constants left out.
```
abbrev 𝔽₂ (n : ℕ) := 𝔽 2 n
```
Mentions: 𝔽
abbrev 𝔽₃ 𝔽₃ n is the vector space $\mathbb{F}_3^n$ line 37 source
Source documentation
𝔽₃ n is the vector space $\mathbb{F}_3^n$.

no axioms what this means
Statement uses: Nat
Proof uses: 𝔽, OfNat.ofNat
1 instances, coercions and auxiliary constants left out.
```
abbrev 𝔽₃ (n : ℕ) := 𝔽 3 n
```
Mentions: 𝔽
abbrev 𝔽₅ 𝔽₅ n is the vector space $\mathbb{F}_5^n$ line 40 source
Source documentation
𝔽₅ n is the vector space $\mathbb{F}_5^n$.

no axioms what this means
Statement uses: Nat
Proof uses: 𝔽, OfNat.ofNat
1 instances, coercions and auxiliary constants left out.
```
abbrev 𝔽₅ (n : ℕ) := 𝔽 5 n
```
Mentions: 𝔽
abbrev 𝔽₇ 𝔽₇ n is the vector space $\mathbb{F}_7^n$ line 43 source
Source documentation
𝔽₇ n is the vector space $\mathbb{F}_7^n$.

no axioms what this means
Statement uses: Nat
Proof uses: 𝔽, OfNat.ofNat
1 instances, coercions and auxiliary constants left out.
```
abbrev 𝔽₇ (n : ℕ) := 𝔽 7 n
```
Mentions: 𝔽