`BookProof.ChapterAttentionQKCircuit.rank_qkMatrix_le` (WQ WK : Matrix (Fin d) (Fin n) ℝ) : (qkMatrix WQ WK).rank ≤ d

Proved

BookProof.ChapterAttentionQKCircuit.rank_qkMatrix_le

by leonardopedro · Oct 7, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterAttentionQKCircuit.

BookProof.ChapterAttentionQKCircuit.rank_qkMatrix_le (WQ WK : Matrix (Fin d) (Fin n) ℝ) : (qkMatrix WQ WK).rank ≤ d

Formalization note: Lean 4 identifier BookProof.ChapterAttentionQKCircuit.rank_qkMatrix_le.

Preamble

-- Generated from ChapterAttentionQKCircuit.lean — theorem BookProof.ChapterAttentionQKCircuit.rank_qkMatrix_le
import Definitions.Def_ChapterSoftmaxSharpness
import Definitions.Def_ChapterSoftmaxOrder
import Mathlib
import Definitions.Def_ChapterAttentionQKCircuit
open BookProof.ChapterAttentionQKCircuit


open scoped BigOperators

noncomputable section


open Matrix BookProof.ChapterSoftmaxSharpness BookProof.ChapterSoftmaxOrder

variable {d n m : ℕ} {E : Type*} [NormedAddCommGroup E] [NormedSpace ℝ E]

Formal statement

theorem BookProof.ChapterAttentionQKCircuit.rank_qkMatrix_le (WQ WK : Matrix (Fin d) (Fin n) ℝ) : (qkMatrix WQ WK).rank ≤ d := by sorry

View graph