Prove2Me

The Lean 4 theorem `sirk_compression_block_le` in the `ChapterH8` chapter of the timepiece formalization

Proved
BookProof.ChapterH8.sirk_compression_block_le

by leonardopedro · Oct 1, 2026 · Mathlib 0df444a (Lean v4.33.1)

timepiece

The Lean 4 theorem sirk_compression_block_le in the ChapterH8 chapter of the timepiece formalization.

Preamble
-- Generated from ChapterH8.lean — theorem BookProof.ChapterH8.sirk_compression_block_le
import Mathlib
import Definitions.Def_ChapterH8
open BookProof.ChapterH8

variable {K E : Type*} [Field K] [AddCommGroup E] [Module K E]
variable {E F G : Type*}
  [NormedAddCommGroup E] [InnerProductSpace ℂ E] [CompleteSpace E]
  [NormedAddCommGroup F] [InnerProductSpace ℂ F] [CompleteSpace F]
  [NormedAddCommGroup G] [InnerProductSpace ℂ G] [CompleteSpace G]
variable {E : Type*} [NormedAddCommGroup E] [InnerProductSpace ℂ E] [CompleteSpace E]
variable {E F G : Type*}
  [NormedAddCommGroup E] [InnerProductSpace ℂ E] [CompleteSpace E]
  [NormedAddCommGroup F] [InnerProductSpace ℂ F] [CompleteSpace F]
  [NormedAddCommGroup G] [InnerProductSpace ℂ G] [CompleteSpace G]
variable {E F G : Type*}
  [NormedAddCommGroup E] [InnerProductSpace ℂ E] [CompleteSpace E]
  [NormedAddCommGroup F] [InnerProductSpace ℂ F] [CompleteSpace F]
  [NormedAddCommGroup G] [InnerProductSpace ℂ G] [CompleteSpace G]


noncomputable section


open BookProof.ChapterH4 BookProof.ChapterH5 BookProof.ChapterH6
Formal statement
theorem BookProof.ChapterH8.sirk_compression_block_le {m n : ℕ} (hmn : m ≤ n) (X : E →L[ℂ] E)
    (Vm : EuclideanSpace ℂ (Fin m) →L[ℂ] E)
    (Vn : EuclideanSpace ℂ (Fin n) →L[ℂ] E)
    (hnest : ∀ i : Fin m, Vm (EuclideanSpace.single i (1 : ℂ))
      = Vn (EuclideanSpace.single (Fin.castLE hmn i) (1 : ℂ)))
    (i j : Fin m) :
    reduceGenerator m Vm X i j
      = reduceGenerator n Vn X (Fin.castLE hmn i) (Fin.castLE hmn j) := by sorry
Source
https://github.com/leonardopedro/timepiece/blob/61595bc/BookProof/ChapterH8.lean

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