`BookProof.SymmetryEntropy.bornCol_eq_zero_iff` (U : Fin n → Fin n → ℂ) (a k : Fin n) : bornCol U a k = 0 ↔ U k a = 0

Proved

BookProof.SymmetryEntropy.bornCol_eq_zero_iff

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSymmetryEntropy.

BookProof.SymmetryEntropy.bornCol_eq_zero_iff (U : Fin n → Fin n → ℂ) (a k : Fin n) : bornCol U a k = 0 ↔ U k a = 0

Formalization note: Lean 4 identifier BookProof.SymmetryEntropy.bornCol_eq_zero_iff.

Preamble

-- Generated from ChapterSymmetryEntropy.lean — theorem BookProof.SymmetryEntropy.bornCol_eq_zero_iff
import Definitions.Def_ChapterMarkovEntropy
import Definitions.Def_ChapterReconstruct
import Mathlib
import Definitions.Def_ChapterSymmetryEntropy
open BookProof.SymmetryEntropy



open Finset
open BookProof.ChapterMarkovEntropy (entropy)
open BookProof.ChapterReconstruct (IsDeterministicCol)

variable {n : ℕ}

Formal statement

theorem BookProof.SymmetryEntropy.bornCol_eq_zero_iff (U : Fin n → Fin n → ℂ) (a k : Fin n) :
    bornCol U a k = 0 ↔ U k a = 0 := by sorry

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