`BookProof.ChapterReconstruct.offDiag_eq_zero_iff` (U : Fin n → Fin n → ℂ) (a : Fin n) : (∀ Ψ : Fin n → ℂ, offDiag U a Ψ = 0) ↔ IsDeterministicCol U a

Proved

BookProof.ChapterReconstruct.offDiag_eq_zero_iff

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterReconstruct.

BookProof.ChapterReconstruct.offDiag_eq_zero_iff (U : Fin n → Fin n → ℂ) (a : Fin n) : (∀ Ψ : Fin n → ℂ, offDiag U a Ψ = 0) ↔ IsDeterministicCol U a

Formalization note: Lean 4 identifier BookProof.ChapterReconstruct.offDiag_eq_zero_iff.

Preamble

-- Generated from ChapterReconstruct.lean — theorem BookProof.ChapterReconstruct.offDiag_eq_zero_iff
import Mathlib
import Definitions.Def_ChapterReconstruct
open BookProof.ChapterReconstruct


open scoped BigOperators
open Finset


variable {n : ℕ}

Formal statement

theorem BookProof.ChapterReconstruct.offDiag_eq_zero_iff (U : Fin n → Fin n → ℂ) (a : Fin n) :
    (∀ Ψ : Fin n → ℂ, offDiag U a Ψ = 0) ↔ IsDeterministicCol U a := by sorry

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