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

Proved

BookProof.ChapterReconstruct.offDiag_eq_zero_iff_isDeterministic

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_isDeterministic (U : Fin n → Fin n → ℂ) : (∀ (a : Fin n) (Ψ : Fin n → ℂ), offDiag U a Ψ = 0) ↔ IsDeterministic U

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

Preamble

-- Generated from ChapterReconstruct.lean — theorem BookProof.ChapterReconstruct.offDiag_eq_zero_iff_isDeterministic
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_isDeterministic (U : Fin n → Fin n → ℂ) :
    (∀ (a : Fin n) (Ψ : Fin n → ℂ), offDiag U a Ψ = 0) ↔ IsDeterministic U := by sorry

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