`BookProof.ChapterReconstruct.offDiag_unit_iff` (U : Fin n → Fin n → ℂ) : (∀ (a : Fin n) (Ψ : Fin n → ℂ), (∑ k : Fin n, ‖Ψ k‖ ^ 2) = 1 → offDiag U a Ψ = 0) ↔ IsDeterministic U

Proved

BookProof.ChapterReconstruct.offDiag_unit_iff

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterReconstruct.

BookProof.ChapterReconstruct.offDiag_unit_iff (U : Fin n → Fin n → ℂ) : (∀ (a : Fin n) (Ψ : Fin n → ℂ), (∑ k : Fin n, ‖Ψ k‖ ^ 2) = 1 → offDiag U a Ψ = 0) ↔ IsDeterministic U

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

Preamble

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


open scoped BigOperators
open Finset


variable {n : ℕ}

Formal statement

theorem BookProof.ChapterReconstruct.offDiag_unit_iff (U : Fin n → Fin n → ℂ) :
    (∀ (a : Fin n) (Ψ : Fin n → ℂ), (∑ k : Fin n, ‖Ψ k‖ ^ 2) = 1 →
        offDiag U a Ψ = 0) ↔ IsDeterministic U := by sorry

View graph