`BookProof.ChapterTrajectory.midProb_sum` (U : Matrix (Fin n) (Fin n) ℂ) (psi : Fin n → ℂ) (hU : Uᴴ * U = 1) : ∑ a, midProb U psi a = ∑ a, ‖psi a‖ ^ 2

Proved

BookProof.ChapterTrajectory.midProb_sum

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterTrajectory.

BookProof.ChapterTrajectory.midProb_sum (U : Matrix (Fin n) (Fin n) ℂ) (psi : Fin n → ℂ) (hU : Uᴴ * U = 1) : ∑ a, midProb U psi a = ∑ a, ‖psi a‖ ^ 2

Formalization note: Lean 4 identifier BookProof.ChapterTrajectory.midProb_sum.

Preamble

-- Generated from ChapterTrajectory.lean — theorem BookProof.ChapterTrajectory.midProb_sum
import Mathlib
import Definitions.Def_ChapterTrajectory
open BookProof.ChapterTrajectory


open scoped BigOperators Matrix


variable {n : ℕ}

Formal statement

theorem BookProof.ChapterTrajectory.midProb_sum (U : Matrix (Fin n) (Fin n) ℂ) (psi : Fin n → ℂ)
    (hU : Uᴴ * U = 1) : ∑ a, midProb U psi a = ∑ a, ‖psi a‖ ^ 2 := by sorry

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