`BookProof.ChapterTrajectory.finalProb_total` (U V : Matrix (Fin n) (Fin n) ℂ) (psi : Fin n → ℂ) (hU : Uᴴ * U = 1) (hV : Vᴴ * V = 1) (hpsi : ∑ a, ‖psi a‖ ^ 2 = 1) : ∑ f, finalProb

Proved

BookProof.ChapterTrajectory.finalProb_total

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterTrajectory.

BookProof.ChapterTrajectory.finalProb_total (U V : Matrix (Fin n) (Fin n) ℂ) (psi : Fin n → ℂ) (hU : Uᴴ * U = 1) (hV : Vᴴ * V = 1) (hpsi : ∑ a, ‖psi a‖ ^ 2 = 1) : ∑ f, finalProb U V psi f = 1

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

Preamble

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


open scoped BigOperators Matrix


variable {n : ℕ}

Formal statement

theorem BookProof.ChapterTrajectory.finalProb_total (U V : Matrix (Fin n) (Fin n) ℂ) (psi : Fin n → ℂ)
    (hU : Uᴴ * U = 1) (hV : Vᴴ * V = 1) (hpsi : ∑ a, ‖psi a‖ ^ 2 = 1) :
    ∑ f, finalProb U V psi f = 1 := by sorry

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