`BookProof.ChapterTrajectory.jointProb_sum_final_eq_midProb` (U V : Matrix (Fin n) (Fin n) ℂ) (psi : Fin n → ℂ) (hV : Vᴴ * V = 1) (a : Fin n) : ∑ f, jointProb U V psi f a = midProb

Proved

BookProof.ChapterTrajectory.jointProb_sum_final_eq_midProb

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterTrajectory.

BookProof.ChapterTrajectory.jointProb_sum_final_eq_midProb (U V : Matrix (Fin n) (Fin n) ℂ) (psi : Fin n → ℂ) (hV : Vᴴ * V = 1) (a : Fin n) : ∑ f, jointProb U V psi f a = midProb U psi a

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

Preamble

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


open scoped BigOperators Matrix


variable {n : ℕ}

Formal statement

theorem BookProof.ChapterTrajectory.jointProb_sum_final_eq_midProb (U V : Matrix (Fin n) (Fin n) ℂ)
    (psi : Fin n → ℂ) (hV : Vᴴ * V = 1) (a : Fin n) :
    ∑ f, jointProb U V psi f a = midProb U psi a := by sorry

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