`BookProof.ChapterTrajectory.transProb_sum` (V : Matrix (Fin n) (Fin n) ℂ) (hV : Vᴴ * V = 1) (a : Fin n) : ∑ f, transProb V f a = 1

Proved

BookProof.ChapterTrajectory.transProb_sum

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterTrajectory.

BookProof.ChapterTrajectory.transProb_sum (V : Matrix (Fin n) (Fin n) ℂ) (hV : Vᴴ * V = 1) (a : Fin n) : ∑ f, transProb V f a = 1

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

Preamble

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


open scoped BigOperators Matrix


variable {n : ℕ}

Formal statement

theorem BookProof.ChapterTrajectory.transProb_sum (V : Matrix (Fin n) (Fin n) ℂ) (hV : Vᴴ * V = 1)
    (a : Fin n) : ∑ f, transProb V f a = 1 := by sorry

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