`BookProof.ChapterEulerStochastic.uniform_to_vertex_singular` (M : Matrix (Fin 2) (Fin 2) ℝ) (hM : PreservesProb M) (hcollapse : M *ᵥ ![1 / 2, 1 / 2] = ![1, 0]) : M.det = 0

Proved

BookProof.ChapterEulerStochastic.uniform_to_vertex_singular

by leonardopedro · Oct 8, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterEulerStochastic.

BookProof.ChapterEulerStochastic.uniform_to_vertex_singular (M : Matrix (Fin 2) (Fin 2) ℝ) (hM : PreservesProb M) (hcollapse : M *ᵥ ![1 / 2, 1 / 2] = ![1, 0]) : M.det = 0

Formalization note: Lean 4 identifier BookProof.ChapterEulerStochastic.uniform_to_vertex_singular.

Preamble

-- Generated from ChapterEulerStochastic.lean — theorem BookProof.ChapterEulerStochastic.uniform_to_vertex_singular
import Mathlib
import Definitions.Def_ChapterEulerStochastic
open BookProof.ChapterEulerStochastic


open scoped Matrix BigOperators

Formal statement

theorem BookProof.ChapterEulerStochastic.uniform_to_vertex_singular (M : Matrix (Fin 2) (Fin 2) ℝ)
    (hM : PreservesProb M) (hcollapse : M *ᵥ ![1 / 2, 1 / 2] = ![1, 0]) :
    M.det = 0 := by sorry

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