`BookProof.ProbabilityClockStochastic.stochastic_uniform_to_deterministic_singular` {M : Matrix (Fin 2) (Fin 2) ℝ} (hM : IsColumnStochastic M) (hMap : M.mulVec ![1 / 2, 1 / 2] = ![

Proved

BookProof.ProbabilityClockStochastic.stochastic_uniform_to_deterministic_singular

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterProbabilityClockStochastic.

BookProof.ProbabilityClockStochastic.stochastic_uniform_to_deterministic_singular {M : Matrix (Fin 2) (Fin 2) ℝ} (hM : IsColumnStochastic M) (hMap : M.mulVec ![1 / 2, 1 / 2] = ![1, 0]) : M.det = 0

Formalization note: Lean 4 identifier BookProof.ProbabilityClockStochastic.stochastic_uniform_to_deterministic_singular.

Preamble

-- Generated from ChapterProbabilityClockStochastic.lean — theorem BookProof.ProbabilityClockStochastic.stochastic_uniform_to_deterministic_singular
import Mathlib
import Definitions.Def_ChapterProbabilityClockStochastic
open BookProof.ProbabilityClockStochastic



open Matrix
open scoped Norms.Operator

Formal statement

theorem BookProof.ProbabilityClockStochastic.stochastic_uniform_to_deterministic_singular
    {M : Matrix (Fin 2) (Fin 2) ℝ} (hM : IsColumnStochastic M)
    (hMap : M.mulVec ![1 / 2, 1 / 2] = ![1, 0]) : M.det = 0 := by sorry

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