`BookProof.ProbabilityClockStochastic.isColumnStochastic_eq_Mab` {M : Matrix (Fin 2) (Fin 2) ℝ} (hM : IsColumnStochastic M) : ∃ a b, M = Mab a b

Proved

BookProof.ProbabilityClockStochastic.isColumnStochastic_eq_Mab

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterProbabilityClockStochastic.

BookProof.ProbabilityClockStochastic.isColumnStochastic_eq_Mab {M : Matrix (Fin 2) (Fin 2) ℝ} (hM : IsColumnStochastic M) : ∃ a b, M = Mab a b

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

Preamble

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



open Matrix
open scoped Norms.Operator

Formal statement

theorem BookProof.ProbabilityClockStochastic.isColumnStochastic_eq_Mab {M : Matrix (Fin 2) (Fin 2) ℝ}
    (hM : IsColumnStochastic M) : ∃ a b, M = Mab a b := by sorry

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