`BookProof.ChapterIrreversible.le_one_of_prob` (p : Fin n → ℝ) (hnn : ∀ a, 0 ≤ p a) (hsum : ∑ a, p a = 1) (a : Fin n) : p a ≤ 1

Proved

BookProof.ChapterIrreversible.le_one_of_prob

by leonardopedro · Oct 9, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterIrreversible.

BookProof.ChapterIrreversible.le_one_of_prob (p : Fin n → ℝ) (hnn : ∀ a, 0 ≤ p a) (hsum : ∑ a, p a = 1) (a : Fin n) : p a ≤ 1

Formalization note: Lean 4 identifier BookProof.ChapterIrreversible.le_one_of_prob.

Preamble

-- Generated from ChapterIrreversible.lean — theorem BookProof.ChapterIrreversible.le_one_of_prob
import Mathlib
import Definitions.Def_ChapterIrreversible
open BookProof.ChapterIrreversible


open scoped BigOperators
open Finset


variable {n : ℕ}

Formal statement

theorem BookProof.ChapterIrreversible.le_one_of_prob (p : Fin n → ℝ) (hnn : ∀ a, 0 ≤ p a)
    (hsum : ∑ a, p a = 1) (a : Fin n) : p a ≤ 1 := by sorry

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