`BookProof.SymmetryEntropy.entropy_pointMass` (a : Fin n) : entropy (fun k => if k = a then (1 : ℝ) else 0) = 0

Proved

BookProof.SymmetryEntropy.entropy_pointMass

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSymmetryEntropy.

BookProof.SymmetryEntropy.entropy_pointMass (a : Fin n) : entropy (fun k => if k = a then (1 : ℝ) else 0) = 0

Formalization note: Lean 4 identifier BookProof.SymmetryEntropy.entropy_pointMass.

Preamble

-- Generated from ChapterSymmetryEntropy.lean — theorem BookProof.SymmetryEntropy.entropy_pointMass
import Definitions.Def_ChapterMarkovEntropy
import Definitions.Def_ChapterReconstruct
import Mathlib
import Definitions.Def_ChapterSymmetryEntropy
import Definitions.Def_ChapterIrreversible
open BookProof.SymmetryEntropy



open Finset
open BookProof.ChapterMarkovEntropy (entropy)
open BookProof.ChapterReconstruct (IsDeterministicCol)

variable {n : ℕ}

Formal statement

theorem BookProof.SymmetryEntropy.entropy_pointMass (a : Fin n) :
    entropy (fun k => if k = a then (1 : ℝ) else 0) = 0 := by sorry

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