`BookProof.ChapterConditional.pMarg_eq_diagBHB` (B : Matrix Y X 𝕜) (x : X) : ((Bᴴ * B) x x) = ((pMarg B x : ℝ) : 𝕜)

Proved

BookProof.ChapterConditional.pMarg_eq_diagBHB

by leonardopedro · Oct 7, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterConditional.

BookProof.ChapterConditional.pMarg_eq_diagBHB (B : Matrix Y X 𝕜) (x : X) : ((Bᴴ * B) x x) = ((pMarg B x : ℝ) : 𝕜)

Formalization note: Lean 4 identifier BookProof.ChapterConditional.pMarg_eq_diagBHB.

Preamble

-- Generated from ChapterConditional.lean — theorem BookProof.ChapterConditional.pMarg_eq_diagBHB
import Mathlib
import Definitions.Def_ChapterConditional
open BookProof.ChapterConditional


open scoped BigOperators Matrix
open Finset


variable {X Y : Type*} [Fintype X] [Fintype Y] [DecidableEq X]
variable {𝕜 : Type*} [RCLike 𝕜]

Formal statement

theorem BookProof.ChapterConditional.pMarg_eq_diagBHB (B : Matrix Y X 𝕜) (x : X) :
    ((Bᴴ * B) x x) = ((pMarg B x : ℝ) : 𝕜) := by sorry

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