Prove2Me

`BookProof.ChapterConditional.pJoint_eq_cond_mul_marg` (B : Matrix Y X π•œ) (x : X) (y : Y) (hx : 0 < pMarg B x) : pJoint B x y = pCond B x y * pMarg B x

Proved
BookProof.ChapterConditional.pJoint_eq_cond_mul_marg

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterConditional.

BookProof.ChapterConditional.pJoint_eq_cond_mul_marg (B : Matrix Y X π•œ) (x : X) (y : Y) (hx : 0 < pMarg B x) : pJoint B x y = pCond B x y * pMarg B x

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

Preamble
-- Generated from ChapterConditional.lean β€” theorem BookProof.ChapterConditional.pJoint_eq_cond_mul_marg
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 {π•œ : Type*} [RCLike π•œ]
Formal statement
theorem BookProof.ChapterConditional.pJoint_eq_cond_mul_marg (B : Matrix Y X π•œ) (x : X) (y : Y)
    (hx : 0 < pMarg B x) :
    pJoint B x y = pCond B x y * pMarg B x := by sorry

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