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`BookProof.FreeFieldConstraint.constraint_preserved_under_bracket` (D H A : R) (hDH : bracket D H = 0) (hDA : bracket D A = 0) : bracket D (bracket H A) = 0

Proved
BookProof.FreeFieldConstraint.constraint_preserved_under_bracket

by leonardopedro · Oct 5, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFreeFieldConstraint.

BookProof.FreeFieldConstraint.constraint_preserved_under_bracket (D H A : R) (hDH : bracket D H = 0) (hDA : bracket D A = 0) : bracket D (bracket H A) = 0

Formalization note: Lean 4 identifier BookProof.FreeFieldConstraint.constraint_preserved_under_bracket.

Preamble
-- Generated from ChapterFreeFieldConstraint.lean — theorem BookProof.FreeFieldConstraint.constraint_preserved_under_bracket
import Mathlib
import Definitions.Def_ChapterFreeFieldConstraint
open BookProof.FreeFieldConstraint

variable {R : Type*} [Ring R]
Formal statement
theorem BookProof.FreeFieldConstraint.constraint_preserved_under_bracket (D H A : R)
    (hDH : bracket D H = 0) (hDA : bracket D A = 0) :
    bracket D (bracket H A) = 0 := by sorry

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