`BookProof.ChapterA3u.trace_decomposition_five` : Matrix.trace (projSym 5) + Matrix.trace (projAnti 5) + Matrix.trace (projMixed 5) = 1024

Proved

BookProof.ChapterA3u.trace_decomposition_five

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA3u.

BookProof.ChapterA3u.trace_decomposition_five : Matrix.trace (projSym 5) + Matrix.trace (projAnti 5) + Matrix.trace (projMixed 5) = 1024

Formalization note: Lean 4 identifier BookProof.ChapterA3u.trace_decomposition_five.

Preamble

-- Generated from ChapterA3u.lean — theorem BookProof.ChapterA3u.trace_decomposition_five
import Definitions.Def_ChapterA3q
import Definitions.Def_ChapterA3r
import Mathlib
import Definitions.Def_ChapterA3u
import Definitions.Def_ChapterA3l
import Definitions.Def_ChapterA3n
import Definitions.Def_ChapterA3o
open BookProof.ChapterA3l
open BookProof.ChapterA3n
open BookProof.ChapterA3o
open BookProof.ChapterA3u


open Matrix
open scoped BigOperators


open BookProof.ChapterA3n BookProof.ChapterA3o BookProof.ChapterA3q
open BookProof.ChapterA3r

Formal statement

theorem BookProof.ChapterA3u.trace_decomposition_five :
    Matrix.trace (projSym 5) + Matrix.trace (projAnti 5)
        + Matrix.trace (projMixed 5) = 1024 := by sorry

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