`BookProof.ChapterA3p.tensorSquare_complete_reducibility` : projSym 2 + projAnti 2 = 1 ∧ projSym 2 * projAnti 2 = 0 ∧ projAnti 2 * projSym 2 = 0 ∧ projSym 2 * projSym 2 = projSym 2

Proved

BookProof.ChapterA3p.tensorSquare_complete_reducibility

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA3p.

BookProof.ChapterA3p.tensorSquare_complete_reducibility : projSym 2 + projAnti 2 = 1 ∧ projSym 2 * projAnti 2 = 0 ∧ projAnti 2 * projSym 2 = 0 ∧ projSym 2 * projSym 2 = projSym 2 ∧ projAnti 2 * projAnti 2 = projAnti 2

Formalization note: Lean 4 identifier BookProof.ChapterA3p.tensorSquare_complete_reducibility.

Preamble

-- Generated from ChapterA3p.lean — theorem BookProof.ChapterA3p.tensorSquare_complete_reducibility
import Definitions.Def_ChapterA3
import Definitions.Def_ChapterA3j
import Mathlib
import Definitions.Def_ChapterA3p
import Definitions.Def_ChapterA3l
import Definitions.Def_ChapterA3n
import Definitions.Def_ChapterA3o
open BookProof.ChapterA3l
open BookProof.ChapterA3n
open BookProof.ChapterA3o
open BookProof.ChapterA3p


open Matrix
open scoped BigOperators


open BookProof.ChapterA3 BookProof.ChapterA3j BookProof.ChapterA3n BookProof.ChapterA3o

Formal statement

theorem BookProof.ChapterA3p.tensorSquare_complete_reducibility :
    projSym 2 + projAnti 2 = 1 ∧
    projSym 2 * projAnti 2 = 0 ∧
    projAnti 2 * projSym 2 = 0 ∧
    projSym 2 * projSym 2 = projSym 2 ∧
    projAnti 2 * projAnti 2 = projAnti 2 := by sorry

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