Prove2Me

`BookProof.ChapterA3w.lemma52_parity_gluing` : (projChirL * mgamma 0 ≠ mgamma 0 * projChirL) ∧ (projChirL * mgamma 0 = mgamma 0 * projChirR) ∧ (parityDiag * projLL ≠ projLL * parit

Proved
BookProof.ChapterA3w.lemma52_parity_gluing

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA3w.

BookProof.ChapterA3w.lemma52_parity_gluing : (projChirL * mgamma 0 ≠ mgamma 0 * projChirL) ∧ (projChirL * mgamma 0 = mgamma 0 * projChirR) ∧ (parityDiag * projLL ≠ projLL * parityDiag) ∧ (parityDiag * projRR = projLL * parityDiag)

Formalization note: Lean 4 identifier BookProof.ChapterA3w.lemma52_parity_gluing.

Preamble
-- Generated from ChapterA3w.lean — theorem BookProof.ChapterA3w.lemma52_parity_gluing
import Definitions.Def_ChapterA3q
import Mathlib
import Definitions.Def_ChapterA3w
import Definitions.Def_ChapterA3
import Definitions.Def_ChapterA3j
import Definitions.Def_ChapterA3k
open BookProof.ChapterA3
open BookProof.ChapterA3j
open BookProof.ChapterA3k
open BookProof.ChapterA3w


open Matrix


open BookProof.ChapterA3 BookProof.ChapterA3j BookProof.ChapterA3k BookProof.ChapterA3q
Formal statement
theorem BookProof.ChapterA3w.lemma52_parity_gluing :
    (projChirL * mgamma 0 ≠ mgamma 0 * projChirL) ∧
    (projChirL * mgamma 0 = mgamma 0 * projChirR) ∧
    (parityDiag * projLL ≠ projLL * parityDiag) ∧
    (parityDiag * projRR = projLL * parityDiag) := by sorry

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