`BookProof.ChapterA3.lambda_two_to_one` (hpf : PauliFundamental) {S S' : Matrix (Fin 4) (Fin 4) ℝ} (hS : IsPin S) (hS' : IsPin S') (h : LambdaOf S = LambdaOf S') : S' = S ∨ S' = -S

Proved

BookProof.ChapterA3.lambda_two_to_one

by leonardopedro · Oct 6, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA3c.

BookProof.ChapterA3.lambda_two_to_one (hpf : PauliFundamental) {S S' : Matrix (Fin 4) (Fin 4) ℝ} (hS : IsPin S) (hS' : IsPin S') (h : LambdaOf S = LambdaOf S') : S' = S ∨ S' = -S

Formalization note: Lean 4 identifier BookProof.ChapterA3.lambda_two_to_one.

Preamble

-- Generated from ChapterA3c.lean — theorem BookProof.ChapterA3.lambda_two_to_one
import Mathlib
import Definitions.Def_ChapterA3c
import Definitions.Def_ChapterA3b
import Definitions.Def_ChapterA3
open BookProof.ChapterA3


open Matrix
open scoped ComplexConjugate

Formal statement

theorem BookProof.ChapterA3.lambda_two_to_one (hpf : PauliFundamental)
    {S S' : Matrix (Fin 4) (Fin 4) ℝ} (hS : IsPin S) (hS' : IsPin S')
    (h : LambdaOf S = LambdaOf S') : S' = S ∨ S' = -S := by sorry

View graph