`BookProof.ChapterWeylSL2Group.exists_factorization` (g : Matrix.SpecialLinearGroup (Fin 2) ℂ) : ∃ x y z w : ℂ, g = uPlus x * uMinus y * uPlus z * uMinus w

Proved

BookProof.ChapterWeylSL2Group.exists_factorization

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterWeylSL2Group.

BookProof.ChapterWeylSL2Group.exists_factorization (g : Matrix.SpecialLinearGroup (Fin 2) ℂ) : ∃ x y z w : ℂ, g = uPlus x * uMinus y * uPlus z * uMinus w

Formalization note: Lean 4 identifier BookProof.ChapterWeylSL2Group.exists_factorization.

Preamble

-- Generated from ChapterWeylSL2Group.lean — theorem BookProof.ChapterWeylSL2Group.exists_factorization
import Definitions.Def_ChapterWeylSl2
import Mathlib
import Definitions.Def_ChapterWeylSL2Group
open BookProof.ChapterWeylSL2Group



open BookProof.ChapterWeylSl2

universe u

variable {V : Type u} [AddCommGroup V] [Module ℂ V]

Formal statement

theorem BookProof.ChapterWeylSL2Group.exists_factorization (g : Matrix.SpecialLinearGroup (Fin 2) ℂ) :
    ∃ x y z w : ℂ, g = uPlus x * uMinus y * uPlus z * uMinus w := by sorry

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