Prove2Me

`BookProof.ChapterA4g.SUtwo_mul_mem` {S T : Matrix (Fin 2) (Fin 2) ℂ} (hS : S ∈ SUtwo) (hT : T ∈ SUtwo) : S * T ∈ SUtwo

Proved
BookProof.ChapterA4g.SUtwo_mul_mem

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA4g.

BookProof.ChapterA4g.SUtwo_mul_mem {S T : Matrix (Fin 2) (Fin 2) ℂ} (hS : S ∈ SUtwo) (hT : T ∈ SUtwo) : S * T ∈ SUtwo

Formalization note: Lean 4 identifier BookProof.ChapterA4g.SUtwo_mul_mem.

Preamble
-- Generated from ChapterA4g.lean — theorem BookProof.ChapterA4g.SUtwo_mul_mem
import Definitions.Def_ChapterA3
import Mathlib
import Definitions.Def_ChapterA4g
import Definitions.Def_ChapterA4c
open BookProof.ChapterA4g


open Matrix
open scoped ComplexConjugate


open BookProof.ChapterA3
Formal statement
theorem BookProof.ChapterA4g.SUtwo_mul_mem {S T : Matrix (Fin 2) (Fin 2) ℂ}
    (hS : S ∈ SUtwo) (hT : T ∈ SUtwo) : S * T ∈ SUtwo := by sorry

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