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

Proved

BookProof.ChapterA4g.SEtwo_mul_mem

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA4g.

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

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

Preamble

-- Generated from ChapterA4g.lean — theorem BookProof.ChapterA4g.SEtwo_mul_mem
import Definitions.Def_ChapterA3
import Mathlib
import Definitions.Def_ChapterA4g
import Definitions.Def_ChapterA4d
open BookProof.ChapterA4g


open Matrix
open scoped ComplexConjugate


open BookProof.ChapterA3

Formal statement

theorem BookProof.ChapterA4g.SEtwo_mul_mem {S T : Matrix (Fin 2) (Fin 2) ℂ}
    (hS : S ∈ SEtwo) (hT : T ∈ SEtwo) : S * T ∈ SEtwo := by sorry

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