`BookProof.ChapterGravityIrrep.frob_antisym_trace` (M : Matrix (Fin 3) (Fin 3) ℝ) : frobInner (antisymPart M) ((M.trace) • (1 : Matrix (Fin 3) (Fin 3) ℝ)) = 0

Proved

BookProof.ChapterGravityIrrep.frob_antisym_trace

by leonardopedro · Oct 8, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterGravityIrrep.

BookProof.ChapterGravityIrrep.frob_antisym_trace (M : Matrix (Fin 3) (Fin 3) ℝ) : frobInner (antisymPart M) ((M.trace) • (1 : Matrix (Fin 3) (Fin 3) ℝ)) = 0

Formalization note: Lean 4 identifier BookProof.ChapterGravityIrrep.frob_antisym_trace.

Preamble

-- Generated from ChapterGravityIrrep.lean — theorem BookProof.ChapterGravityIrrep.frob_antisym_trace
import Mathlib
import Definitions.Def_ChapterGravityIrrep
open BookProof.ChapterGravityIrrep



open Matrix
open scoped BigOperators

Formal statement

theorem BookProof.ChapterGravityIrrep.frob_antisym_trace (M : Matrix (Fin 3) (Fin 3) ℝ) :
    frobInner (antisymPart M) ((M.trace) • (1 : Matrix (Fin 3) (Fin 3) ℝ)) = 0 := by sorry

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