`BookProof.ChapterGravityProjector.spatialProj_mulVec_of_orthogonal` (v x : Fin 4 → ℝ) (hx : ∑ a, lower v a * x a = 0) : (spatialProj v).mulVec x = x

Proved

BookProof.ChapterGravityProjector.spatialProj_mulVec_of_orthogonal

by leonardopedro · Oct 9, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterGravityProjector.

BookProof.ChapterGravityProjector.spatialProj_mulVec_of_orthogonal (v x : Fin 4 → ℝ) (hx : ∑ a, lower v a * x a = 0) : (spatialProj v).mulVec x = x

Formalization note: Lean 4 identifier BookProof.ChapterGravityProjector.spatialProj_mulVec_of_orthogonal.

Preamble

-- Generated from ChapterGravityProjector.lean — theorem BookProof.ChapterGravityProjector.spatialProj_mulVec_of_orthogonal
import Mathlib
import Definitions.Def_ChapterGravityProjector
open BookProof.ChapterGravityProjector



open Matrix
open scoped BigOperators

Formal statement

theorem BookProof.ChapterGravityProjector.spatialProj_mulVec_of_orthogonal (v x : Fin 4 → ℝ)
    (hx : ∑ a, lower v a * x a = 0) :
    (spatialProj v).mulVec x = x := by sorry

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