`BookProof.ChapterGravityMetric.spatialMetric_quadForm_nonneg` (v x : Fin 4 → ℝ) (hv : minkSq v = -1) : 0 ≤ x ⬝ᵥ ((spatialMetric v).mulVec x)

Proved

BookProof.ChapterGravityMetric.spatialMetric_quadForm_nonneg

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterGravityMetric.

BookProof.ChapterGravityMetric.spatialMetric_quadForm_nonneg (v x : Fin 4 → ℝ) (hv : minkSq v = -1) : 0 ≤ x ⬝ᵥ ((spatialMetric v).mulVec x)

Formalization note: Lean 4 identifier BookProof.ChapterGravityMetric.spatialMetric_quadForm_nonneg.

Preamble

-- Generated from ChapterGravityMetric.lean — theorem BookProof.ChapterGravityMetric.spatialMetric_quadForm_nonneg
import Mathlib
import Definitions.Def_ChapterGravityMetric
import Definitions.Def_ChapterGravityProjector
open BookProof.ChapterGravityProjector
open BookProof.ChapterGravityMetric



open Matrix
open scoped BigOperators
open BookProof.ChapterGravityProjector

Formal statement

theorem BookProof.ChapterGravityMetric.spatialMetric_quadForm_nonneg (v x : Fin 4 → ℝ) (hv : minkSq v = -1) :
    0 ≤ x ⬝ᵥ ((spatialMetric v).mulVec x) := by sorry

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