Prove2Me

EF5: explicit inverse

Proved
ExactVacuumAtlas.EinsteinMaxwell.EF5.inv_mul_EF5

by He Wang · Oct 28, 2026 · Mathlib 0df444a (Lean v4.33.1)

einstein-maxwellexact-spacetime-atlas-viexact-vacuum-atlasfive-dimensional-gravitygeneral-relativity

EF5: explicit inverse

For all real μ, β and x ∈ domU5: metricMatrix (giEF5 μ β) x * metricMatrix (gEF5 μ β) x = 1.

Scope. Exactly the hypotheses printed in the formal statement.

中文摘要 EF5 显式逆度规。

Preamble
import Mathlib
import Definitions.Def_Atlas_Core_Basic
import Definitions.Def_Atlas_Core_Certificate
import Definitions.Def_Atlas_EinsteinMaxwell_Basic
import Definitions.Def_Atlas_EinsteinMaxwell_D_Basic
import Definitions.Def_Atlas_EinsteinMaxwell_EF5_Defs
open scoped ContDiff
open ExactVacuumAtlas ExactVacuumAtlas.EinsteinMaxwell ExactVacuumAtlas.EinsteinMaxwell.D
open ExactVacuumAtlas
open ExactVacuumAtlas.EinsteinMaxwell
open ExactVacuumAtlas.EinsteinMaxwell.EF5
set_option maxHeartbeats 4000000
set_option linter.unusedVariables false
Formal statement
theorem ExactVacuumAtlas.EinsteinMaxwell.EF5.inv_mul_EF5 (mu beta : ℝ) {x : Pt 5} (hx : x ∈ domU5) :
    metricMatrix (giEF5 mu beta) x * metricMatrix (gEF5 mu beta) x = 1 := by sorry
Source
He Wang, Exact Spacetime Atlas VI: Five-Dimensional Einstein–Maxwell Certificates and Equal-Spin Radial Reduction. Local source, no public repository; commit 4a4048a; Atlas/EinsteinMaxwell/EF5/Defs.lean#L62-L69; SHA-256 f231f4a9949f874f4e55d1d1a5d115dc989dd2dea043b61580e11ec6dcfcc0ca. Registered definitions: mission/PHYSICS_BOUNDARY.md (§N–§O); literature: R. C. Myers, M. J. Perry, Ann. Phys. 172 (1986) 304; F. R. Tangherlini, Nuovo Cimento 27 (1963) 636.
Human review

  • Endorsed by Shuze Chen · Oct 29, 2026

    Confirmed by the moderator at approval.

  • Endorsed by He Wang · Oct 29, 2026

    Confirmed by the mission captain (proposal self-audit).

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