Prove2Me

RN inverse is a true inverse

Proved
ExactVacuumAtlas.EinsteinMaxwell.RN.EF.inv_mul

by He Wang · Oct 21, 2026 · Mathlib 0df444a (Lean v4.33.1)

einstein-maxwellexact-spacetime-atlas-ivexact-vacuum-atlasgeneral-relativity

RN inverse is a true inverse

giRN M b · gRN M b = 1 on domRN, every real M, b.

Scope. Exactly the hypotheses printed in the formal statement.

中文摘要 RN 逆矩阵检验。

Preamble
import Mathlib
import Definitions.Def_Atlas_Core_Basic
import Definitions.Def_Atlas_Core_Certificate
import Definitions.Def_Atlas_Core_Lift
import Definitions.Def_Atlas_EinsteinMaxwell_Basic
import Definitions.Def_Atlas_EinsteinMaxwell_Certificate
import Definitions.Def_Atlas_EinsteinMaxwell_RN_Defs
import Definitions.Def_Atlas_EinsteinMaxwell_RN_Frame
open Real
open scoped ContDiff
open ExactVacuumAtlas ExactVacuumAtlas.EinsteinMaxwell ExactVacuumAtlas.EinsteinMaxwell.RN
open ExactVacuumAtlas
open ExactVacuumAtlas.EinsteinMaxwell
open ExactVacuumAtlas.EinsteinMaxwell.RN
set_option maxHeartbeats 4000000
Formal statement
theorem ExactVacuumAtlas.EinsteinMaxwell.RN.EF.inv_mul (M b : ℝ) {x : Pt 4} (hx : x ∈ domRN) :
    metricMatrix (giRN M b) x * metricMatrix (gRN M b) x = 1 := by sorry
Source
He Wang, Exact Spacetime Atlas IV: Certified Einstein–Maxwell Backgrounds and First Variations. Local source, no public repository; commit 543904bfcfa3bb169f43fc4d9dbd569999b71886; Atlas/EinsteinMaxwell/RN/EFCert.lean#L61-L67; SHA-256 357f1c6dcc9d4b1de6bc91d8180a4c7e5b75316199ee7ef426a62e658987ab64. Registered definitions and literature: mission/PHYSICS_BOUNDARY.md (§H–§J); Müller–Grave arXiv:0904.4184; Newman et al., J. Math. Phys. 6 (1965) 918.
Human review

  • Endorsed by Shuze Chen · Oct 21, 2026

    Confirmed by the moderator at approval.

  • Endorsed by He Wang · Oct 21, 2026

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

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