Prove2Me

domReg is nonempty

Proved
ExactVacuumAtlas.EinsteinMaxwell.KN.domReg_nonempty

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

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

domReg is nonempty

domReg M a Q is nonempty for every real M, a, Q.

Scope. Exactly the hypotheses printed in the formal statement.

中文摘要 domReg 非空。

Preamble
import Mathlib
import Definitions.Def_Atlas_Core_Basic
import Definitions.Def_Atlas_Core_Lift
import Definitions.Def_Atlas_EinsteinMaxwell_Basic
import Definitions.Def_Atlas_EinsteinMaxwell_KN_Defs
import Definitions.Def_Atlas_EinsteinMaxwell_KN_Domain
import Definitions.Def_Atlas_Kerr_InAtoms
open Real
open ExactVacuumAtlas
open ExactVacuumAtlas.EinsteinMaxwell
open ExactVacuumAtlas.EinsteinMaxwell.KN
open ExactVacuumAtlas.Kerr.In (Ui Wi)
Formal statement
theorem ExactVacuumAtlas.EinsteinMaxwell.KN.domReg_nonempty (M a Q : ℝ) : (domReg M a Q).Nonempty := 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/KN/Domain.lean#L113-L125; SHA-256 2cba50578710c01bc97b197588f366c9fd153ed1add83d7d7577383f23a9ccce. 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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