Prove2Me

Certificate restriction to an open subset

Proved
ExactVacuumAtlas.EinsteinMaxwell.EinsteinMaxwellCertificate.mono

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

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

Certificate restriction to an open subset

An Einstein–Maxwell certificate on U restricts to every open nonempty V ⊆ U.

Scope. Exactly the hypotheses printed in the formal statement.

中文摘要 证书限制到开子集。

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_Certificate
open scoped ContDiff
open ExactVacuumAtlas
open ExactVacuumAtlas.EinsteinMaxwell
variable {g ginv : Metric 4} {F : TwoForm 4} {U : Set (Pt 4)}
Formal statement
theorem ExactVacuumAtlas.EinsteinMaxwell.EinsteinMaxwellCertificate.mono (h : EinsteinMaxwellCertificate g ginv F U) {V : Set (Pt 4)} (hVU : V ⊆ U)
    (hV : IsOpen V) (hne : V.Nonempty) : EinsteinMaxwellCertificate g ginv F V := 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/Transfer.lean#L33-L47; SHA-256 406c2eab6eaa154112760347f130ff5f2181e38eaa0539f514f2ab3e9a58c93c. 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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