Prove2Me

Certificate transfer along componentwise equality

Proved
ExactVacuumAtlas.EinsteinMaxwell.EinsteinMaxwellCertificate.congr

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

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

Certificate transfer along componentwise equality

An Einstein–Maxwell certificate on U transfers to data (g′, ginv′, F′) that agree componentwise with (g, ginv, F) on U (all residuals are local).

Scope. Exactly the hypotheses printed in the formal statement.

中文摘要 分量相等时证书的转移。

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.congr (h : EinsteinMaxwellCertificate g ginv F U) {g' ginv' : Metric 4} {F' : TwoForm 4}
    (hg : ∀ i j, Set.EqOn (g i j) (g' i j) U) (hgi : ∀ i j, Set.EqOn (ginv i j) (ginv' i j) U)
    (hF : ∀ i j, Set.EqOn (F i j) (F' i j) U) : EinsteinMaxwellCertificate g' ginv' F' U := 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#L49-L97; 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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