EMCertificateD transfers along EqOn data
ProvedExactVacuumAtlas.EinsteinMaxwell.D.EMCertificateD.congreinstein-maxwellexact-spacetime-atlas-viexact-vacuum-atlasfive-dimensional-gravitygeneral-relativity
EMCertificateD transfers along EqOn data
If EMCertificateD g ginv F U holds and g', ginv', F' agree componentwise with g, ginv, F on U, then EMCertificateD g' ginv' F' U (total dimension n + 1).
Scope. Exactly the hypotheses printed in the formal statement.
中文摘要 EMCertificateD 沿 U 上逐分量相等的数据传递。
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
open scoped ContDiff
open ExactVacuumAtlas ExactVacuumAtlas.EinsteinMaxwell
open ExactVacuumAtlas
open ExactVacuumAtlas.EinsteinMaxwell
open ExactVacuumAtlas.EinsteinMaxwell.D
variable {n : ℕ} {g ginv : Metric (n + 1)} {F : TwoForm (n + 1)} {U : Set (Pt (n + 1))}
Formal statement
theorem ExactVacuumAtlas.EinsteinMaxwell.D.EMCertificateD.congr (h : EMCertificateD g ginv F U) {g' ginv' : Metric (n + 1)} {F' : TwoForm (n + 1)}
(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) : EMCertificateD g' ginv' F' U := by sorrySource
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/D/Transfer.lean#L20-L68; SHA-256 78a5207d09bd50bfc82e646cb5b085123303f7fabe24854bf0e65d16f2d7d9ae. 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
Confirmed by the mission captain (proposal self-audit).
Confirmed by the moderator at approval.