Prove2Me

Inner isotropic branch relation (0 < ρ < M/2 ↔ r > 2M), M > 0

Proved
ExactVacuumAtlas.Schwarzschild.Iso.relation_in

by He Wang · Oct 15, 2026 · Mathlib 0df444a (Lean v4.33.1)

exact-vacuum-atlasgeneral-relativitylean4mathlib

For every real M > 0: CoordRelation (gIso M) (gStd M) (domIsoIn M) (domStdExt M) (toStd M) (fromStdIn M) (jacIso M) (conjunct (ii) of isotropic_branches).

Preamble
import Mathlib
import Definitions.Def_Atlas_Core_Basic
import Definitions.Def_Atlas_Core_Relation
import Definitions.Def_Atlas_Isotropic_Defs
import Definitions.Def_Atlas_Schwarzschild_Defs
import Definitions.Def_Atlas_Schwarzschild_Domain
open Real Matrix
open scoped ContDiff
open ExactVacuumAtlas ExactVacuumAtlas.Schwarzschild
open ExactVacuumAtlas
open ExactVacuumAtlas.Schwarzschild
open ExactVacuumAtlas.Schwarzschild.Iso
set_option maxHeartbeats 4000000
variable (M : ℝ)
Formal statement
theorem ExactVacuumAtlas.Schwarzschild.Iso.relation_in (hM : 0 < M) :
    CoordRelation (gIso M) (gStd M) (domIsoIn M) (domStdExt M) (toStd M) (fromStdIn M) (jacIso M) := by sorry
Source
He Wang, Exact Vacuum Atlas II, local source snapshot (public Git repository not yet available), commit 11fb317259353b71a41d6daed466c495cffd7db4; Atlas/Isotropic/Relation.lean#L286-L296; SHA-256 7da94260c91052d64d731cd40ce965798ffa54f3a09bf2d8d615e3c5c657d5ad. Mathematical background: See mission/PHYSICS_BOUNDARY.md §A-F for registered definitions and literature references (Wald, Müller-Grave arXiv:0904.4184, Visser arXiv:0706.0622, Martel-Poisson gr-qc/0001069).
Human review

  • Endorsed by Shuze Chen · Oct 18, 2026

    Confirmed by the moderator at approval.

  • Endorsed by He Wang · Oct 18, 2026

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

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