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Prove bianchi_second#57

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MathNetwork:mainfrom
dxww123:codex/bianchi-second
Open

Prove bianchi_second#57
dxww123 wants to merge 1 commit into
MathNetwork:mainfrom
dxww123:codex/bianchi-second

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@dxww123 dxww123 commented May 19, 2026

Closes #12.

Summary

Proves OpenGALib/Riemannian/Connection/LeviCivita.lean :: bianchi_second and closes the remaining statement-only sorry for the differential Bianchi identity.

The implementation takes a connection-algebra route:

  • expands covDerivRiemann into the torsion-free commutator form of curvature
  • groups the six connection-difference pairs into Lie-bracket terms via covDeriv_sub_swap_eq_mlieBracket
  • collapses the grouped terms using section-level torsion-freeness rewrites
  • finishes with SmoothVectorField.mlieBracket_jacobi

It also updates the CI sorry baseline from EXPECTED=36 to EXPECTED=35.

Validation

  • lake build OpenGALib.Riemannian.Connection.LeviCivita
  • sorry count regex over OpenGALib/**/*.lean: 35

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Prove bianchi_second (differential Bianchi identity)

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