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formal statement (Lean)
120structure HilbertVariationCert where
121 flat_ok : hilbert_variation_holds minkowski minkowski_inverse
122 (fun _ _ _ => 0) (fun _ _ _ _ => 0)
123 eh_flat : ∀ det_g kappa : ℝ, kappa ≠ 0 → eh_lagrangian_density 0 det_g kappa = 0
124 einstein_symmetric : ∀ met ginv gamma dgamma,
125 (∀ mu nu, ricci_tensor gamma dgamma mu nu = ricci_tensor gamma dgamma nu mu) →
126 ∀ mu nu, einstein_tensor met ginv gamma dgamma mu nu =
127 einstein_tensor met ginv gamma dgamma nu mu
128 einstein_flat : ∀ mu nu, einstein_tensor minkowski minkowski_inverse
129 (fun _ _ _ => 0) (fun _ _ _ _ => 0) mu nu = 0
130
used by (1)
From the project-wide theorem graph. These declarations reference this one in their body.
depends on (17)
Lean names referenced from this declaration's body.
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gamma
in IndisputableMonolith.Constants.EulerMascheroni
decl_use
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mu
in IndisputableMonolith.Cost.Ndim.Projector
decl_use
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minkowski
in IndisputableMonolith.Gravity.Connection
decl_use
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minkowski_inverse
in IndisputableMonolith.Gravity.Connection
decl_use
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eh_flat
in IndisputableMonolith.Gravity.EinsteinHilbertAction
decl_use
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eh_lagrangian_density
in IndisputableMonolith.Gravity.EinsteinHilbertAction
decl_use
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hilbert_variation_holds
in IndisputableMonolith.Gravity.EinsteinHilbertAction
decl_use
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einstein_flat
in IndisputableMonolith.Gravity.RicciTensor
decl_use
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einstein_symmetric
in IndisputableMonolith.Gravity.RicciTensor
decl_use
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einstein_tensor
in IndisputableMonolith.Gravity.RicciTensor
decl_use
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ricci_tensor
in IndisputableMonolith.Gravity.RicciTensor
decl_use
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kappa
in IndisputableMonolith.Materials.ThermalConductivityRegimesFromPhiLadder
decl_use
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gamma
in IndisputableMonolith.NetworkScience.SmallWorldFromSigma
decl_use
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kappa
in IndisputableMonolith.NumberTheory.AnnularCost
decl_use
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einstein_tensor
in IndisputableMonolith.Relativity.Geometry.Curvature
decl_use
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ricci_tensor
in IndisputableMonolith.Relativity.Geometry.Curvature
decl_use
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gamma
in IndisputableMonolith.Relativity.ILG.PPN
decl_use