structure
definition
def or abbrev
MetricTensor
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formal statement (Lean)
11structure MetricTensor where
12 g : BilinearForm
13 symmetric : ∀ x up low, g x up low = g x up (fun i => if (i : ℕ) = 0 then low 1 else low 0)
14
15@[ext]
16lemma MetricTensor.ext (g1 g2 : MetricTensor) (h : g1.g = g2.g) : g1 = g2 := by
proof body
Definition body.
17 cases g1; cases g2; simp_all
18
used by (40)
-
energy_conservation -
HamiltonianDensity -
hamiltonian_equivalence -
H_EnergyConservation -
H_HamiltonianEquivalence -
inverse_metric -
IsTimeTranslationInvariant -
metric_det -
MetricTensor -
StressEnergyTensor -
TotalHamiltonian -
metric_compatibility -
MetricTensor -
minkowski -
hilbert_variation_holds -
jacobi_variation -
jacobi_variation_structural -
einstein_symmetric -
einstein_tensor -
sourced_efe_coord -
vacuum_efe_coord -
contracted_bianchi -
efe_with_source -
perfect_fluid -
vacuum_is_special_case -
H_HomogenizationLimit -
homogenization_limit -
metric_det -
MetricTensor -
metric_FRW