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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)

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depends on (8)

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