theorem
proved
term proof
positive_eigenvalue_count
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formal statement (Lean)
153theorem positive_eigenvalue_count :
154 (Finset.univ.filter (fun i : Fin 4 => 0 < η i i)).card = 3 := by
proof body
Term-mode proof.
155 suffices h : Finset.univ.filter (fun i : Fin 4 => 0 < η i i) =
156 {(1 : Fin 4), (2 : Fin 4), (3 : Fin 4)} by
157 rw [h]; decide
158 ext i; fin_cases i <;>
159 simp [Finset.mem_filter, η_00, η_11, η_22, η_33, Fin.ext_iff]
160
161/-- **SE-004: The metric signature is (1, 3) — Lorentzian.** -/