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theorem proved tactic proof

sbh_saturation_positive

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formal statement (Lean)

  68theorem sbh_saturation_positive (Rs : ℝ) (h_Rs : Rs > 0) :
  69    0 < HorizonArea Rs / (4 * ell0^2) := by

proof body

Tactic-mode proof.

  70  have hA : 0 < HorizonArea Rs := horizon_area_pos Rs h_Rs
  71  have hden : 0 < 4 * ell0 ^ 2 := by
  72    nlinarith [sq_pos_of_pos ell0_pos]
  73  exact div_pos hA hden
  74
  75/-- The BH entropy saturation value is nonzero for `Rs > 0`. -/

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