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theorem proved term proof

phi_ladder_tc_monotone

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formal statement (Lean)

  88theorem phi_ladder_tc_monotone (n : ℤ) : T_c_rung n < T_c_rung (n + 1) := by

proof body

Term-mode proof.

  89  unfold T_c_rung
  90  rw [zpow_add_one₀ phi_ne_zero]
  91  have hphi_gt1 : 1 < phi := one_lt_phi
  92  have hpos : 0 < phi ^ n := zpow_pos phi_pos n
  93  exact lt_mul_of_one_lt_right hpos hphi_gt1
  94
  95/-- **THEOREM EN-002.6**: The φ-ladder spans all temperature scales.
  96    For any temperature T > 0, there exists a rung n such that T_c(n) > T. -/

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