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theorem proved tactic proof

linkRate_strict_anti

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formal statement (Lean)

  43theorem linkRate_strict_anti {n m : ℕ} (h : n < m) :
  44    linkRate m < linkRate n := by

proof body

Tactic-mode proof.

  45  unfold linkRate
  46  have hp1 : 0 < phi ^ n := pow_pos phi_pos _
  47  have h_pow : phi ^ n < phi ^ m := pow_lt_pow_right₀ one_lt_phi h
  48  -- R_0 / φ^m < R_0 / φ^n  ↔  φ^n < φ^m (since R_0 > 0).
  49  have h_R_pos : (0 : ℝ) < R_0 := by unfold R_0; norm_num
  50  exact div_lt_div_of_pos_left h_R_pos hp1 h_pow
  51

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