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theorem proved term proof

exp_factor_bounded

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formal statement (Lean)

  71theorem exp_factor_bounded (hfg : 0 ≤ f_gap) :
  72    0 < Real.exp (-(f_gap / alpha_seed)) ∧ Real.exp (-(f_gap / alpha_seed)) ≤ 1 := by

proof body

Term-mode proof.

  73  constructor
  74  · exact Real.exp_pos _
  75  · apply Real.exp_le_one_iff.mpr
  76    apply neg_nonpos_of_nonneg
  77    exact div_nonneg hfg (le_of_lt alpha_seed_positive)
  78
  79/-- The ratio alphaInv/alpha_seed equals the exponential factor. -/

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