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lemma proved term proof

Jlog_pos_iff

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formal statement (Lean)

  29@[simp] lemma Jlog_pos_iff (t : ℝ) : 0 < Jlog t ↔ t ≠ 0 := by

proof body

Term-mode proof.

  30  -- rewrite to `0 < cosh t - 1` and use `one_lt_cosh`
  31  rw [Jlog_eq_cosh_sub_one]
  32  constructor
  33  · intro ht
  34    have : (1 : ℝ) < Real.cosh t := (sub_pos).1 ht
  35    exact (Real.one_lt_cosh (x := t)).1 this
  36  · intro hne
  37    have : (1 : ℝ) < Real.cosh t := (Real.one_lt_cosh (x := t)).2 hne
  38    exact (sub_pos).2 this
  39

used by (2)

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depends on (6)

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