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lemma proved tactic proof

hasDerivAt_Jlog

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formal statement (Lean)

 180lemma hasDerivAt_Jlog (t : ℝ) : HasDerivAt Jlog (Real.sinh t) t := by

proof body

Tactic-mode proof.

 181  have h1 : Jlog = fun t => Real.cosh t - 1 := by
 182    ext t
 183    exact Jlog_as_cosh t
 184  rw [h1]
 185  have h_cosh : HasDerivAt Real.cosh (Real.sinh t) t := Real.hasDerivAt_cosh t
 186  have h_const : HasDerivAt (fun _ => (1 : ℝ)) 0 t := hasDerivAt_const t 1
 187  have h_sub := h_cosh.sub h_const
 188  simp at h_sub
 189  exact h_sub
 190

used by (5)

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