Tanh has Temperate Growth
tanh_hasTemperateGrowth
Plain-language statement
tanh has temperate growth
Exact Lean statement
lemma tanh_hasTemperateGrowth : Function.HasTemperateGrowth Real.tanh
Formal artifact
Lean source
lemma tanh_hasTemperateGrowth : Function.HasTemperateGrowth Real.tanh := by constructor · apply contDiff_top_tanh · intro n use 0 obtain ⟨C, hC⟩ := iteratedDeriv_tanh_bounded n use C intro x have h_equiv : ‖iteratedFDeriv ℝ n Real.tanh x‖ = |iteratedDeriv n Real.tanh x| := by rw [← iteratedFDerivWithin_univ] rw [← iteratedDerivWithin_univ] rw [← norm_eq_abs] rw [norm_iteratedFDerivWithin_eq_norm_iteratedDerivWithin] rw [h_equiv] simp only [pow_zero, mul_one] exact hC x- Project
- Physlib
- License
- Apache-2.0
- Commit
- dd43e9e65791
- Source
- Physlib/Mathematics/Trigonometry/Tanh.lean:140-155
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