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AlexKontorovich/PrimeNumberTheoremAnd
Source indexedlemma · leanprover/lean4:v4.32.0

FKS2.hasDerivAt_Li

PrimeNumberTheoremAnd.IEANTN.FKS2 · PrimeNumberTheoremAnd/IEANTN/FKS2.lean:2762 to 2770

Mathematical statement

Exact Lean statement

lemma hasDerivAt_Li {x : ℝ} (hx : x ∈ Set.Ioi 6.58) : HasDerivAt Li (1 / log x) x

Complete declaration

Lean source

Canonical source
Full Lean sourceLean 4
lemma hasDerivAt_Li {x : } (hx : x  Set.Ioi 6.58) : HasDerivAt Li (1 / log x) x := by  have hf (x) (hx : x  Set.Ioi 6.58) : ContinuousAt (fun x  1 / log x) x := by    have := log_pos (by linarith [Set.mem_Ioi.mp hx]) |>.ne'    fun_prop (disch := simp_all)  refine intervalIntegral.integral_hasDerivAt_right ?_ ?_ (hf x hx)  · have := Set.uIcc_of_le (show 2  x by linarith [Set.mem_Ioi.mp hx])    apply intervalIntegral.intervalIntegrable_one_div (by grind [log_eq_zero])    fun_prop (disch := grind)  · grind [ContinuousAt.stronglyMeasurableAtFilter isOpen_Ioi hf]