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) xComplete declaration
Lean source
Full Lean sourceLean 4
lemma hasDerivAt_Li {x : ℝ} (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]