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Update holomorphic_primitive2.lean

This commit is contained in:
Stefan Kebekus 2024-08-07 13:29:58 +02:00
parent fc3a4ae3f3
commit 951c25624e
1 changed files with 12 additions and 4 deletions
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Nevanlinna/holomorphic_primitive2.lean
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@ -97,7 +97,16 @@ theorem primitive_fderivAtBasepointZero
have B : Metric.ball (f 0) (c / 4) ∈ nhds (f 0) := by have B : Metric.ball (f 0) (c / 4) ∈ nhds (f 0) := by
apply Metric.ball_mem_nhds (f 0) apply Metric.ball_mem_nhds (f 0)
linarith linarith
exact eventually_nhds_iff.mp (continuousAt_def.1 hf (Metric.ball (f 0) (c / (4 : ℝ))) B) apply eventually_nhds_iff.mp
apply continuousAt_def.1
apply Continuous.continuousAt
fun_prop
apply continuousAt_def.1
apply hf.continuousAt
exact Metric.ball_mem_nhds 0 hR
apply Metric.ball_mem_nhds (f 0)
simpa
obtain ⟨ε, h₁ε, h₂ε⟩ : ∃ ε > 0, (Metric.ball 0 ε) ×ℂ (Metric.ball 0 ε) ⊆ s := by obtain ⟨ε, h₁ε, h₂ε⟩ : ∃ ε > 0, (Metric.ball 0 ε) ×ℂ (Metric.ball 0 ε) ⊆ s := by
obtain ⟨ε', h₁ε', h₂ε'⟩ : ∃ ε' > 0, Metric.ball 0 ε' ⊆ s ∩ Metric.ball 0 R := by obtain ⟨ε', h₁ε', h₂ε'⟩ : ∃ ε' > 0, Metric.ball 0 ε' ⊆ s ∩ Metric.ball 0 R := by
@ -108,13 +117,12 @@ theorem primitive_fderivAtBasepointZero
exact Metric.isOpen_ball exact Metric.isOpen_ball
constructor constructor
· exact h₂s.2 · exact h₂s.2
· simp · simpa
sorry
use (2 : ℝ)⁻¹ * ε' use (2 : ℝ)⁻¹ * ε'
constructor constructor
· simpa · simpa
· intro x hx · intro x hx
apply Set.inter_subset_left
apply h₂ε' apply h₂ε'
simp simp
calc Complex.abs x calc Complex.abs x