diff --git a/Nevanlinna/holomorphic_primitive2.lean b/Nevanlinna/holomorphic_primitive2.lean index 78454b4..8791614 100644 --- a/Nevanlinna/holomorphic_primitive2.lean +++ b/Nevanlinna/holomorphic_primitive2.lean @@ -538,12 +538,11 @@ theorem primitive_additivity theorem primitive_additivity' {E : Type u} [NormedAddCommGroup E] [NormedSpace ℂ E] [CompleteSpace E] - (f : ℂ → E) - (z₀ : ℂ) - (R : ℝ) + {f : ℂ → E} + {z₀ z₁ : ℂ} + {R : ℝ} (hf : DifferentiableOn ℂ f (Metric.ball z₀ R)) - (z₁ : ℂ) - (hz₁ : z₁ ∈ (Metric.ball z₀ R)) + (hz₁ : z₁ ∈ Metric.ball z₀ R) : primitive z₀ f =ᶠ[nhds z₁] fun z ↦ (primitive z₁ f z) + (primitive z₀ f z₁) := by sorry @@ -551,14 +550,14 @@ theorem primitive_additivity' theorem primitive_hasDerivAt {E : Type u} [NormedAddCommGroup E] [NormedSpace ℂ E] [CompleteSpace E] - (f : ℂ → E) - (z₀ z : ℂ) - (R : ℝ) + {f : ℂ → E} + {z₀ z : ℂ} + {R : ℝ} (hf : DifferentiableOn ℂ f (Metric.ball z₀ R)) (hz : z ∈ Metric.ball z₀ R) : HasDerivAt (primitive z₀ f) (f z) z := by - let A := primitive_additivity' f z₀ R hf z hz + let A := primitive_additivity' hf hz rw [Filter.EventuallyEq.hasDerivAt_iff A] rw [← add_zero (f z)] apply HasDerivAt.add @@ -579,7 +578,7 @@ theorem primitive_differentiable DifferentiableOn ℂ (primitive z₀ f) (Metric.ball z₀ R) := by intro z hz apply DifferentiableAt.differentiableWithinAt - exact (primitive_hasDerivAt f z₀ z R hf hz).differentiableAt + exact (primitive_hasDerivAt hf hz).differentiableAt theorem primitive_hasFderivAt @@ -593,27 +592,27 @@ theorem primitive_hasFderivAt intro z hz rw [hasFDerivAt_iff_hasDerivAt] simp - apply primitive_hasDerivAt f z₀ z R hf hz + apply primitive_hasDerivAt hf hz theorem primitive_hasFderivAt' {f : ℂ → ℂ} - (z₀ : ℂ) - (R : ℝ) + {z₀ : ℂ} + {R : ℝ} (hf : DifferentiableOn ℂ f (Metric.ball z₀ R)) : ∀ z ∈ Metric.ball z₀ R, HasFDerivAt (primitive z₀ f) (ContinuousLinearMap.lsmul ℂ ℂ (f z)) z := by intro z hz rw [hasFDerivAt_iff_hasDerivAt] simp - exact primitive_hasDerivAt f z₀ z R hf hz + exact primitive_hasDerivAt hf hz theorem primitive_fderiv {E : Type u} [NormedAddCommGroup E] [NormedSpace ℂ E] [CompleteSpace E] {f : ℂ → E} - (z₀ : ℂ) - (R : ℝ) + {z₀ : ℂ} + {R : ℝ} (hf : DifferentiableOn ℂ f (Metric.ball z₀ R)) : ∀ z ∈ Metric.ball z₀ R, (fderiv ℂ (primitive z₀ f) z) = (ContinuousLinearMap.lsmul ℂ ℂ).flip (f z) := by @@ -624,11 +623,11 @@ theorem primitive_fderiv theorem primitive_fderiv' {f : ℂ → ℂ} - (z₀ : ℂ) - (R : ℝ) + {z₀ : ℂ} + {R : ℝ} (hf : DifferentiableOn ℂ f (Metric.ball z₀ R)) : ∀ z ∈ Metric.ball z₀ R, (fderiv ℂ (primitive z₀ f) z) = ContinuousLinearMap.lsmul ℂ ℂ (f z) := by intro z hz apply HasFDerivAt.fderiv - exact primitive_hasFderivAt' z₀ R hf z hz + exact primitive_hasFderivAt' hf z hz