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Update holomorphic_primitive2.lean

This commit is contained in:
Stefan Kebekus 2024-08-07 09:17:35 +02:00
parent 6bdb910b7c
commit a2d3793df2
1 changed files with 17 additions and 10 deletions
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Nevanlinna/holomorphic_primitive2.lean
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@ -533,7 +533,6 @@ theorem primitive_additivity'
rw [← Complex.dist_eq_re_im]; simp rw [← Complex.dist_eq_re_im]; simp
exact hz₁ exact hz₁
obtain ⟨ε, h₁ε, h₂ε⟩ := Metric.isOpen_iff.1 lem₀Ω 0 lem₁Ω obtain ⟨ε, h₁ε, h₂ε⟩ := Metric.isOpen_iff.1 lem₀Ω 0 lem₁Ω
have h'₁ε : 0 < ε := by exact h₁ε
let ε' := (2 : ℝ)⁻¹ * ε let ε' := (2 : ℝ)⁻¹ * ε
@ -571,20 +570,28 @@ theorem primitive_additivity'
simp simp
rw [Complex.dist_eq_re_im] rw [Complex.dist_eq_re_im]
have : dist x.re z₀.re < rx := Metric.mem_ball.mp hx.1 have t₀ : dist x.re z₀.re < rx := Metric.mem_ball.mp hx.1
have : dist x.im z₀.im < ry := Metric.mem_ball.mp hx.2 have t₁ : dist x.im z₀.im < ry := Metric.mem_ball.mp hx.2
have t₂ : √((x.re - z₀.re) ^ 2 + (x.im - z₀.im) ^ 2) < √( rx ^ 2 + ry ^ 2) := by
have t₀ : √((x.re - z₀.re) ^ 2 + (x.im - z₀.im) ^ 2) < √( rx ^ 2 + ry ^ 2) := by
rw [Real.sqrt_lt_sqrt_iff] rw [Real.sqrt_lt_sqrt_iff]
apply add_lt_add apply add_lt_add
· dsimp [rx] · rw [sq_lt_sq]
dsimp [dist] at t₀
sorry nth_rw 2 [abs_of_nonneg]
· sorry assumption
apply add_nonneg dist_nonneg (le_of_lt h₀ε)
· rw [sq_lt_sq]
dsimp [dist] at t₁
nth_rw 2 [abs_of_nonneg]
assumption
apply add_nonneg dist_nonneg (le_of_lt h₀ε)
apply add_nonneg
exact sq_nonneg (x.re - z₀.re)
exact sq_nonneg (x.im - z₀.im)
calc √((x.re - z₀.re) ^ 2 + (x.im - z₀.im) ^ 2) calc √((x.re - z₀.re) ^ 2 + (x.im - z₀.im) ^ 2)
_ < √( rx ^ 2 + ry ^ 2) := by _ < √( rx ^ 2 + ry ^ 2) := by
exact t₀ exact t₂
_ = d ε := by dsimp [d, rx, ry] _ = d ε := by dsimp [d, rx, ry]
_ < R := by exact h₁ε _ < R := by exact h₁ε