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Update meromorphicOn.lean

This commit is contained in:
Stefan Kebekus 2024-11-18 18:44:42 +01:00
parent 22d9b8aa95
commit 12888b75fb
1 changed files with 22 additions and 3 deletions
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Nevanlinna/meromorphicOn.lean
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@ -18,19 +18,38 @@ theorem MeromorphicOn.open_of_order_eq_top
apply isOpen_iff_forall_mem_open.mpr apply isOpen_iff_forall_mem_open.mpr
intro z hz intro z hz
simp at hz simp at hz
have h₁z := hz
rw [MeromorphicAt.order_eq_top_iff] at hz rw [MeromorphicAt.order_eq_top_iff] at hz
rw [eventually_nhdsWithin_iff] at hz rw [eventually_nhdsWithin_iff] at hz
rw [eventually_nhds_iff] at hz rw [eventually_nhds_iff] at hz
obtain ⟨t', h₁t', h₂t', h₃t'⟩ := hz obtain ⟨t', h₁t', h₂t', h₃t'⟩ := hz
let t : Set U := Subtype.val ⁻¹' t' let t : Set U := Subtype.val ⁻¹' t'
use t use t
constructor constructor
· intro w hw · intro w hw
simp simp
by_cases h₁w : w = z
· rwa [h₁w]
· --
rw [MeromorphicAt.order_eq_top_iff] rw [MeromorphicAt.order_eq_top_iff]
rw [eventually_nhdsWithin_iff]
rw [eventually_nhds_iff]
use t' \ {z.1}
constructor
· intro y h₁y h₂y
apply h₁t'
exact Set.mem_of_mem_diff h₁y
exact Set.mem_of_mem_inter_right h₁y
· constructor
· apply IsOpen.sdiff h₂t'
exact isClosed_singleton
· rw [Set.mem_diff]
constructor
· exact hw
· simp
exact Subtype.coe_ne_coe.mpr h₁w
sorry
· constructor · constructor
· exact isOpen_induced h₂t' · exact isOpen_induced h₂t'
· exact h₃t' · exact h₃t'