url stringclasses 147
values | commit stringclasses 147
values | file_path stringlengths 7 101 | full_name stringlengths 1 94 | start stringlengths 6 10 | end stringlengths 6 11 | tactic stringlengths 1 11.2k | state_before stringlengths 3 2.09M | state_after stringlengths 6 2.09M | input stringlengths 73 2.09M |
|---|---|---|---|---|---|---|---|---|---|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | NontrivialHolomorphicAt.anti | [308, 1] | [316, 58] | refine ⟨⟨fa, ?_⟩, ⟨ga, ?_⟩⟩ | X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticManifold 𝓘(ℂ... | case refine_1
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : Analyti... | Please generate a tactic in lean4 to solve the state.
STATE:
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : Topologica... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | NontrivialHolomorphicAt.anti | [308, 1] | [316, 58] | contrapose h | case refine_1
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : Analyti... | case refine_1
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : Analyti... | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_1
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | NontrivialHolomorphicAt.anti | [308, 1] | [316, 58] | simp only [Filter.not_frequently, not_not] at h ⊢ | case refine_1
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : Analyti... | case refine_1
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : Analyti... | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_1
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | NontrivialHolomorphicAt.anti | [308, 1] | [316, 58] | exact (ga.continuousAt.eventually h).mp (eventually_of_forall fun _ h ↦ h) | case refine_1
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : Analyti... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_1
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | NontrivialHolomorphicAt.anti | [308, 1] | [316, 58] | contrapose h | case refine_2
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : Analyti... | case refine_2
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : Analyti... | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_2
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | NontrivialHolomorphicAt.anti | [308, 1] | [316, 58] | simp only [Filter.not_frequently, not_not] at h ⊢ | case refine_2
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : Analyti... | case refine_2
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : Analyti... | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_2
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | NontrivialHolomorphicAt.anti | [308, 1] | [316, 58] | exact h.mp (eventually_of_forall fun x h ↦ by rw [h]) | case refine_2
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : Analyti... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_2
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | NontrivialHolomorphicAt.anti | [308, 1] | [316, 58] | rw [h] | X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticManifold 𝓘(ℂ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : Topologica... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | nontrivialHolomorphicAt_id | [320, 1] | [342, 64] | use holomorphicAt_id | X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticManifold 𝓘(ℂ... | case nonconst
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : Analyti... | Please generate a tactic in lean4 to solve the state.
STATE:
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : Topologica... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | nontrivialHolomorphicAt_id | [320, 1] | [342, 64] | rw [Filter.frequently_iff] | case nonconst
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : Analyti... | case nonconst
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : Analyti... | Please generate a tactic in lean4 to solve the state.
STATE:
case nonconst
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | nontrivialHolomorphicAt_id | [320, 1] | [342, 64] | intro s sz | case nonconst
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : Analyti... | case nonconst
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : Analyti... | Please generate a tactic in lean4 to solve the state.
STATE:
case nonconst
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | nontrivialHolomorphicAt_id | [320, 1] | [342, 64] | rcases mem_nhds_iff.mp sz with ⟨t, ts, ot, zt⟩ | case nonconst
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : Analyti... | case nonconst.intro.intro.intro
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace... | Please generate a tactic in lean4 to solve the state.
STATE:
case nonconst
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | nontrivialHolomorphicAt_id | [320, 1] | [342, 64] | generalize hu : (extChartAt I z).target ∩ (extChartAt I z).symm ⁻¹' t = u | case nonconst.intro.intro.intro
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace... | case nonconst.intro.intro.intro
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace... | Please generate a tactic in lean4 to solve the state.
STATE:
case nonconst.intro.intro.intro
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | nontrivialHolomorphicAt_id | [320, 1] | [342, 64] | have uo : IsOpen u := by
rw [← hu]
exact (continuousOn_extChartAt_symm I z).isOpen_inter_preimage (isOpen_extChartAt_target _ _) ot | case nonconst.intro.intro.intro
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace... | case nonconst.intro.intro.intro
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace... | Please generate a tactic in lean4 to solve the state.
STATE:
case nonconst.intro.intro.intro
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | nontrivialHolomorphicAt_id | [320, 1] | [342, 64] | have zu : extChartAt I z z ∈ u := by
simp only [mem_inter_iff, mem_extChartAt_target, true_and_iff, mem_preimage,
PartialEquiv.left_inv _ (mem_extChartAt_source I z), zt, ← hu] | case nonconst.intro.intro.intro
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace... | case nonconst.intro.intro.intro
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace... | Please generate a tactic in lean4 to solve the state.
STATE:
case nonconst.intro.intro.intro
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | nontrivialHolomorphicAt_id | [320, 1] | [342, 64] | rcases Metric.isOpen_iff.mp uo _ zu with ⟨r, rp, ru⟩ | case nonconst.intro.intro.intro
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace... | case nonconst.intro.intro.intro.intro.intro
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ... | Please generate a tactic in lean4 to solve the state.
STATE:
case nonconst.intro.intro.intro
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | nontrivialHolomorphicAt_id | [320, 1] | [342, 64] | generalize ha : extChartAt I z z + r / 2 = a | case nonconst.intro.intro.intro.intro.intro
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ... | case nonconst.intro.intro.intro.intro.intro
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ... | Please generate a tactic in lean4 to solve the state.
STATE:
case nonconst.intro.intro.intro.intro.intro
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticMani... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | nontrivialHolomorphicAt_id | [320, 1] | [342, 64] | have au : a ∈ u := by
rw [← ha]; apply ru; simp only [Metric.mem_ball, Complex.dist_eq, add_sub_cancel_left]
simp only [map_div₀, Complex.abs_ofReal, abs_of_pos rp, Complex.abs_two]; exact half_lt_self rp | case nonconst.intro.intro.intro.intro.intro
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ... | case nonconst.intro.intro.intro.intro.intro
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ... | Please generate a tactic in lean4 to solve the state.
STATE:
case nonconst.intro.intro.intro.intro.intro
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticMani... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | nontrivialHolomorphicAt_id | [320, 1] | [342, 64] | use (extChartAt I z).symm a | case nonconst.intro.intro.intro.intro.intro
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ... | case h
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticManifo... | Please generate a tactic in lean4 to solve the state.
STATE:
case nonconst.intro.intro.intro.intro.intro
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticMani... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | nontrivialHolomorphicAt_id | [320, 1] | [342, 64] | rw [← hu] at au | case h
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticManifo... | case h
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticManifo... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : Top... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | nontrivialHolomorphicAt_id | [320, 1] | [342, 64] | use ts au.2 | case h
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticManifo... | case right
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticMa... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : Top... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | nontrivialHolomorphicAt_id | [320, 1] | [342, 64] | rw [← (PartialEquiv.injOn _).ne_iff ((extChartAt I z).map_target au.1) (mem_extChartAt_source I z)] | case right
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticMa... | case right
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticMa... | Please generate a tactic in lean4 to solve the state.
STATE:
case right
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ :... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | nontrivialHolomorphicAt_id | [320, 1] | [342, 64] | rw [PartialEquiv.right_inv _ au.1, ← ha] | case right
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticMa... | case right
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticMa... | Please generate a tactic in lean4 to solve the state.
STATE:
case right
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ :... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | nontrivialHolomorphicAt_id | [320, 1] | [342, 64] | simp only [Ne, add_right_eq_self, div_eq_zero_iff, Complex.ofReal_eq_zero, bit0_eq_zero,
one_ne_zero, or_false_iff, rp.ne', not_false_iff] | case right
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticMa... | case right
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticMa... | Please generate a tactic in lean4 to solve the state.
STATE:
case right
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ :... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | nontrivialHolomorphicAt_id | [320, 1] | [342, 64] | norm_num | case right
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticMa... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case right
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ :... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | nontrivialHolomorphicAt_id | [320, 1] | [342, 64] | rw [← hu] | X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticManifold 𝓘(ℂ... | X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticManifold 𝓘(ℂ... | Please generate a tactic in lean4 to solve the state.
STATE:
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : Topologica... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | nontrivialHolomorphicAt_id | [320, 1] | [342, 64] | exact (continuousOn_extChartAt_symm I z).isOpen_inter_preimage (isOpen_extChartAt_target _ _) ot | X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticManifold 𝓘(ℂ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : Topologica... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | nontrivialHolomorphicAt_id | [320, 1] | [342, 64] | simp only [mem_inter_iff, mem_extChartAt_target, true_and_iff, mem_preimage,
PartialEquiv.left_inv _ (mem_extChartAt_source I z), zt, ← hu] | X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticManifold 𝓘(ℂ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : Topologica... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | nontrivialHolomorphicAt_id | [320, 1] | [342, 64] | rw [← ha] | X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticManifold 𝓘(ℂ... | X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticManifold 𝓘(ℂ... | Please generate a tactic in lean4 to solve the state.
STATE:
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : Topologica... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | nontrivialHolomorphicAt_id | [320, 1] | [342, 64] | apply ru | X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticManifold 𝓘(ℂ... | case a
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticManifo... | Please generate a tactic in lean4 to solve the state.
STATE:
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : Topologica... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | nontrivialHolomorphicAt_id | [320, 1] | [342, 64] | simp only [Metric.mem_ball, Complex.dist_eq, add_sub_cancel_left] | case a
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticManifo... | case a
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticManifo... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : Top... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | nontrivialHolomorphicAt_id | [320, 1] | [342, 64] | simp only [map_div₀, Complex.abs_ofReal, abs_of_pos rp, Complex.abs_two] | case a
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticManifo... | case a
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticManifo... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : Top... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | nontrivialHolomorphicAt_id | [320, 1] | [342, 64] | exact half_lt_self rp | case a
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticManifo... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : Top... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | nontrivialHolomorphicAt_of_order | [345, 1] | [353, 89] | use fa.holomorphicAt I I | X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticManifold 𝓘(ℂ... | case nonconst
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : Analyti... | Please generate a tactic in lean4 to solve the state.
STATE:
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : Topologica... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | nontrivialHolomorphicAt_of_order | [345, 1] | [353, 89] | contrapose h | case nonconst
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : Analyti... | case nonconst
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : Analyti... | Please generate a tactic in lean4 to solve the state.
STATE:
case nonconst
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | nontrivialHolomorphicAt_of_order | [345, 1] | [353, 89] | simp only [Filter.not_frequently, not_not] at h ⊢ | case nonconst
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : Analyti... | case nonconst
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : Analyti... | Please generate a tactic in lean4 to solve the state.
STATE:
case nonconst
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | nontrivialHolomorphicAt_of_order | [345, 1] | [353, 89] | have fp : HasFPowerSeriesAt f (constFormalMultilinearSeries ℂ ℂ (f z)) z :=
hasFPowerSeriesAt_const.congr (Filter.EventuallyEq.symm h) | case nonconst
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : Analyti... | case nonconst
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : Analyti... | Please generate a tactic in lean4 to solve the state.
STATE:
case nonconst
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | nontrivialHolomorphicAt_of_order | [345, 1] | [353, 89] | simp only [fp.orderAt_unique] | case nonconst
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : Analyti... | case nonconst
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : Analyti... | Please generate a tactic in lean4 to solve the state.
STATE:
case nonconst
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | nontrivialHolomorphicAt_of_order | [345, 1] | [353, 89] | by_contra p0 | case nonconst
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : Analyti... | case nonconst
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : Analyti... | Please generate a tactic in lean4 to solve the state.
STATE:
case nonconst
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | nontrivialHolomorphicAt_of_order | [345, 1] | [353, 89] | have b := FormalMultilinearSeries.apply_order_ne_zero' p0 | case nonconst
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : Analyti... | case nonconst
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : Analyti... | Please generate a tactic in lean4 to solve the state.
STATE:
case nonconst
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | nontrivialHolomorphicAt_of_order | [345, 1] | [353, 89] | simp only [constFormalMultilinearSeries_apply p0, Ne, eq_self_iff_true, not_true] at b | case nonconst
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : Analyti... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case nonconst
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | NontrivialHolomorphicAt.pow_iff | [367, 1] | [371, 69] | refine ⟨?_, (nontrivialHolomorphicAtPow d0).comp⟩ | X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticManifold 𝓘(ℂ... | X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticManifold 𝓘(ℂ... | Please generate a tactic in lean4 to solve the state.
STATE:
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : Topologica... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | NontrivialHolomorphicAt.pow_iff | [367, 1] | [371, 69] | have pa : HolomorphicAt I I (fun z ↦ z ^ d) (f z) := HolomorphicAt.pow holomorphicAt_id | X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticManifold 𝓘(ℂ... | X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticManifold 𝓘(ℂ... | Please generate a tactic in lean4 to solve the state.
STATE:
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : Topologica... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | NontrivialHolomorphicAt.pow_iff | [367, 1] | [371, 69] | intro h | X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticManifold 𝓘(ℂ... | X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticManifold 𝓘(ℂ... | Please generate a tactic in lean4 to solve the state.
STATE:
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : Topologica... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | NontrivialHolomorphicAt.pow_iff | [367, 1] | [371, 69] | refine (NontrivialHolomorphicAt.anti ?_ pa fa).2 | X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticManifold 𝓘(ℂ... | X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticManifold 𝓘(ℂ... | Please generate a tactic in lean4 to solve the state.
STATE:
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : Topologica... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | NontrivialHolomorphicAt.pow_iff | [367, 1] | [371, 69] | exact h | X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticManifold 𝓘(ℂ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : Topologica... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | NontrivialHolomorphicAt.congr | [374, 1] | [378, 31] | use n.holomorphicAt.congr e | X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticManifold 𝓘(ℂ... | case nonconst
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : Analyti... | Please generate a tactic in lean4 to solve the state.
STATE:
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : Topologica... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | NontrivialHolomorphicAt.congr | [374, 1] | [378, 31] | refine n.nonconst.mp (e.mp (eventually_of_forall fun w ew n ↦ ?_)) | case nonconst
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : Analyti... | case nonconst
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : Analyti... | Please generate a tactic in lean4 to solve the state.
STATE:
case nonconst
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | NontrivialHolomorphicAt.congr | [374, 1] | [378, 31] | rwa [← ew, ← e.self_of_nhds] | case nonconst
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : Analyti... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case nonconst
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | HolomorphicOn.eq_of_locally_eq | [397, 1] | [449, 99] | generalize ht : {x | f =ᶠ[𝓝 x] g} = t | X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : AnalyticManif... | X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : AnalyticManif... | Please generate a tactic in lean4 to solve the state.
STATE:
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : Topo... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | HolomorphicOn.eq_of_locally_eq | [397, 1] | [449, 99] | suffices h : s ⊆ interior t by
simp only [subset_interior_iff_mem_nhdsSet, ← Filter.eventually_iff, ← ht] at h
exact h.mp (eventually_of_forall fun _ e ↦ e.self_of_nhds) | X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : AnalyticManif... | X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : AnalyticManif... | Please generate a tactic in lean4 to solve the state.
STATE:
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : Topo... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | HolomorphicOn.eq_of_locally_eq | [397, 1] | [449, 99] | apply sp.relative_clopen | X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : AnalyticManif... | case ne
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : Analy... | Please generate a tactic in lean4 to solve the state.
STATE:
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : Topo... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | HolomorphicOn.eq_of_locally_eq | [397, 1] | [449, 99] | simp only [subset_interior_iff_mem_nhdsSet, ← Filter.eventually_iff, ← ht] at h | X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : AnalyticManif... | X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : AnalyticManif... | Please generate a tactic in lean4 to solve the state.
STATE:
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : Topo... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | HolomorphicOn.eq_of_locally_eq | [397, 1] | [449, 99] | exact h.mp (eventually_of_forall fun _ e ↦ e.self_of_nhds) | X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : AnalyticManif... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : Topo... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | HolomorphicOn.eq_of_locally_eq | [397, 1] | [449, 99] | rw [← ht] | case ne
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : Analy... | case ne
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : Analy... | Please generate a tactic in lean4 to solve the state.
STATE:
case ne
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | HolomorphicOn.eq_of_locally_eq | [397, 1] | [449, 99] | exact e | case ne
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : Analy... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case ne
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | HolomorphicOn.eq_of_locally_eq | [397, 1] | [449, 99] | intro x ⟨_, xt⟩ | case op
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : Analy... | case op
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : Analy... | Please generate a tactic in lean4 to solve the state.
STATE:
case op
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | HolomorphicOn.eq_of_locally_eq | [397, 1] | [449, 99] | simp only [mem_interior_iff_mem_nhds, ← ht] at xt ⊢ | case op
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : Analy... | case op
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : Analy... | Please generate a tactic in lean4 to solve the state.
STATE:
case op
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | HolomorphicOn.eq_of_locally_eq | [397, 1] | [449, 99] | exact xt.eventually_nhds | case op
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : Analy... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case op
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | HolomorphicOn.eq_of_locally_eq | [397, 1] | [449, 99] | intro x ⟨xs, xt⟩ | case cl
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : Analy... | case cl
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : Analy... | Please generate a tactic in lean4 to solve the state.
STATE:
case cl
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | HolomorphicOn.eq_of_locally_eq | [397, 1] | [449, 99] | rw [mem_closure_iff_frequently] at xt | case cl
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : Analy... | case cl
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : Analy... | Please generate a tactic in lean4 to solve the state.
STATE:
case cl
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | HolomorphicOn.eq_of_locally_eq | [397, 1] | [449, 99] | have ex' : ∃ᶠ y in 𝓝 x, f y = g y := by
rw [← ht] at xt; exact xt.mp (eventually_of_forall fun _ e ↦ e.self_of_nhds) | case cl
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : Analy... | case cl
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : Analy... | Please generate a tactic in lean4 to solve the state.
STATE:
case cl
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | HolomorphicOn.eq_of_locally_eq | [397, 1] | [449, 99] | have ex : f x = g x :=
tendsto_nhds_unique_of_frequently_eq (fa _ xs).continuousAt (ga _ xs).continuousAt ex' | case cl
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : Analy... | case cl
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : Analy... | Please generate a tactic in lean4 to solve the state.
STATE:
case cl
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | HolomorphicOn.eq_of_locally_eq | [397, 1] | [449, 99] | generalize hd : (fun y : E ↦
extChartAt K (f x) (f ((extChartAt J x).symm y)) -
extChartAt K (g x) (g ((extChartAt J x).symm y))) = d | case cl
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : Analy... | case cl
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : Analy... | Please generate a tactic in lean4 to solve the state.
STATE:
case cl
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | HolomorphicOn.eq_of_locally_eq | [397, 1] | [449, 99] | generalize hz : extChartAt J x x = z | case cl
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : Analy... | case cl
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : Analy... | Please generate a tactic in lean4 to solve the state.
STATE:
case cl
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | HolomorphicOn.eq_of_locally_eq | [397, 1] | [449, 99] | suffices h : d =ᶠ[𝓝 z] 0 by
simp only [← hz, ← extChartAt_map_nhds' J x, Filter.eventually_map, Filter.EventuallyEq,
← ht] at h ⊢
refine
h.mp (((isOpen_extChartAt_source J x).eventually_mem (mem_extChartAt_source J x)).mp ?_)
apply ((fa _ xs).continuousAt.eventually_mem ((isOpen_extChartAt_source _ _).me... | case cl
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : Analy... | case cl
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : Analy... | Please generate a tactic in lean4 to solve the state.
STATE:
case cl
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | HolomorphicOn.eq_of_locally_eq | [397, 1] | [449, 99] | have d0 : ∃ᶠ y in 𝓝 z, d =ᶠ[𝓝 y] 0 := by
rw [← hz]
have xt' : ∃ᶠ y in 𝓝 x, (extChartAt J x).symm (extChartAt J x y) ∈ t := by
apply xt.mp
apply ((isOpen_extChartAt_source J x).eventually_mem (mem_extChartAt_source J x)).mp
refine eventually_of_forall fun y m e ↦ ?_; rw [(extChartAt J x).left_inv m]; ... | case cl
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : Analy... | case cl
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : Analy... | Please generate a tactic in lean4 to solve the state.
STATE:
case cl
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | HolomorphicOn.eq_of_locally_eq | [397, 1] | [449, 99] | have da : AnalyticAt ℂ d z := by rw [← hd, ← hz]; exact (fa _ xs).2.sub (ga _ xs).2 | case cl
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : Analy... | case cl
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : Analy... | Please generate a tactic in lean4 to solve the state.
STATE:
case cl
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | HolomorphicOn.eq_of_locally_eq | [397, 1] | [449, 99] | clear hd ex ex' xt t e fa ga f g xs hz x sp ht | case cl
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : Analy... | case cl
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : Analy... | Please generate a tactic in lean4 to solve the state.
STATE:
case cl
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | HolomorphicOn.eq_of_locally_eq | [397, 1] | [449, 99] | rcases da.exists_ball_analyticOn with ⟨r, rp, da⟩ | case cl
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : Analy... | case cl.intro.intro
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U... | Please generate a tactic in lean4 to solve the state.
STATE:
case cl
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | HolomorphicOn.eq_of_locally_eq | [397, 1] | [449, 99] | rcases Filter.frequently_iff.mp d0 (isOpen_ball.mem_nhds (mem_ball_self rp)) with ⟨z0, m0, ze⟩ | case cl.intro.intro
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U... | case cl.intro.intro.intro.intro
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : Char... | Please generate a tactic in lean4 to solve the state.
STATE:
case cl.intro.intro
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U :... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | HolomorphicOn.eq_of_locally_eq | [397, 1] | [449, 99] | refine eventually_nhds_iff.mpr ⟨_, ?_, isOpen_ball, mem_ball_self rp⟩ | case cl.intro.intro.intro.intro
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : Char... | case cl.intro.intro.intro.intro
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : Char... | Please generate a tactic in lean4 to solve the state.
STATE:
case cl.intro.intro.intro.intro
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | HolomorphicOn.eq_of_locally_eq | [397, 1] | [449, 99] | exact da.eqOn_zero_of_preconnected_of_eventuallyEq_zero (convex_ball _ _).isPreconnected m0 ze | case cl.intro.intro.intro.intro
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : Char... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case cl.intro.intro.intro.intro
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | HolomorphicOn.eq_of_locally_eq | [397, 1] | [449, 99] | rw [← ht] at xt | X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : AnalyticManif... | X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : AnalyticManif... | Please generate a tactic in lean4 to solve the state.
STATE:
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : Topo... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | HolomorphicOn.eq_of_locally_eq | [397, 1] | [449, 99] | exact xt.mp (eventually_of_forall fun _ e ↦ e.self_of_nhds) | X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : AnalyticManif... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : Topo... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | HolomorphicOn.eq_of_locally_eq | [397, 1] | [449, 99] | simp only [← hz, ← extChartAt_map_nhds' J x, Filter.eventually_map, Filter.EventuallyEq,
← ht] at h ⊢ | X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : AnalyticManif... | X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : AnalyticManif... | Please generate a tactic in lean4 to solve the state.
STATE:
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : Topo... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | HolomorphicOn.eq_of_locally_eq | [397, 1] | [449, 99] | refine
h.mp (((isOpen_extChartAt_source J x).eventually_mem (mem_extChartAt_source J x)).mp ?_) | X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : AnalyticManif... | X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : AnalyticManif... | Please generate a tactic in lean4 to solve the state.
STATE:
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : Topo... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | HolomorphicOn.eq_of_locally_eq | [397, 1] | [449, 99] | apply ((fa _ xs).continuousAt.eventually_mem ((isOpen_extChartAt_source _ _).mem_nhds
(mem_extChartAt_source K (f x)))).mp | X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : AnalyticManif... | X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : AnalyticManif... | Please generate a tactic in lean4 to solve the state.
STATE:
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : Topo... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | HolomorphicOn.eq_of_locally_eq | [397, 1] | [449, 99] | apply ((ga _ xs).continuousAt.eventually_mem ((isOpen_extChartAt_source _ _).mem_nhds
(mem_extChartAt_source K (g x)))).mp | X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : AnalyticManif... | X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : AnalyticManif... | Please generate a tactic in lean4 to solve the state.
STATE:
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : Topo... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | HolomorphicOn.eq_of_locally_eq | [397, 1] | [449, 99] | refine eventually_of_forall fun y gm fm m e ↦ ?_ | X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : AnalyticManif... | X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : AnalyticManif... | Please generate a tactic in lean4 to solve the state.
STATE:
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : Topo... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | HolomorphicOn.eq_of_locally_eq | [397, 1] | [449, 99] | rw [← hd, Pi.zero_apply, sub_eq_zero, (extChartAt J x).left_inv m, ex] at e | X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : AnalyticManif... | X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : AnalyticManif... | Please generate a tactic in lean4 to solve the state.
STATE:
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : Topo... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | HolomorphicOn.eq_of_locally_eq | [397, 1] | [449, 99] | rw [ex] at fm | X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : AnalyticManif... | X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : AnalyticManif... | Please generate a tactic in lean4 to solve the state.
STATE:
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : Topo... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | HolomorphicOn.eq_of_locally_eq | [397, 1] | [449, 99] | exact (extChartAt K (g x)).injOn fm gm e | X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : AnalyticManif... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : Topo... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | HolomorphicOn.eq_of_locally_eq | [397, 1] | [449, 99] | rw [← hz] | X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : AnalyticManif... | X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : AnalyticManif... | Please generate a tactic in lean4 to solve the state.
STATE:
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : Topo... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | HolomorphicOn.eq_of_locally_eq | [397, 1] | [449, 99] | have xt' : ∃ᶠ y in 𝓝 x, (extChartAt J x).symm (extChartAt J x y) ∈ t := by
apply xt.mp
apply ((isOpen_extChartAt_source J x).eventually_mem (mem_extChartAt_source J x)).mp
refine eventually_of_forall fun y m e ↦ ?_; rw [(extChartAt J x).left_inv m]; exact e | X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : AnalyticManif... | X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : AnalyticManif... | Please generate a tactic in lean4 to solve the state.
STATE:
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : Topo... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | HolomorphicOn.eq_of_locally_eq | [397, 1] | [449, 99] | apply (Filter.Tendsto.frequently (p := fun y ↦ (extChartAt J x).symm y ∈ t)
(continuousAt_extChartAt J x) xt').mp | X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : AnalyticManif... | X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : AnalyticManif... | Please generate a tactic in lean4 to solve the state.
STATE:
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : Topo... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | HolomorphicOn.eq_of_locally_eq | [397, 1] | [449, 99] | apply ((isOpen_extChartAt_target J x).eventually_mem (mem_extChartAt_target J x)).mp | X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : AnalyticManif... | X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : AnalyticManif... | Please generate a tactic in lean4 to solve the state.
STATE:
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : Topo... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | HolomorphicOn.eq_of_locally_eq | [397, 1] | [449, 99] | refine eventually_of_forall fun y m e ↦ ?_ | X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : AnalyticManif... | X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : AnalyticManif... | Please generate a tactic in lean4 to solve the state.
STATE:
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : Topo... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | HolomorphicOn.eq_of_locally_eq | [397, 1] | [449, 99] | simp only [← ht] at e | X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : AnalyticManif... | X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : AnalyticManif... | Please generate a tactic in lean4 to solve the state.
STATE:
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : Topo... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | HolomorphicOn.eq_of_locally_eq | [397, 1] | [449, 99] | apply ((continuousAt_extChartAt_symm'' J m).eventually e).mp | X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : AnalyticManif... | X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : AnalyticManif... | Please generate a tactic in lean4 to solve the state.
STATE:
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : Topo... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | HolomorphicOn.eq_of_locally_eq | [397, 1] | [449, 99] | refine eventually_of_forall fun z e ↦ ?_ | X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : AnalyticManif... | X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : AnalyticManif... | Please generate a tactic in lean4 to solve the state.
STATE:
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : Topo... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | HolomorphicOn.eq_of_locally_eq | [397, 1] | [449, 99] | simp only [← hd, Pi.zero_apply, sub_eq_zero, ex, e] | X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : AnalyticManif... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : Topo... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | HolomorphicOn.eq_of_locally_eq | [397, 1] | [449, 99] | apply xt.mp | X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : AnalyticManif... | X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : AnalyticManif... | Please generate a tactic in lean4 to solve the state.
STATE:
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : Topo... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | HolomorphicOn.eq_of_locally_eq | [397, 1] | [449, 99] | apply ((isOpen_extChartAt_source J x).eventually_mem (mem_extChartAt_source J x)).mp | X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : AnalyticManif... | X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : AnalyticManif... | Please generate a tactic in lean4 to solve the state.
STATE:
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : Topo... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | HolomorphicOn.eq_of_locally_eq | [397, 1] | [449, 99] | refine eventually_of_forall fun y m e ↦ ?_ | X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : AnalyticManif... | X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : AnalyticManif... | Please generate a tactic in lean4 to solve the state.
STATE:
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : Topo... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | HolomorphicOn.eq_of_locally_eq | [397, 1] | [449, 99] | rw [(extChartAt J x).left_inv m] | X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : AnalyticManif... | X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : AnalyticManif... | Please generate a tactic in lean4 to solve the state.
STATE:
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : Topo... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | HolomorphicOn.eq_of_locally_eq | [397, 1] | [449, 99] | exact e | X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : AnalyticManif... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : Topo... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | HolomorphicOn.eq_of_locally_eq | [397, 1] | [449, 99] | rw [← hd, ← hz] | X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : AnalyticManif... | X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : AnalyticManif... | Please generate a tactic in lean4 to solve the state.
STATE:
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : Topo... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/Nontrivial.lean | HolomorphicOn.eq_of_locally_eq | [397, 1] | [449, 99] | exact (fa _ xs).2.sub (ga _ xs).2 | X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : TopologicalSpace U
inst✝¹⁷ : ChartedSpace ℂ U
cmu : AnalyticManif... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
X : Type
inst✝²³ : TopologicalSpace X
S : Type
inst✝²² : TopologicalSpace S
inst✝²¹ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝²⁰ : TopologicalSpace T
inst✝¹⁹ : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹⁸ : Topo... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Max.lean | convexOn_max | [20, 1] | [22, 34] | apply ConvexOn.sup | ⊢ ConvexOn ℝ univ fun p => max p.1 p.2 | case hf
⊢ ConvexOn ℝ univ fun p => p.1
case hg
⊢ ConvexOn ℝ univ fun p => p.2 | Please generate a tactic in lean4 to solve the state.
STATE:
⊢ ConvexOn ℝ univ fun p => max p.1 p.2
TACTIC:
|
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