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/AnalyticManifold.lean
analyticGroupoid_prod
[79, 1]
[150, 72]
simp only [ModelWithCorners.prod, ModelWithCorners.source_eq, mem_univ, and_self, setOf_true, PartialEquiv.prod_target, ModelWithCorners.target_eq, ModelWithCorners.mk_coe, mem_inter_iff, mem_preimage, mem_prod] at m ⊢
case refine_1.hg 𝕜 : Type inst✝⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝⁵ : NormedAddCommGroup E inst✝⁴ : NormedSpace 𝕜 E inst✝³ : TopologicalSpace A F B : Type inst✝² : NormedAddCommGroup F inst✝¹ : NormedSpace 𝕜 F inst✝ : TopologicalSpace B I : ModelWithCorners 𝕜 E A J : ModelWithCorners 𝕜 F B f : PartialH...
case refine_1.hg 𝕜 : Type inst✝⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝⁵ : NormedAddCommGroup E inst✝⁴ : NormedSpace 𝕜 E inst✝³ : TopologicalSpace A F B : Type inst✝² : NormedAddCommGroup F inst✝¹ : NormedSpace 𝕜 F inst✝ : TopologicalSpace B I : ModelWithCorners 𝕜 E A J : ModelWithCorners 𝕜 F B f : PartialH...
Please generate a tactic in lean4 to solve the state. STATE: case refine_1.hg 𝕜 : Type inst✝⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝⁵ : NormedAddCommGroup E inst✝⁴ : NormedSpace 𝕜 E inst✝³ : TopologicalSpace A F B : Type inst✝² : NormedAddCommGroup F inst✝¹ : NormedSpace 𝕜 F inst✝ : TopologicalSpace B I : Mod...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
analyticGroupoid_prod
[79, 1]
[150, 72]
exact ⟨m.1.2, (subset_of_eq ei m.2).2⟩
case refine_1.hg 𝕜 : Type inst✝⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝⁵ : NormedAddCommGroup E inst✝⁴ : NormedSpace 𝕜 E inst✝³ : TopologicalSpace A F B : Type inst✝² : NormedAddCommGroup F inst✝¹ : NormedSpace 𝕜 F inst✝ : TopologicalSpace B I : ModelWithCorners 𝕜 E A J : ModelWithCorners 𝕜 F B f : PartialH...
no goals
Please generate a tactic in lean4 to solve the state. STATE: case refine_1.hg 𝕜 : Type inst✝⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝⁵ : NormedAddCommGroup E inst✝⁴ : NormedSpace 𝕜 E inst✝³ : TopologicalSpace A F B : Type inst✝² : NormedAddCommGroup F inst✝¹ : NormedSpace 𝕜 F inst✝ : TopologicalSpace B I : Mod...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
analyticGroupoid_prod
[79, 1]
[150, 72]
simp only [ModelWithCorners.prod, ModelWithCorners.source_eq, mem_univ, and_self, setOf_true, PartialEquiv.prod_target, ModelWithCorners.target_eq, ModelWithCorners.mk_symm, PartialEquiv.coe_symm_mk, PartialHomeomorph.prod_apply, ModelWithCorners.mk_coe, PartialHomeomorph.prod_toPartialEquiv, PartialEquiv.prod_so...
case refine_2 𝕜 : Type inst✝⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝⁵ : NormedAddCommGroup E inst✝⁴ : NormedSpace 𝕜 E inst✝³ : TopologicalSpace A F B : Type inst✝² : NormedAddCommGroup F inst✝¹ : NormedSpace 𝕜 F inst✝ : TopologicalSpace B I : ModelWithCorners 𝕜 E A J : ModelWithCorners 𝕜 F B f : PartialHome...
case refine_2 𝕜 : Type inst✝⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝⁵ : NormedAddCommGroup E inst✝⁴ : NormedSpace 𝕜 E inst✝³ : TopologicalSpace A F B : Type inst✝² : NormedAddCommGroup F inst✝¹ : NormedSpace 𝕜 F inst✝ : TopologicalSpace B I : ModelWithCorners 𝕜 E A J : ModelWithCorners 𝕜 F B f : PartialHome...
Please generate a tactic in lean4 to solve the state. STATE: case refine_2 𝕜 : Type inst✝⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝⁵ : NormedAddCommGroup E inst✝⁴ : NormedSpace 𝕜 E inst✝³ : TopologicalSpace A F B : Type inst✝² : NormedAddCommGroup F inst✝¹ : NormedSpace 𝕜 F inst✝ : TopologicalSpace B I : ModelW...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
analyticGroupoid_prod
[79, 1]
[150, 72]
intro x ⟨⟨m0,m1⟩,m2⟩
case refine_2 𝕜 : Type inst✝⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝⁵ : NormedAddCommGroup E inst✝⁴ : NormedSpace 𝕜 E inst✝³ : TopologicalSpace A F B : Type inst✝² : NormedAddCommGroup F inst✝¹ : NormedSpace 𝕜 F inst✝ : TopologicalSpace B I : ModelWithCorners 𝕜 E A J : ModelWithCorners 𝕜 F B f : PartialHome...
case refine_2 𝕜 : Type inst✝⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝⁵ : NormedAddCommGroup E inst✝⁴ : NormedSpace 𝕜 E inst✝³ : TopologicalSpace A F B : Type inst✝² : NormedAddCommGroup F inst✝¹ : NormedSpace 𝕜 F inst✝ : TopologicalSpace B I : ModelWithCorners 𝕜 E A J : ModelWithCorners 𝕜 F B f : PartialHome...
Please generate a tactic in lean4 to solve the state. STATE: case refine_2 𝕜 : Type inst✝⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝⁵ : NormedAddCommGroup E inst✝⁴ : NormedSpace 𝕜 E inst✝³ : TopologicalSpace A F B : Type inst✝² : NormedAddCommGroup F inst✝¹ : NormedSpace 𝕜 F inst✝ : TopologicalSpace B I : ModelW...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
analyticGroupoid_prod
[79, 1]
[150, 72]
replace m2 := subset_of_eq ei m2
case refine_2 𝕜 : Type inst✝⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝⁵ : NormedAddCommGroup E inst✝⁴ : NormedSpace 𝕜 E inst✝³ : TopologicalSpace A F B : Type inst✝² : NormedAddCommGroup F inst✝¹ : NormedSpace 𝕜 F inst✝ : TopologicalSpace B I : ModelWithCorners 𝕜 E A J : ModelWithCorners 𝕜 F B f : PartialHome...
case refine_2 𝕜 : Type inst✝⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝⁵ : NormedAddCommGroup E inst✝⁴ : NormedSpace 𝕜 E inst✝³ : TopologicalSpace A F B : Type inst✝² : NormedAddCommGroup F inst✝¹ : NormedSpace 𝕜 F inst✝ : TopologicalSpace B I : ModelWithCorners 𝕜 E A J : ModelWithCorners 𝕜 F B f : PartialHome...
Please generate a tactic in lean4 to solve the state. STATE: case refine_2 𝕜 : Type inst✝⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝⁵ : NormedAddCommGroup E inst✝⁴ : NormedSpace 𝕜 E inst✝³ : TopologicalSpace A F B : Type inst✝² : NormedAddCommGroup F inst✝¹ : NormedSpace 𝕜 F inst✝ : TopologicalSpace B I : ModelW...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
analyticGroupoid_prod
[79, 1]
[150, 72]
exact subset_of_eq ei.symm ⟨fa.2.1.2 ⟨m0,m2.1⟩, ga.2.1.2 ⟨m1,m2.2⟩⟩
case refine_2 𝕜 : Type inst✝⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝⁵ : NormedAddCommGroup E inst✝⁴ : NormedSpace 𝕜 E inst✝³ : TopologicalSpace A F B : Type inst✝² : NormedAddCommGroup F inst✝¹ : NormedSpace 𝕜 F inst✝ : TopologicalSpace B I : ModelWithCorners 𝕜 E A J : ModelWithCorners 𝕜 F B f : PartialHome...
no goals
Please generate a tactic in lean4 to solve the state. STATE: case refine_2 𝕜 : Type inst✝⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝⁵ : NormedAddCommGroup E inst✝⁴ : NormedSpace 𝕜 E inst✝³ : TopologicalSpace A F B : Type inst✝² : NormedAddCommGroup F inst✝¹ : NormedSpace 𝕜 F inst✝ : TopologicalSpace B I : ModelW...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
analyticGroupoid_prod
[79, 1]
[150, 72]
apply AnalyticOn.prod
case refine_3 𝕜 : Type inst✝⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝⁵ : NormedAddCommGroup E inst✝⁴ : NormedSpace 𝕜 E inst✝³ : TopologicalSpace A F B : Type inst✝² : NormedAddCommGroup F inst✝¹ : NormedSpace 𝕜 F inst✝ : TopologicalSpace B I : ModelWithCorners 𝕜 E A J : ModelWithCorners 𝕜 F B f : PartialHome...
case refine_3.hf 𝕜 : Type inst✝⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝⁵ : NormedAddCommGroup E inst✝⁴ : NormedSpace 𝕜 E inst✝³ : TopologicalSpace A F B : Type inst✝² : NormedAddCommGroup F inst✝¹ : NormedSpace 𝕜 F inst✝ : TopologicalSpace B I : ModelWithCorners 𝕜 E A J : ModelWithCorners 𝕜 F B f : PartialH...
Please generate a tactic in lean4 to solve the state. STATE: case refine_3 𝕜 : Type inst✝⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝⁵ : NormedAddCommGroup E inst✝⁴ : NormedSpace 𝕜 E inst✝³ : TopologicalSpace A F B : Type inst✝² : NormedAddCommGroup F inst✝¹ : NormedSpace 𝕜 F inst✝ : TopologicalSpace B I : ModelW...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
analyticGroupoid_prod
[79, 1]
[150, 72]
simp only [ModelWithCorners.symm, modelWithCorners_prod_toPartialEquiv, PartialEquiv.prod_symm, PartialEquiv.prod_coe, ModelWithCorners.toPartialEquiv_coe_symm, PartialHomeomorph.prod_apply, PartialHomeomorph.prod_toPartialEquiv, PartialEquiv.prod_source]
case refine_3.hf 𝕜 : Type inst✝⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝⁵ : NormedAddCommGroup E inst✝⁴ : NormedSpace 𝕜 E inst✝³ : TopologicalSpace A F B : Type inst✝² : NormedAddCommGroup F inst✝¹ : NormedSpace 𝕜 F inst✝ : TopologicalSpace B I : ModelWithCorners 𝕜 E A J : ModelWithCorners 𝕜 F B f : PartialH...
case refine_3.hf 𝕜 : Type inst✝⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝⁵ : NormedAddCommGroup E inst✝⁴ : NormedSpace 𝕜 E inst✝³ : TopologicalSpace A F B : Type inst✝² : NormedAddCommGroup F inst✝¹ : NormedSpace 𝕜 F inst✝ : TopologicalSpace B I : ModelWithCorners 𝕜 E A J : ModelWithCorners 𝕜 F B f : PartialH...
Please generate a tactic in lean4 to solve the state. STATE: case refine_3.hf 𝕜 : Type inst✝⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝⁵ : NormedAddCommGroup E inst✝⁴ : NormedSpace 𝕜 E inst✝³ : TopologicalSpace A F B : Type inst✝² : NormedAddCommGroup F inst✝¹ : NormedSpace 𝕜 F inst✝ : TopologicalSpace B I : Mod...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
analyticGroupoid_prod
[79, 1]
[150, 72]
refine fa.2.2.1.comp (analyticOn_fst _) ?_
case refine_3.hf 𝕜 : Type inst✝⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝⁵ : NormedAddCommGroup E inst✝⁴ : NormedSpace 𝕜 E inst✝³ : TopologicalSpace A F B : Type inst✝² : NormedAddCommGroup F inst✝¹ : NormedSpace 𝕜 F inst✝ : TopologicalSpace B I : ModelWithCorners 𝕜 E A J : ModelWithCorners 𝕜 F B f : PartialH...
case refine_3.hf 𝕜 : Type inst✝⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝⁵ : NormedAddCommGroup E inst✝⁴ : NormedSpace 𝕜 E inst✝³ : TopologicalSpace A F B : Type inst✝² : NormedAddCommGroup F inst✝¹ : NormedSpace 𝕜 F inst✝ : TopologicalSpace B I : ModelWithCorners 𝕜 E A J : ModelWithCorners 𝕜 F B f : PartialH...
Please generate a tactic in lean4 to solve the state. STATE: case refine_3.hf 𝕜 : Type inst✝⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝⁵ : NormedAddCommGroup E inst✝⁴ : NormedSpace 𝕜 E inst✝³ : TopologicalSpace A F B : Type inst✝² : NormedAddCommGroup F inst✝¹ : NormedSpace 𝕜 F inst✝ : TopologicalSpace B I : Mod...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
analyticGroupoid_prod
[79, 1]
[150, 72]
intro x m
case refine_3.hf 𝕜 : Type inst✝⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝⁵ : NormedAddCommGroup E inst✝⁴ : NormedSpace 𝕜 E inst✝³ : TopologicalSpace A F B : Type inst✝² : NormedAddCommGroup F inst✝¹ : NormedSpace 𝕜 F inst✝ : TopologicalSpace B I : ModelWithCorners 𝕜 E A J : ModelWithCorners 𝕜 F B f : PartialH...
case refine_3.hf 𝕜 : Type inst✝⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝⁵ : NormedAddCommGroup E inst✝⁴ : NormedSpace 𝕜 E inst✝³ : TopologicalSpace A F B : Type inst✝² : NormedAddCommGroup F inst✝¹ : NormedSpace 𝕜 F inst✝ : TopologicalSpace B I : ModelWithCorners 𝕜 E A J : ModelWithCorners 𝕜 F B f : PartialH...
Please generate a tactic in lean4 to solve the state. STATE: case refine_3.hf 𝕜 : Type inst✝⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝⁵ : NormedAddCommGroup E inst✝⁴ : NormedSpace 𝕜 E inst✝³ : TopologicalSpace A F B : Type inst✝² : NormedAddCommGroup F inst✝¹ : NormedSpace 𝕜 F inst✝ : TopologicalSpace B I : Mod...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
analyticGroupoid_prod
[79, 1]
[150, 72]
simp only [ModelWithCorners.prod, ModelWithCorners.source_eq, mem_univ, and_self, setOf_true, PartialEquiv.prod_target, ModelWithCorners.target_eq, ModelWithCorners.mk_coe, mem_inter_iff, mem_preimage, mem_prod] at m ⊢
case refine_3.hf 𝕜 : Type inst✝⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝⁵ : NormedAddCommGroup E inst✝⁴ : NormedSpace 𝕜 E inst✝³ : TopologicalSpace A F B : Type inst✝² : NormedAddCommGroup F inst✝¹ : NormedSpace 𝕜 F inst✝ : TopologicalSpace B I : ModelWithCorners 𝕜 E A J : ModelWithCorners 𝕜 F B f : PartialH...
case refine_3.hf 𝕜 : Type inst✝⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝⁵ : NormedAddCommGroup E inst✝⁴ : NormedSpace 𝕜 E inst✝³ : TopologicalSpace A F B : Type inst✝² : NormedAddCommGroup F inst✝¹ : NormedSpace 𝕜 F inst✝ : TopologicalSpace B I : ModelWithCorners 𝕜 E A J : ModelWithCorners 𝕜 F B f : PartialH...
Please generate a tactic in lean4 to solve the state. STATE: case refine_3.hf 𝕜 : Type inst✝⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝⁵ : NormedAddCommGroup E inst✝⁴ : NormedSpace 𝕜 E inst✝³ : TopologicalSpace A F B : Type inst✝² : NormedAddCommGroup F inst✝¹ : NormedSpace 𝕜 F inst✝ : TopologicalSpace B I : Mod...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
analyticGroupoid_prod
[79, 1]
[150, 72]
exact ⟨m.1.1, (subset_of_eq ei m.2).1⟩
case refine_3.hf 𝕜 : Type inst✝⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝⁵ : NormedAddCommGroup E inst✝⁴ : NormedSpace 𝕜 E inst✝³ : TopologicalSpace A F B : Type inst✝² : NormedAddCommGroup F inst✝¹ : NormedSpace 𝕜 F inst✝ : TopologicalSpace B I : ModelWithCorners 𝕜 E A J : ModelWithCorners 𝕜 F B f : PartialH...
no goals
Please generate a tactic in lean4 to solve the state. STATE: case refine_3.hf 𝕜 : Type inst✝⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝⁵ : NormedAddCommGroup E inst✝⁴ : NormedSpace 𝕜 E inst✝³ : TopologicalSpace A F B : Type inst✝² : NormedAddCommGroup F inst✝¹ : NormedSpace 𝕜 F inst✝ : TopologicalSpace B I : Mod...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
analyticGroupoid_prod
[79, 1]
[150, 72]
simp only [ModelWithCorners.symm, modelWithCorners_prod_toPartialEquiv, PartialEquiv.prod_symm, PartialEquiv.prod_coe, ModelWithCorners.toPartialEquiv_coe_symm, PartialHomeomorph.prod_apply, PartialHomeomorph.prod_toPartialEquiv, PartialEquiv.prod_source]
case refine_3.hg 𝕜 : Type inst✝⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝⁵ : NormedAddCommGroup E inst✝⁴ : NormedSpace 𝕜 E inst✝³ : TopologicalSpace A F B : Type inst✝² : NormedAddCommGroup F inst✝¹ : NormedSpace 𝕜 F inst✝ : TopologicalSpace B I : ModelWithCorners 𝕜 E A J : ModelWithCorners 𝕜 F B f : PartialH...
case refine_3.hg 𝕜 : Type inst✝⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝⁵ : NormedAddCommGroup E inst✝⁴ : NormedSpace 𝕜 E inst✝³ : TopologicalSpace A F B : Type inst✝² : NormedAddCommGroup F inst✝¹ : NormedSpace 𝕜 F inst✝ : TopologicalSpace B I : ModelWithCorners 𝕜 E A J : ModelWithCorners 𝕜 F B f : PartialH...
Please generate a tactic in lean4 to solve the state. STATE: case refine_3.hg 𝕜 : Type inst✝⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝⁵ : NormedAddCommGroup E inst✝⁴ : NormedSpace 𝕜 E inst✝³ : TopologicalSpace A F B : Type inst✝² : NormedAddCommGroup F inst✝¹ : NormedSpace 𝕜 F inst✝ : TopologicalSpace B I : Mod...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
analyticGroupoid_prod
[79, 1]
[150, 72]
refine ga.2.2.1.comp (analyticOn_snd _) ?_
case refine_3.hg 𝕜 : Type inst✝⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝⁵ : NormedAddCommGroup E inst✝⁴ : NormedSpace 𝕜 E inst✝³ : TopologicalSpace A F B : Type inst✝² : NormedAddCommGroup F inst✝¹ : NormedSpace 𝕜 F inst✝ : TopologicalSpace B I : ModelWithCorners 𝕜 E A J : ModelWithCorners 𝕜 F B f : PartialH...
case refine_3.hg 𝕜 : Type inst✝⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝⁵ : NormedAddCommGroup E inst✝⁴ : NormedSpace 𝕜 E inst✝³ : TopologicalSpace A F B : Type inst✝² : NormedAddCommGroup F inst✝¹ : NormedSpace 𝕜 F inst✝ : TopologicalSpace B I : ModelWithCorners 𝕜 E A J : ModelWithCorners 𝕜 F B f : PartialH...
Please generate a tactic in lean4 to solve the state. STATE: case refine_3.hg 𝕜 : Type inst✝⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝⁵ : NormedAddCommGroup E inst✝⁴ : NormedSpace 𝕜 E inst✝³ : TopologicalSpace A F B : Type inst✝² : NormedAddCommGroup F inst✝¹ : NormedSpace 𝕜 F inst✝ : TopologicalSpace B I : Mod...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
analyticGroupoid_prod
[79, 1]
[150, 72]
intro x m
case refine_3.hg 𝕜 : Type inst✝⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝⁵ : NormedAddCommGroup E inst✝⁴ : NormedSpace 𝕜 E inst✝³ : TopologicalSpace A F B : Type inst✝² : NormedAddCommGroup F inst✝¹ : NormedSpace 𝕜 F inst✝ : TopologicalSpace B I : ModelWithCorners 𝕜 E A J : ModelWithCorners 𝕜 F B f : PartialH...
case refine_3.hg 𝕜 : Type inst✝⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝⁵ : NormedAddCommGroup E inst✝⁴ : NormedSpace 𝕜 E inst✝³ : TopologicalSpace A F B : Type inst✝² : NormedAddCommGroup F inst✝¹ : NormedSpace 𝕜 F inst✝ : TopologicalSpace B I : ModelWithCorners 𝕜 E A J : ModelWithCorners 𝕜 F B f : PartialH...
Please generate a tactic in lean4 to solve the state. STATE: case refine_3.hg 𝕜 : Type inst✝⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝⁵ : NormedAddCommGroup E inst✝⁴ : NormedSpace 𝕜 E inst✝³ : TopologicalSpace A F B : Type inst✝² : NormedAddCommGroup F inst✝¹ : NormedSpace 𝕜 F inst✝ : TopologicalSpace B I : Mod...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
analyticGroupoid_prod
[79, 1]
[150, 72]
simp only [ModelWithCorners.prod, ModelWithCorners.source_eq, mem_univ, and_self, setOf_true, PartialEquiv.prod_target, ModelWithCorners.target_eq, ModelWithCorners.mk_coe, mem_inter_iff, mem_preimage, mem_prod] at m ⊢
case refine_3.hg 𝕜 : Type inst✝⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝⁵ : NormedAddCommGroup E inst✝⁴ : NormedSpace 𝕜 E inst✝³ : TopologicalSpace A F B : Type inst✝² : NormedAddCommGroup F inst✝¹ : NormedSpace 𝕜 F inst✝ : TopologicalSpace B I : ModelWithCorners 𝕜 E A J : ModelWithCorners 𝕜 F B f : PartialH...
case refine_3.hg 𝕜 : Type inst✝⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝⁵ : NormedAddCommGroup E inst✝⁴ : NormedSpace 𝕜 E inst✝³ : TopologicalSpace A F B : Type inst✝² : NormedAddCommGroup F inst✝¹ : NormedSpace 𝕜 F inst✝ : TopologicalSpace B I : ModelWithCorners 𝕜 E A J : ModelWithCorners 𝕜 F B f : PartialH...
Please generate a tactic in lean4 to solve the state. STATE: case refine_3.hg 𝕜 : Type inst✝⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝⁵ : NormedAddCommGroup E inst✝⁴ : NormedSpace 𝕜 E inst✝³ : TopologicalSpace A F B : Type inst✝² : NormedAddCommGroup F inst✝¹ : NormedSpace 𝕜 F inst✝ : TopologicalSpace B I : Mod...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
analyticGroupoid_prod
[79, 1]
[150, 72]
exact ⟨m.1.2, (subset_of_eq ei m.2).2⟩
case refine_3.hg 𝕜 : Type inst✝⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝⁵ : NormedAddCommGroup E inst✝⁴ : NormedSpace 𝕜 E inst✝³ : TopologicalSpace A F B : Type inst✝² : NormedAddCommGroup F inst✝¹ : NormedSpace 𝕜 F inst✝ : TopologicalSpace B I : ModelWithCorners 𝕜 E A J : ModelWithCorners 𝕜 F B f : PartialH...
no goals
Please generate a tactic in lean4 to solve the state. STATE: case refine_3.hg 𝕜 : Type inst✝⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝⁵ : NormedAddCommGroup E inst✝⁴ : NormedSpace 𝕜 E inst✝³ : TopologicalSpace A F B : Type inst✝² : NormedAddCommGroup F inst✝¹ : NormedSpace 𝕜 F inst✝ : TopologicalSpace B I : Mod...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
analyticGroupoid_prod
[79, 1]
[150, 72]
simp only [ModelWithCorners.prod, ModelWithCorners.source_eq, mem_univ, and_self, setOf_true, PartialEquiv.prod_target, ModelWithCorners.target_eq, ModelWithCorners.mk_symm, PartialEquiv.coe_symm_mk, PartialHomeomorph.prod_apply, ModelWithCorners.mk_coe, PartialHomeomorph.prod_toPartialEquiv, PartialEquiv.prod_so...
case refine_4 𝕜 : Type inst✝⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝⁵ : NormedAddCommGroup E inst✝⁴ : NormedSpace 𝕜 E inst✝³ : TopologicalSpace A F B : Type inst✝² : NormedAddCommGroup F inst✝¹ : NormedSpace 𝕜 F inst✝ : TopologicalSpace B I : ModelWithCorners 𝕜 E A J : ModelWithCorners 𝕜 F B f : PartialHome...
case refine_4 𝕜 : Type inst✝⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝⁵ : NormedAddCommGroup E inst✝⁴ : NormedSpace 𝕜 E inst✝³ : TopologicalSpace A F B : Type inst✝² : NormedAddCommGroup F inst✝¹ : NormedSpace 𝕜 F inst✝ : TopologicalSpace B I : ModelWithCorners 𝕜 E A J : ModelWithCorners 𝕜 F B f : PartialHome...
Please generate a tactic in lean4 to solve the state. STATE: case refine_4 𝕜 : Type inst✝⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝⁵ : NormedAddCommGroup E inst✝⁴ : NormedSpace 𝕜 E inst✝³ : TopologicalSpace A F B : Type inst✝² : NormedAddCommGroup F inst✝¹ : NormedSpace 𝕜 F inst✝ : TopologicalSpace B I : ModelW...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
analyticGroupoid_prod
[79, 1]
[150, 72]
intro x ⟨⟨m0,m1⟩,m2⟩
case refine_4 𝕜 : Type inst✝⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝⁵ : NormedAddCommGroup E inst✝⁴ : NormedSpace 𝕜 E inst✝³ : TopologicalSpace A F B : Type inst✝² : NormedAddCommGroup F inst✝¹ : NormedSpace 𝕜 F inst✝ : TopologicalSpace B I : ModelWithCorners 𝕜 E A J : ModelWithCorners 𝕜 F B f : PartialHome...
case refine_4 𝕜 : Type inst✝⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝⁵ : NormedAddCommGroup E inst✝⁴ : NormedSpace 𝕜 E inst✝³ : TopologicalSpace A F B : Type inst✝² : NormedAddCommGroup F inst✝¹ : NormedSpace 𝕜 F inst✝ : TopologicalSpace B I : ModelWithCorners 𝕜 E A J : ModelWithCorners 𝕜 F B f : PartialHome...
Please generate a tactic in lean4 to solve the state. STATE: case refine_4 𝕜 : Type inst✝⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝⁵ : NormedAddCommGroup E inst✝⁴ : NormedSpace 𝕜 E inst✝³ : TopologicalSpace A F B : Type inst✝² : NormedAddCommGroup F inst✝¹ : NormedSpace 𝕜 F inst✝ : TopologicalSpace B I : ModelW...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
analyticGroupoid_prod
[79, 1]
[150, 72]
replace m2 := subset_of_eq ei m2
case refine_4 𝕜 : Type inst✝⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝⁵ : NormedAddCommGroup E inst✝⁴ : NormedSpace 𝕜 E inst✝³ : TopologicalSpace A F B : Type inst✝² : NormedAddCommGroup F inst✝¹ : NormedSpace 𝕜 F inst✝ : TopologicalSpace B I : ModelWithCorners 𝕜 E A J : ModelWithCorners 𝕜 F B f : PartialHome...
case refine_4 𝕜 : Type inst✝⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝⁵ : NormedAddCommGroup E inst✝⁴ : NormedSpace 𝕜 E inst✝³ : TopologicalSpace A F B : Type inst✝² : NormedAddCommGroup F inst✝¹ : NormedSpace 𝕜 F inst✝ : TopologicalSpace B I : ModelWithCorners 𝕜 E A J : ModelWithCorners 𝕜 F B f : PartialHome...
Please generate a tactic in lean4 to solve the state. STATE: case refine_4 𝕜 : Type inst✝⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝⁵ : NormedAddCommGroup E inst✝⁴ : NormedSpace 𝕜 E inst✝³ : TopologicalSpace A F B : Type inst✝² : NormedAddCommGroup F inst✝¹ : NormedSpace 𝕜 F inst✝ : TopologicalSpace B I : ModelW...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
analyticGroupoid_prod
[79, 1]
[150, 72]
exact subset_of_eq ei.symm ⟨fa.2.2.2 ⟨m0,m2.1⟩, ga.2.2.2 ⟨m1,m2.2⟩⟩
case refine_4 𝕜 : Type inst✝⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝⁵ : NormedAddCommGroup E inst✝⁴ : NormedSpace 𝕜 E inst✝³ : TopologicalSpace A F B : Type inst✝² : NormedAddCommGroup F inst✝¹ : NormedSpace 𝕜 F inst✝ : TopologicalSpace B I : ModelWithCorners 𝕜 E A J : ModelWithCorners 𝕜 F B f : PartialHome...
no goals
Please generate a tactic in lean4 to solve the state. STATE: case refine_4 𝕜 : Type inst✝⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝⁵ : NormedAddCommGroup E inst✝⁴ : NormedSpace 𝕜 E inst✝³ : TopologicalSpace A F B : Type inst✝² : NormedAddCommGroup F inst✝¹ : NormedSpace 𝕜 F inst✝ : TopologicalSpace B I : ModelW...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
extChartAt_self_analytic
[208, 1]
[223, 25]
apply AnalyticOn.congr (f := fun z ↦ z)
𝕜 : Type inst✝³ : NontriviallyNormedField 𝕜 E : Type inst✝² : NormedAddCommGroup E inst✝¹ : NormedSpace 𝕜 E M : Type inst✝ : TopologicalSpace M f : PartialHomeomorph M E ⊢ AnalyticOn 𝕜 (↑𝓘(𝕜, E) ∘ ↑(f.symm.trans f) ∘ ↑𝓘(𝕜, E).symm) (↑𝓘(𝕜, E) '' (f.symm.trans f).source)
case hs 𝕜 : Type inst✝³ : NontriviallyNormedField 𝕜 E : Type inst✝² : NormedAddCommGroup E inst✝¹ : NormedSpace 𝕜 E M : Type inst✝ : TopologicalSpace M f : PartialHomeomorph M E ⊢ IsOpen (↑𝓘(𝕜, E) '' (f.symm.trans f).source) case hf 𝕜 : Type inst✝³ : NontriviallyNormedField 𝕜 E : Type inst✝² : NormedAddCommGrou...
Please generate a tactic in lean4 to solve the state. STATE: 𝕜 : Type inst✝³ : NontriviallyNormedField 𝕜 E : Type inst✝² : NormedAddCommGroup E inst✝¹ : NormedSpace 𝕜 E M : Type inst✝ : TopologicalSpace M f : PartialHomeomorph M E ⊢ AnalyticOn 𝕜 (↑𝓘(𝕜, E) ∘ ↑(f.symm.trans f) ∘ ↑𝓘(𝕜, E).symm) (↑𝓘(𝕜, E) '' (f.s...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
extChartAt_self_analytic
[208, 1]
[223, 25]
simp only [modelWithCornersSelf_coe, id_eq, image_id', PartialHomeomorph.trans_toPartialEquiv, PartialHomeomorph.symm_toPartialEquiv, PartialEquiv.trans_source, PartialEquiv.symm_source, PartialHomeomorph.coe_coe_symm]
case hs 𝕜 : Type inst✝³ : NontriviallyNormedField 𝕜 E : Type inst✝² : NormedAddCommGroup E inst✝¹ : NormedSpace 𝕜 E M : Type inst✝ : TopologicalSpace M f : PartialHomeomorph M E ⊢ IsOpen (↑𝓘(𝕜, E) '' (f.symm.trans f).source)
case hs 𝕜 : Type inst✝³ : NontriviallyNormedField 𝕜 E : Type inst✝² : NormedAddCommGroup E inst✝¹ : NormedSpace 𝕜 E M : Type inst✝ : TopologicalSpace M f : PartialHomeomorph M E ⊢ IsOpen (f.target ∩ ↑f.symm ⁻¹' f.source)
Please generate a tactic in lean4 to solve the state. STATE: case hs 𝕜 : Type inst✝³ : NontriviallyNormedField 𝕜 E : Type inst✝² : NormedAddCommGroup E inst✝¹ : NormedSpace 𝕜 E M : Type inst✝ : TopologicalSpace M f : PartialHomeomorph M E ⊢ IsOpen (↑𝓘(𝕜, E) '' (f.symm.trans f).source) TACTIC:
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
extChartAt_self_analytic
[208, 1]
[223, 25]
exact f.isOpen_inter_preimage_symm f.open_source
case hs 𝕜 : Type inst✝³ : NontriviallyNormedField 𝕜 E : Type inst✝² : NormedAddCommGroup E inst✝¹ : NormedSpace 𝕜 E M : Type inst✝ : TopologicalSpace M f : PartialHomeomorph M E ⊢ IsOpen (f.target ∩ ↑f.symm ⁻¹' f.source)
no goals
Please generate a tactic in lean4 to solve the state. STATE: case hs 𝕜 : Type inst✝³ : NontriviallyNormedField 𝕜 E : Type inst✝² : NormedAddCommGroup E inst✝¹ : NormedSpace 𝕜 E M : Type inst✝ : TopologicalSpace M f : PartialHomeomorph M E ⊢ IsOpen (f.target ∩ ↑f.symm ⁻¹' f.source) TACTIC:
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
extChartAt_self_analytic
[208, 1]
[223, 25]
exact analyticOn_id _
case hf 𝕜 : Type inst✝³ : NontriviallyNormedField 𝕜 E : Type inst✝² : NormedAddCommGroup E inst✝¹ : NormedSpace 𝕜 E M : Type inst✝ : TopologicalSpace M f : PartialHomeomorph M E ⊢ AnalyticOn 𝕜 (fun z => z) (↑𝓘(𝕜, E) '' (f.symm.trans f).source)
no goals
Please generate a tactic in lean4 to solve the state. STATE: case hf 𝕜 : Type inst✝³ : NontriviallyNormedField 𝕜 E : Type inst✝² : NormedAddCommGroup E inst✝¹ : NormedSpace 𝕜 E M : Type inst✝ : TopologicalSpace M f : PartialHomeomorph M E ⊢ AnalyticOn 𝕜 (fun z => z) (↑𝓘(𝕜, E) '' (f.symm.trans f).source) TACTIC:
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
extChartAt_self_analytic
[208, 1]
[223, 25]
intro x m
case hg 𝕜 : Type inst✝³ : NontriviallyNormedField 𝕜 E : Type inst✝² : NormedAddCommGroup E inst✝¹ : NormedSpace 𝕜 E M : Type inst✝ : TopologicalSpace M f : PartialHomeomorph M E ⊢ EqOn (fun z => z) (↑𝓘(𝕜, E) ∘ ↑(f.symm.trans f) ∘ ↑𝓘(𝕜, E).symm) (↑𝓘(𝕜, E) '' (f.symm.trans f).source)
case hg 𝕜 : Type inst✝³ : NontriviallyNormedField 𝕜 E : Type inst✝² : NormedAddCommGroup E inst✝¹ : NormedSpace 𝕜 E M : Type inst✝ : TopologicalSpace M f : PartialHomeomorph M E x : E m : x ∈ ↑𝓘(𝕜, E) '' (f.symm.trans f).source ⊢ (fun z => z) x = (↑𝓘(𝕜, E) ∘ ↑(f.symm.trans f) ∘ ↑𝓘(𝕜, E).symm) x
Please generate a tactic in lean4 to solve the state. STATE: case hg 𝕜 : Type inst✝³ : NontriviallyNormedField 𝕜 E : Type inst✝² : NormedAddCommGroup E inst✝¹ : NormedSpace 𝕜 E M : Type inst✝ : TopologicalSpace M f : PartialHomeomorph M E ⊢ EqOn (fun z => z) (↑𝓘(𝕜, E) ∘ ↑(f.symm.trans f) ∘ ↑𝓘(𝕜, E).symm) (↑𝓘(𝕜...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
extChartAt_self_analytic
[208, 1]
[223, 25]
simp only [modelWithCornersSelf_coe, id, image_id', PartialHomeomorph.trans_toPartialEquiv, PartialHomeomorph.symm_toPartialEquiv, PartialEquiv.trans_source, PartialEquiv.symm_source, PartialHomeomorph.coe_coe_symm, mem_inter_iff, mem_preimage, Function.comp, modelWithCornersSelf_coe_symm, PartialHomeomorph.coe_t...
case hg 𝕜 : Type inst✝³ : NontriviallyNormedField 𝕜 E : Type inst✝² : NormedAddCommGroup E inst✝¹ : NormedSpace 𝕜 E M : Type inst✝ : TopologicalSpace M f : PartialHomeomorph M E x : E m : x ∈ ↑𝓘(𝕜, E) '' (f.symm.trans f).source ⊢ (fun z => z) x = (↑𝓘(𝕜, E) ∘ ↑(f.symm.trans f) ∘ ↑𝓘(𝕜, E).symm) x
case hg 𝕜 : Type inst✝³ : NontriviallyNormedField 𝕜 E : Type inst✝² : NormedAddCommGroup E inst✝¹ : NormedSpace 𝕜 E M : Type inst✝ : TopologicalSpace M f : PartialHomeomorph M E x : E m : x ∈ f.target ∧ ↑f.symm x ∈ f.source ⊢ x = ↑f (↑f.symm x)
Please generate a tactic in lean4 to solve the state. STATE: case hg 𝕜 : Type inst✝³ : NontriviallyNormedField 𝕜 E : Type inst✝² : NormedAddCommGroup E inst✝¹ : NormedSpace 𝕜 E M : Type inst✝ : TopologicalSpace M f : PartialHomeomorph M E x : E m : x ∈ ↑𝓘(𝕜, E) '' (f.symm.trans f).source ⊢ (fun z => z) x = (↑𝓘(𝕜...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
extChartAt_self_analytic
[208, 1]
[223, 25]
rw [f.right_inv m.1]
case hg 𝕜 : Type inst✝³ : NontriviallyNormedField 𝕜 E : Type inst✝² : NormedAddCommGroup E inst✝¹ : NormedSpace 𝕜 E M : Type inst✝ : TopologicalSpace M f : PartialHomeomorph M E x : E m : x ∈ f.target ∧ ↑f.symm x ∈ f.source ⊢ x = ↑f (↑f.symm x)
no goals
Please generate a tactic in lean4 to solve the state. STATE: case hg 𝕜 : Type inst✝³ : NontriviallyNormedField 𝕜 E : Type inst✝² : NormedAddCommGroup E inst✝¹ : NormedSpace 𝕜 E M : Type inst✝ : TopologicalSpace M f : PartialHomeomorph M E x : E m : x ∈ f.target ∧ ↑f.symm x ∈ f.source ⊢ x = ↑f (↑f.symm x) TACTIC:
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
holomorphicAt_iff
[263, 1]
[267, 54]
simp only [HolomorphicAt, ChartedSpace.liftPropAt_iff, extChartAt, PartialHomeomorph.extend_coe, PartialHomeomorph.extend_coe_symm, Function.comp]
𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type inst✝¹⁷ : Norm...
no goals
Please generate a tactic in lean4 to solve the state. STATE: 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteS...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
holomorphic_iff
[270, 1]
[274, 92]
simp only [Holomorphic, holomorphicAt_iff, continuous_iff_continuousAt]
𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type inst✝¹⁷ : Norm...
𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type inst✝¹⁷ : Norm...
Please generate a tactic in lean4 to solve the state. STATE: 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteS...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
holomorphic_iff
[270, 1]
[274, 92]
exact forall_and
𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type inst✝¹⁷ : Norm...
no goals
Please generate a tactic in lean4 to solve the state. STATE: 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteS...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
analyticAt_iff_holomorphicAt
[295, 1]
[300, 32]
simp only [holomorphicAt_iff, extChartAt_eq_refl, PartialEquiv.refl_coe, PartialEquiv.refl_symm, Function.id_comp, Function.comp_id, id_eq, iff_and_self]
𝕜 : Type inst✝³² : NontriviallyNormedField 𝕜 E A : Type inst✝³¹ : NormedAddCommGroup E inst✝³⁰ : NormedSpace 𝕜 E inst✝²⁹ : CompleteSpace E inst✝²⁸ : TopologicalSpace A F B : Type inst✝²⁷ : NormedAddCommGroup F inst✝²⁶ : NormedSpace 𝕜 F inst✝²⁵ : CompleteSpace F inst✝²⁴ : TopologicalSpace B G C : Type inst✝²³ : Norm...
𝕜 : Type inst✝³² : NontriviallyNormedField 𝕜 E A : Type inst✝³¹ : NormedAddCommGroup E inst✝³⁰ : NormedSpace 𝕜 E inst✝²⁹ : CompleteSpace E inst✝²⁸ : TopologicalSpace A F B : Type inst✝²⁷ : NormedAddCommGroup F inst✝²⁶ : NormedSpace 𝕜 F inst✝²⁵ : CompleteSpace F inst✝²⁴ : TopologicalSpace B G C : Type inst✝²³ : Norm...
Please generate a tactic in lean4 to solve the state. STATE: 𝕜 : Type inst✝³² : NontriviallyNormedField 𝕜 E A : Type inst✝³¹ : NormedAddCommGroup E inst✝³⁰ : NormedSpace 𝕜 E inst✝²⁹ : CompleteSpace E inst✝²⁸ : TopologicalSpace A F B : Type inst✝²⁷ : NormedAddCommGroup F inst✝²⁶ : NormedSpace 𝕜 F inst✝²⁵ : CompleteS...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
analyticAt_iff_holomorphicAt
[295, 1]
[300, 32]
exact AnalyticAt.continuousAt
𝕜 : Type inst✝³² : NontriviallyNormedField 𝕜 E A : Type inst✝³¹ : NormedAddCommGroup E inst✝³⁰ : NormedSpace 𝕜 E inst✝²⁹ : CompleteSpace E inst✝²⁸ : TopologicalSpace A F B : Type inst✝²⁷ : NormedAddCommGroup F inst✝²⁶ : NormedSpace 𝕜 F inst✝²⁵ : CompleteSpace F inst✝²⁴ : TopologicalSpace B G C : Type inst✝²³ : Norm...
no goals
Please generate a tactic in lean4 to solve the state. STATE: 𝕜 : Type inst✝³² : NontriviallyNormedField 𝕜 E A : Type inst✝³¹ : NormedAddCommGroup E inst✝³⁰ : NormedSpace 𝕜 E inst✝²⁹ : CompleteSpace E inst✝²⁸ : TopologicalSpace A F B : Type inst✝²⁷ : NormedAddCommGroup F inst✝²⁶ : NormedSpace 𝕜 F inst✝²⁵ : CompleteS...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
HolomorphicAt.comp
[321, 1]
[338, 38]
rw [holomorphicAt_iff] at fh gh ⊢
𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type inst✝¹⁷ : Norm...
𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type inst✝¹⁷ : Norm...
Please generate a tactic in lean4 to solve the state. STATE: 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteS...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
HolomorphicAt.comp
[321, 1]
[338, 38]
use fh.1.comp gh.1
𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type inst✝¹⁷ : Norm...
case right 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type ins...
Please generate a tactic in lean4 to solve the state. STATE: 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteS...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
HolomorphicAt.comp
[321, 1]
[338, 38]
have e : extChartAt J (g x) (g x) = (extChartAt J (g x) ∘ g ∘ (extChartAt I x).symm) (extChartAt I x x) := by simp only [Function.comp_apply, PartialEquiv.left_inv _ (mem_extChartAt_source I x)]
case right 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type ins...
case right 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type ins...
Please generate a tactic in lean4 to solve the state. STATE: case right 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ ...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
HolomorphicAt.comp
[321, 1]
[338, 38]
rw [e] at fh
case right 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type ins...
case right 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type ins...
Please generate a tactic in lean4 to solve the state. STATE: case right 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ ...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
HolomorphicAt.comp
[321, 1]
[338, 38]
apply (fh.2.comp gh.2).congr
case right 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type ins...
case right 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type ins...
Please generate a tactic in lean4 to solve the state. STATE: case right 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ ...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
HolomorphicAt.comp
[321, 1]
[338, 38]
clear e fh
case right 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type ins...
case right 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type ins...
Please generate a tactic in lean4 to solve the state. STATE: case right 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ ...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
HolomorphicAt.comp
[321, 1]
[338, 38]
simp only [Function.comp]
case right 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type ins...
case right 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type ins...
Please generate a tactic in lean4 to solve the state. STATE: case right 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ ...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
HolomorphicAt.comp
[321, 1]
[338, 38]
refine m.mp (eventually_of_forall fun y m ↦ ?_)
case right 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type ins...
case right 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type ins...
Please generate a tactic in lean4 to solve the state. STATE: case right 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ ...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
HolomorphicAt.comp
[321, 1]
[338, 38]
simp_rw [PartialEquiv.left_inv _ m]
case right 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type ins...
no goals
Please generate a tactic in lean4 to solve the state. STATE: case right 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ ...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
HolomorphicAt.comp
[321, 1]
[338, 38]
simp only [Function.comp_apply, PartialEquiv.left_inv _ (mem_extChartAt_source I x)]
𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type inst✝¹⁷ : Norm...
no goals
Please generate a tactic in lean4 to solve the state. STATE: 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteS...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
HolomorphicAt.comp
[321, 1]
[338, 38]
apply ContinuousAt.eventually_mem
𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type inst✝¹⁷ : Norm...
case hf 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type inst✝¹...
Please generate a tactic in lean4 to solve the state. STATE: 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteS...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
HolomorphicAt.comp
[321, 1]
[338, 38]
apply ContinuousAt.comp
case hf 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type inst✝¹...
case hf.hg 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type ins...
Please generate a tactic in lean4 to solve the state. STATE: case hf 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : C...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
HolomorphicAt.comp
[321, 1]
[338, 38]
rw [PartialEquiv.left_inv _ (mem_extChartAt_source _ _)]
case hf.hg 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type ins...
case hf.hg 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type ins...
Please generate a tactic in lean4 to solve the state. STATE: case hf.hg 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ ...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
HolomorphicAt.comp
[321, 1]
[338, 38]
exact gh.1
case hf.hg 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type ins...
no goals
Please generate a tactic in lean4 to solve the state. STATE: case hf.hg 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ ...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
HolomorphicAt.comp
[321, 1]
[338, 38]
exact continuousAt_extChartAt_symm I x
case hf.hf 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type ins...
no goals
Please generate a tactic in lean4 to solve the state. STATE: case hf.hf 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ ...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
HolomorphicAt.comp
[321, 1]
[338, 38]
rw [PartialEquiv.left_inv _ (mem_extChartAt_source _ _)]
case hs 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type inst✝¹...
case hs 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type inst✝¹...
Please generate a tactic in lean4 to solve the state. STATE: case hs 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : C...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
HolomorphicAt.comp
[321, 1]
[338, 38]
exact extChartAt_source_mem_nhds _ _
case hs 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type inst✝¹...
no goals
Please generate a tactic in lean4 to solve the state. STATE: case hs 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : C...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
HolomorphicAt.comp_of_eq
[345, 1]
[348, 35]
rw [← e] at fh
𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type inst✝¹⁷ : Norm...
𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type inst✝¹⁷ : Norm...
Please generate a tactic in lean4 to solve the state. STATE: 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteS...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
HolomorphicAt.comp_of_eq
[345, 1]
[348, 35]
exact fh.comp gh
𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type inst✝¹⁷ : Norm...
no goals
Please generate a tactic in lean4 to solve the state. STATE: 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteS...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
HolomorphicAt.prod
[351, 1]
[355, 76]
rw [holomorphicAt_iff] at fh gh ⊢
𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type inst✝¹⁷ : Norm...
𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type inst✝¹⁷ : Norm...
Please generate a tactic in lean4 to solve the state. STATE: 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteS...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
HolomorphicAt.prod
[351, 1]
[355, 76]
use fh.1.prod gh.1
𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type inst✝¹⁷ : Norm...
case right 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type ins...
Please generate a tactic in lean4 to solve the state. STATE: 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteS...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
HolomorphicAt.prod
[351, 1]
[355, 76]
refine (fh.2.prod gh.2).congr (eventually_of_forall fun y ↦ ?_)
case right 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type ins...
case right 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type ins...
Please generate a tactic in lean4 to solve the state. STATE: case right 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ ...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
HolomorphicAt.prod
[351, 1]
[355, 76]
simp only [extChartAt_prod, Function.comp, PartialEquiv.prod_coe]
case right 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type ins...
no goals
Please generate a tactic in lean4 to solve the state. STATE: case right 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ ...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
HolomorphicAt.comp₂_of_eq
[368, 1]
[371, 91]
rw [← e] at ha
𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type inst✝¹⁷ : Norm...
𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type inst✝¹⁷ : Norm...
Please generate a tactic in lean4 to solve the state. STATE: 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteS...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
HolomorphicAt.comp₂_of_eq
[368, 1]
[371, 91]
exact ha.comp₂ fa ga
𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type inst✝¹⁷ : Norm...
no goals
Please generate a tactic in lean4 to solve the state. STATE: 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteS...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
holomorphicAt_id
[374, 1]
[378, 60]
rw [holomorphicAt_iff]
𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type inst✝¹⁷ : Norm...
𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type inst✝¹⁷ : Norm...
Please generate a tactic in lean4 to solve the state. STATE: 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteS...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
holomorphicAt_id
[374, 1]
[378, 60]
use continuousAt_id
𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type inst✝¹⁷ : Norm...
case right 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type ins...
Please generate a tactic in lean4 to solve the state. STATE: 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteS...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
holomorphicAt_id
[374, 1]
[378, 60]
apply (analyticAt_id _ _).congr
case right 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type ins...
case right 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type ins...
Please generate a tactic in lean4 to solve the state. STATE: case right 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ ...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
holomorphicAt_id
[374, 1]
[378, 60]
filter_upwards [((isOpen_extChartAt_target I x).eventually_mem (mem_extChartAt_target I x))]
case right 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type ins...
case h 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type inst✝¹⁷...
Please generate a tactic in lean4 to solve the state. STATE: case right 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ ...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
holomorphicAt_id
[374, 1]
[378, 60]
intro y m
case h 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type inst✝¹⁷...
case h 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type inst✝¹⁷...
Please generate a tactic in lean4 to solve the state. STATE: case h 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : Co...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
holomorphicAt_id
[374, 1]
[378, 60]
simp only [Function.comp, PartialEquiv.right_inv _ m, id]
case h 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type inst✝¹⁷...
no goals
Please generate a tactic in lean4 to solve the state. STATE: case h 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : Co...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
holomorphicAt_const
[384, 1]
[386, 70]
rw [holomorphicAt_iff]
𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type inst✝¹⁷ : Norm...
𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type inst✝¹⁷ : Norm...
Please generate a tactic in lean4 to solve the state. STATE: 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteS...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
holomorphicAt_const
[384, 1]
[386, 70]
use continuousAt_const
𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type inst✝¹⁷ : Norm...
case right 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type ins...
Please generate a tactic in lean4 to solve the state. STATE: 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteS...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
holomorphicAt_const
[384, 1]
[386, 70]
simp only [Prod.fst_comp_mk, Function.comp]
case right 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type ins...
case right 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type ins...
Please generate a tactic in lean4 to solve the state. STATE: case right 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ ...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
holomorphicAt_const
[384, 1]
[386, 70]
exact analyticAt_const
case right 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type ins...
no goals
Please generate a tactic in lean4 to solve the state. STATE: case right 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ ...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
holomorphicAt_fst
[411, 1]
[419, 48]
rw [holomorphicAt_iff]
𝕜 : Type inst✝²⁸ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁷ : NormedAddCommGroup E inst✝²⁶ : NormedSpace 𝕜 E inst✝²⁵ : CompleteSpace E inst✝²⁴ : TopologicalSpace A F B : Type inst✝²³ : NormedAddCommGroup F inst✝²² : NormedSpace 𝕜 F inst✝²¹ : CompleteSpace F inst✝²⁰ : TopologicalSpace B G C : Type inst✝¹⁹ : Norm...
𝕜 : Type inst✝²⁸ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁷ : NormedAddCommGroup E inst✝²⁶ : NormedSpace 𝕜 E inst✝²⁵ : CompleteSpace E inst✝²⁴ : TopologicalSpace A F B : Type inst✝²³ : NormedAddCommGroup F inst✝²² : NormedSpace 𝕜 F inst✝²¹ : CompleteSpace F inst✝²⁰ : TopologicalSpace B G C : Type inst✝¹⁹ : Norm...
Please generate a tactic in lean4 to solve the state. STATE: 𝕜 : Type inst✝²⁸ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁷ : NormedAddCommGroup E inst✝²⁶ : NormedSpace 𝕜 E inst✝²⁵ : CompleteSpace E inst✝²⁴ : TopologicalSpace A F B : Type inst✝²³ : NormedAddCommGroup F inst✝²² : NormedSpace 𝕜 F inst✝²¹ : CompleteS...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
holomorphicAt_fst
[411, 1]
[419, 48]
use continuousAt_fst
𝕜 : Type inst✝²⁸ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁷ : NormedAddCommGroup E inst✝²⁶ : NormedSpace 𝕜 E inst✝²⁵ : CompleteSpace E inst✝²⁴ : TopologicalSpace A F B : Type inst✝²³ : NormedAddCommGroup F inst✝²² : NormedSpace 𝕜 F inst✝²¹ : CompleteSpace F inst✝²⁰ : TopologicalSpace B G C : Type inst✝¹⁹ : Norm...
case right 𝕜 : Type inst✝²⁸ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁷ : NormedAddCommGroup E inst✝²⁶ : NormedSpace 𝕜 E inst✝²⁵ : CompleteSpace E inst✝²⁴ : TopologicalSpace A F B : Type inst✝²³ : NormedAddCommGroup F inst✝²² : NormedSpace 𝕜 F inst✝²¹ : CompleteSpace F inst✝²⁰ : TopologicalSpace B G C : Type ins...
Please generate a tactic in lean4 to solve the state. STATE: 𝕜 : Type inst✝²⁸ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁷ : NormedAddCommGroup E inst✝²⁶ : NormedSpace 𝕜 E inst✝²⁵ : CompleteSpace E inst✝²⁴ : TopologicalSpace A F B : Type inst✝²³ : NormedAddCommGroup F inst✝²² : NormedSpace 𝕜 F inst✝²¹ : CompleteS...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
holomorphicAt_fst
[411, 1]
[419, 48]
refine (analyticAt_fst _).congr ?_
case right 𝕜 : Type inst✝²⁸ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁷ : NormedAddCommGroup E inst✝²⁶ : NormedSpace 𝕜 E inst✝²⁵ : CompleteSpace E inst✝²⁴ : TopologicalSpace A F B : Type inst✝²³ : NormedAddCommGroup F inst✝²² : NormedSpace 𝕜 F inst✝²¹ : CompleteSpace F inst✝²⁰ : TopologicalSpace B G C : Type ins...
case right 𝕜 : Type inst✝²⁸ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁷ : NormedAddCommGroup E inst✝²⁶ : NormedSpace 𝕜 E inst✝²⁵ : CompleteSpace E inst✝²⁴ : TopologicalSpace A F B : Type inst✝²³ : NormedAddCommGroup F inst✝²² : NormedSpace 𝕜 F inst✝²¹ : CompleteSpace F inst✝²⁰ : TopologicalSpace B G C : Type ins...
Please generate a tactic in lean4 to solve the state. STATE: case right 𝕜 : Type inst✝²⁸ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁷ : NormedAddCommGroup E inst✝²⁶ : NormedSpace 𝕜 E inst✝²⁵ : CompleteSpace E inst✝²⁴ : TopologicalSpace A F B : Type inst✝²³ : NormedAddCommGroup F inst✝²² : NormedSpace 𝕜 F inst✝²¹ ...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
holomorphicAt_fst
[411, 1]
[419, 48]
filter_upwards [((isOpen_extChartAt_target _ x).eventually_mem (mem_extChartAt_target _ _))]
case right 𝕜 : Type inst✝²⁸ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁷ : NormedAddCommGroup E inst✝²⁶ : NormedSpace 𝕜 E inst✝²⁵ : CompleteSpace E inst✝²⁴ : TopologicalSpace A F B : Type inst✝²³ : NormedAddCommGroup F inst✝²² : NormedSpace 𝕜 F inst✝²¹ : CompleteSpace F inst✝²⁰ : TopologicalSpace B G C : Type ins...
case h 𝕜 : Type inst✝²⁸ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁷ : NormedAddCommGroup E inst✝²⁶ : NormedSpace 𝕜 E inst✝²⁵ : CompleteSpace E inst✝²⁴ : TopologicalSpace A F B : Type inst✝²³ : NormedAddCommGroup F inst✝²² : NormedSpace 𝕜 F inst✝²¹ : CompleteSpace F inst✝²⁰ : TopologicalSpace B G C : Type inst✝¹⁹...
Please generate a tactic in lean4 to solve the state. STATE: case right 𝕜 : Type inst✝²⁸ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁷ : NormedAddCommGroup E inst✝²⁶ : NormedSpace 𝕜 E inst✝²⁵ : CompleteSpace E inst✝²⁴ : TopologicalSpace A F B : Type inst✝²³ : NormedAddCommGroup F inst✝²² : NormedSpace 𝕜 F inst✝²¹ ...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
holomorphicAt_fst
[411, 1]
[419, 48]
intro y m
case h 𝕜 : Type inst✝²⁸ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁷ : NormedAddCommGroup E inst✝²⁶ : NormedSpace 𝕜 E inst✝²⁵ : CompleteSpace E inst✝²⁴ : TopologicalSpace A F B : Type inst✝²³ : NormedAddCommGroup F inst✝²² : NormedSpace 𝕜 F inst✝²¹ : CompleteSpace F inst✝²⁰ : TopologicalSpace B G C : Type inst✝¹⁹...
case h 𝕜 : Type inst✝²⁸ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁷ : NormedAddCommGroup E inst✝²⁶ : NormedSpace 𝕜 E inst✝²⁵ : CompleteSpace E inst✝²⁴ : TopologicalSpace A F B : Type inst✝²³ : NormedAddCommGroup F inst✝²² : NormedSpace 𝕜 F inst✝²¹ : CompleteSpace F inst✝²⁰ : TopologicalSpace B G C : Type inst✝¹⁹...
Please generate a tactic in lean4 to solve the state. STATE: case h 𝕜 : Type inst✝²⁸ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁷ : NormedAddCommGroup E inst✝²⁶ : NormedSpace 𝕜 E inst✝²⁵ : CompleteSpace E inst✝²⁴ : TopologicalSpace A F B : Type inst✝²³ : NormedAddCommGroup F inst✝²² : NormedSpace 𝕜 F inst✝²¹ : Co...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
holomorphicAt_fst
[411, 1]
[419, 48]
rw [extChartAt_prod] at m
case h 𝕜 : Type inst✝²⁸ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁷ : NormedAddCommGroup E inst✝²⁶ : NormedSpace 𝕜 E inst✝²⁵ : CompleteSpace E inst✝²⁴ : TopologicalSpace A F B : Type inst✝²³ : NormedAddCommGroup F inst✝²² : NormedSpace 𝕜 F inst✝²¹ : CompleteSpace F inst✝²⁰ : TopologicalSpace B G C : Type inst✝¹⁹...
case h 𝕜 : Type inst✝²⁸ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁷ : NormedAddCommGroup E inst✝²⁶ : NormedSpace 𝕜 E inst✝²⁵ : CompleteSpace E inst✝²⁴ : TopologicalSpace A F B : Type inst✝²³ : NormedAddCommGroup F inst✝²² : NormedSpace 𝕜 F inst✝²¹ : CompleteSpace F inst✝²⁰ : TopologicalSpace B G C : Type inst✝¹⁹...
Please generate a tactic in lean4 to solve the state. STATE: case h 𝕜 : Type inst✝²⁸ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁷ : NormedAddCommGroup E inst✝²⁶ : NormedSpace 𝕜 E inst✝²⁵ : CompleteSpace E inst✝²⁴ : TopologicalSpace A F B : Type inst✝²³ : NormedAddCommGroup F inst✝²² : NormedSpace 𝕜 F inst✝²¹ : Co...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
holomorphicAt_fst
[411, 1]
[419, 48]
simp only [PartialHomeomorph.prod_toPartialEquiv, PartialEquiv.prod_target, mem_prod] at m
case h 𝕜 : Type inst✝²⁸ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁷ : NormedAddCommGroup E inst✝²⁶ : NormedSpace 𝕜 E inst✝²⁵ : CompleteSpace E inst✝²⁴ : TopologicalSpace A F B : Type inst✝²³ : NormedAddCommGroup F inst✝²² : NormedSpace 𝕜 F inst✝²¹ : CompleteSpace F inst✝²⁰ : TopologicalSpace B G C : Type inst✝¹⁹...
case h 𝕜 : Type inst✝²⁸ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁷ : NormedAddCommGroup E inst✝²⁶ : NormedSpace 𝕜 E inst✝²⁵ : CompleteSpace E inst✝²⁴ : TopologicalSpace A F B : Type inst✝²³ : NormedAddCommGroup F inst✝²² : NormedSpace 𝕜 F inst✝²¹ : CompleteSpace F inst✝²⁰ : TopologicalSpace B G C : Type inst✝¹⁹...
Please generate a tactic in lean4 to solve the state. STATE: case h 𝕜 : Type inst✝²⁸ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁷ : NormedAddCommGroup E inst✝²⁶ : NormedSpace 𝕜 E inst✝²⁵ : CompleteSpace E inst✝²⁴ : TopologicalSpace A F B : Type inst✝²³ : NormedAddCommGroup F inst✝²² : NormedSpace 𝕜 F inst✝²¹ : Co...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
holomorphicAt_fst
[411, 1]
[419, 48]
simp only [extChartAt_prod, Function.comp, PartialEquiv.prod_coe_symm]
case h 𝕜 : Type inst✝²⁸ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁷ : NormedAddCommGroup E inst✝²⁶ : NormedSpace 𝕜 E inst✝²⁵ : CompleteSpace E inst✝²⁴ : TopologicalSpace A F B : Type inst✝²³ : NormedAddCommGroup F inst✝²² : NormedSpace 𝕜 F inst✝²¹ : CompleteSpace F inst✝²⁰ : TopologicalSpace B G C : Type inst✝¹⁹...
case h 𝕜 : Type inst✝²⁸ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁷ : NormedAddCommGroup E inst✝²⁶ : NormedSpace 𝕜 E inst✝²⁵ : CompleteSpace E inst✝²⁴ : TopologicalSpace A F B : Type inst✝²³ : NormedAddCommGroup F inst✝²² : NormedSpace 𝕜 F inst✝²¹ : CompleteSpace F inst✝²⁰ : TopologicalSpace B G C : Type inst✝¹⁹...
Please generate a tactic in lean4 to solve the state. STATE: case h 𝕜 : Type inst✝²⁸ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁷ : NormedAddCommGroup E inst✝²⁶ : NormedSpace 𝕜 E inst✝²⁵ : CompleteSpace E inst✝²⁴ : TopologicalSpace A F B : Type inst✝²³ : NormedAddCommGroup F inst✝²² : NormedSpace 𝕜 F inst✝²¹ : Co...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
holomorphicAt_fst
[411, 1]
[419, 48]
exact ((extChartAt I x.1).right_inv m.1).symm
case h 𝕜 : Type inst✝²⁸ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁷ : NormedAddCommGroup E inst✝²⁶ : NormedSpace 𝕜 E inst✝²⁵ : CompleteSpace E inst✝²⁴ : TopologicalSpace A F B : Type inst✝²³ : NormedAddCommGroup F inst✝²² : NormedSpace 𝕜 F inst✝²¹ : CompleteSpace F inst✝²⁰ : TopologicalSpace B G C : Type inst✝¹⁹...
no goals
Please generate a tactic in lean4 to solve the state. STATE: case h 𝕜 : Type inst✝²⁸ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁷ : NormedAddCommGroup E inst✝²⁶ : NormedSpace 𝕜 E inst✝²⁵ : CompleteSpace E inst✝²⁴ : TopologicalSpace A F B : Type inst✝²³ : NormedAddCommGroup F inst✝²² : NormedSpace 𝕜 F inst✝²¹ : Co...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
holomorphicAt_snd
[422, 1]
[430, 48]
rw [holomorphicAt_iff]
𝕜 : Type inst✝²⁸ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁷ : NormedAddCommGroup E inst✝²⁶ : NormedSpace 𝕜 E inst✝²⁵ : CompleteSpace E inst✝²⁴ : TopologicalSpace A F B : Type inst✝²³ : NormedAddCommGroup F inst✝²² : NormedSpace 𝕜 F inst✝²¹ : CompleteSpace F inst✝²⁰ : TopologicalSpace B G C : Type inst✝¹⁹ : Norm...
𝕜 : Type inst✝²⁸ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁷ : NormedAddCommGroup E inst✝²⁶ : NormedSpace 𝕜 E inst✝²⁵ : CompleteSpace E inst✝²⁴ : TopologicalSpace A F B : Type inst✝²³ : NormedAddCommGroup F inst✝²² : NormedSpace 𝕜 F inst✝²¹ : CompleteSpace F inst✝²⁰ : TopologicalSpace B G C : Type inst✝¹⁹ : Norm...
Please generate a tactic in lean4 to solve the state. STATE: 𝕜 : Type inst✝²⁸ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁷ : NormedAddCommGroup E inst✝²⁶ : NormedSpace 𝕜 E inst✝²⁵ : CompleteSpace E inst✝²⁴ : TopologicalSpace A F B : Type inst✝²³ : NormedAddCommGroup F inst✝²² : NormedSpace 𝕜 F inst✝²¹ : CompleteS...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
holomorphicAt_snd
[422, 1]
[430, 48]
use continuousAt_snd
𝕜 : Type inst✝²⁸ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁷ : NormedAddCommGroup E inst✝²⁶ : NormedSpace 𝕜 E inst✝²⁵ : CompleteSpace E inst✝²⁴ : TopologicalSpace A F B : Type inst✝²³ : NormedAddCommGroup F inst✝²² : NormedSpace 𝕜 F inst✝²¹ : CompleteSpace F inst✝²⁰ : TopologicalSpace B G C : Type inst✝¹⁹ : Norm...
case right 𝕜 : Type inst✝²⁸ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁷ : NormedAddCommGroup E inst✝²⁶ : NormedSpace 𝕜 E inst✝²⁵ : CompleteSpace E inst✝²⁴ : TopologicalSpace A F B : Type inst✝²³ : NormedAddCommGroup F inst✝²² : NormedSpace 𝕜 F inst✝²¹ : CompleteSpace F inst✝²⁰ : TopologicalSpace B G C : Type ins...
Please generate a tactic in lean4 to solve the state. STATE: 𝕜 : Type inst✝²⁸ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁷ : NormedAddCommGroup E inst✝²⁶ : NormedSpace 𝕜 E inst✝²⁵ : CompleteSpace E inst✝²⁴ : TopologicalSpace A F B : Type inst✝²³ : NormedAddCommGroup F inst✝²² : NormedSpace 𝕜 F inst✝²¹ : CompleteS...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
holomorphicAt_snd
[422, 1]
[430, 48]
refine (analyticAt_snd _).congr ?_
case right 𝕜 : Type inst✝²⁸ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁷ : NormedAddCommGroup E inst✝²⁶ : NormedSpace 𝕜 E inst✝²⁵ : CompleteSpace E inst✝²⁴ : TopologicalSpace A F B : Type inst✝²³ : NormedAddCommGroup F inst✝²² : NormedSpace 𝕜 F inst✝²¹ : CompleteSpace F inst✝²⁰ : TopologicalSpace B G C : Type ins...
case right 𝕜 : Type inst✝²⁸ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁷ : NormedAddCommGroup E inst✝²⁶ : NormedSpace 𝕜 E inst✝²⁵ : CompleteSpace E inst✝²⁴ : TopologicalSpace A F B : Type inst✝²³ : NormedAddCommGroup F inst✝²² : NormedSpace 𝕜 F inst✝²¹ : CompleteSpace F inst✝²⁰ : TopologicalSpace B G C : Type ins...
Please generate a tactic in lean4 to solve the state. STATE: case right 𝕜 : Type inst✝²⁸ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁷ : NormedAddCommGroup E inst✝²⁶ : NormedSpace 𝕜 E inst✝²⁵ : CompleteSpace E inst✝²⁴ : TopologicalSpace A F B : Type inst✝²³ : NormedAddCommGroup F inst✝²² : NormedSpace 𝕜 F inst✝²¹ ...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
holomorphicAt_snd
[422, 1]
[430, 48]
filter_upwards [((isOpen_extChartAt_target _ x).eventually_mem (mem_extChartAt_target _ _))]
case right 𝕜 : Type inst✝²⁸ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁷ : NormedAddCommGroup E inst✝²⁶ : NormedSpace 𝕜 E inst✝²⁵ : CompleteSpace E inst✝²⁴ : TopologicalSpace A F B : Type inst✝²³ : NormedAddCommGroup F inst✝²² : NormedSpace 𝕜 F inst✝²¹ : CompleteSpace F inst✝²⁰ : TopologicalSpace B G C : Type ins...
case h 𝕜 : Type inst✝²⁸ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁷ : NormedAddCommGroup E inst✝²⁶ : NormedSpace 𝕜 E inst✝²⁵ : CompleteSpace E inst✝²⁴ : TopologicalSpace A F B : Type inst✝²³ : NormedAddCommGroup F inst✝²² : NormedSpace 𝕜 F inst✝²¹ : CompleteSpace F inst✝²⁰ : TopologicalSpace B G C : Type inst✝¹⁹...
Please generate a tactic in lean4 to solve the state. STATE: case right 𝕜 : Type inst✝²⁸ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁷ : NormedAddCommGroup E inst✝²⁶ : NormedSpace 𝕜 E inst✝²⁵ : CompleteSpace E inst✝²⁴ : TopologicalSpace A F B : Type inst✝²³ : NormedAddCommGroup F inst✝²² : NormedSpace 𝕜 F inst✝²¹ ...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
holomorphicAt_snd
[422, 1]
[430, 48]
intro y m
case h 𝕜 : Type inst✝²⁸ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁷ : NormedAddCommGroup E inst✝²⁶ : NormedSpace 𝕜 E inst✝²⁵ : CompleteSpace E inst✝²⁴ : TopologicalSpace A F B : Type inst✝²³ : NormedAddCommGroup F inst✝²² : NormedSpace 𝕜 F inst✝²¹ : CompleteSpace F inst✝²⁰ : TopologicalSpace B G C : Type inst✝¹⁹...
case h 𝕜 : Type inst✝²⁸ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁷ : NormedAddCommGroup E inst✝²⁶ : NormedSpace 𝕜 E inst✝²⁵ : CompleteSpace E inst✝²⁴ : TopologicalSpace A F B : Type inst✝²³ : NormedAddCommGroup F inst✝²² : NormedSpace 𝕜 F inst✝²¹ : CompleteSpace F inst✝²⁰ : TopologicalSpace B G C : Type inst✝¹⁹...
Please generate a tactic in lean4 to solve the state. STATE: case h 𝕜 : Type inst✝²⁸ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁷ : NormedAddCommGroup E inst✝²⁶ : NormedSpace 𝕜 E inst✝²⁵ : CompleteSpace E inst✝²⁴ : TopologicalSpace A F B : Type inst✝²³ : NormedAddCommGroup F inst✝²² : NormedSpace 𝕜 F inst✝²¹ : Co...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
holomorphicAt_snd
[422, 1]
[430, 48]
rw [extChartAt_prod] at m
case h 𝕜 : Type inst✝²⁸ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁷ : NormedAddCommGroup E inst✝²⁶ : NormedSpace 𝕜 E inst✝²⁵ : CompleteSpace E inst✝²⁴ : TopologicalSpace A F B : Type inst✝²³ : NormedAddCommGroup F inst✝²² : NormedSpace 𝕜 F inst✝²¹ : CompleteSpace F inst✝²⁰ : TopologicalSpace B G C : Type inst✝¹⁹...
case h 𝕜 : Type inst✝²⁸ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁷ : NormedAddCommGroup E inst✝²⁶ : NormedSpace 𝕜 E inst✝²⁵ : CompleteSpace E inst✝²⁴ : TopologicalSpace A F B : Type inst✝²³ : NormedAddCommGroup F inst✝²² : NormedSpace 𝕜 F inst✝²¹ : CompleteSpace F inst✝²⁰ : TopologicalSpace B G C : Type inst✝¹⁹...
Please generate a tactic in lean4 to solve the state. STATE: case h 𝕜 : Type inst✝²⁸ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁷ : NormedAddCommGroup E inst✝²⁶ : NormedSpace 𝕜 E inst✝²⁵ : CompleteSpace E inst✝²⁴ : TopologicalSpace A F B : Type inst✝²³ : NormedAddCommGroup F inst✝²² : NormedSpace 𝕜 F inst✝²¹ : Co...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
holomorphicAt_snd
[422, 1]
[430, 48]
simp only [PartialHomeomorph.prod_toPartialEquiv, PartialEquiv.prod_target, mem_prod] at m
case h 𝕜 : Type inst✝²⁸ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁷ : NormedAddCommGroup E inst✝²⁶ : NormedSpace 𝕜 E inst✝²⁵ : CompleteSpace E inst✝²⁴ : TopologicalSpace A F B : Type inst✝²³ : NormedAddCommGroup F inst✝²² : NormedSpace 𝕜 F inst✝²¹ : CompleteSpace F inst✝²⁰ : TopologicalSpace B G C : Type inst✝¹⁹...
case h 𝕜 : Type inst✝²⁸ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁷ : NormedAddCommGroup E inst✝²⁶ : NormedSpace 𝕜 E inst✝²⁵ : CompleteSpace E inst✝²⁴ : TopologicalSpace A F B : Type inst✝²³ : NormedAddCommGroup F inst✝²² : NormedSpace 𝕜 F inst✝²¹ : CompleteSpace F inst✝²⁰ : TopologicalSpace B G C : Type inst✝¹⁹...
Please generate a tactic in lean4 to solve the state. STATE: case h 𝕜 : Type inst✝²⁸ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁷ : NormedAddCommGroup E inst✝²⁶ : NormedSpace 𝕜 E inst✝²⁵ : CompleteSpace E inst✝²⁴ : TopologicalSpace A F B : Type inst✝²³ : NormedAddCommGroup F inst✝²² : NormedSpace 𝕜 F inst✝²¹ : Co...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
holomorphicAt_snd
[422, 1]
[430, 48]
simp only [extChartAt_prod, Function.comp, PartialEquiv.prod_coe_symm]
case h 𝕜 : Type inst✝²⁸ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁷ : NormedAddCommGroup E inst✝²⁶ : NormedSpace 𝕜 E inst✝²⁵ : CompleteSpace E inst✝²⁴ : TopologicalSpace A F B : Type inst✝²³ : NormedAddCommGroup F inst✝²² : NormedSpace 𝕜 F inst✝²¹ : CompleteSpace F inst✝²⁰ : TopologicalSpace B G C : Type inst✝¹⁹...
case h 𝕜 : Type inst✝²⁸ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁷ : NormedAddCommGroup E inst✝²⁶ : NormedSpace 𝕜 E inst✝²⁵ : CompleteSpace E inst✝²⁴ : TopologicalSpace A F B : Type inst✝²³ : NormedAddCommGroup F inst✝²² : NormedSpace 𝕜 F inst✝²¹ : CompleteSpace F inst✝²⁰ : TopologicalSpace B G C : Type inst✝¹⁹...
Please generate a tactic in lean4 to solve the state. STATE: case h 𝕜 : Type inst✝²⁸ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁷ : NormedAddCommGroup E inst✝²⁶ : NormedSpace 𝕜 E inst✝²⁵ : CompleteSpace E inst✝²⁴ : TopologicalSpace A F B : Type inst✝²³ : NormedAddCommGroup F inst✝²² : NormedSpace 𝕜 F inst✝²¹ : Co...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
holomorphicAt_snd
[422, 1]
[430, 48]
exact ((extChartAt J x.2).right_inv m.2).symm
case h 𝕜 : Type inst✝²⁸ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁷ : NormedAddCommGroup E inst✝²⁶ : NormedSpace 𝕜 E inst✝²⁵ : CompleteSpace E inst✝²⁴ : TopologicalSpace A F B : Type inst✝²³ : NormedAddCommGroup F inst✝²² : NormedSpace 𝕜 F inst✝²¹ : CompleteSpace F inst✝²⁰ : TopologicalSpace B G C : Type inst✝¹⁹...
no goals
Please generate a tactic in lean4 to solve the state. STATE: case h 𝕜 : Type inst✝²⁸ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁷ : NormedAddCommGroup E inst✝²⁶ : NormedSpace 𝕜 E inst✝²⁵ : CompleteSpace E inst✝²⁴ : TopologicalSpace A F B : Type inst✝²³ : NormedAddCommGroup F inst✝²² : NormedSpace 𝕜 F inst✝²¹ : Co...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
HolomorphicAt.extChartAt
[448, 1]
[466, 47]
rw [holomorphicAt_iff]
𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type inst✝¹⁷ : Norm...
𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type inst✝¹⁷ : Norm...
Please generate a tactic in lean4 to solve the state. STATE: 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteS...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
HolomorphicAt.extChartAt
[448, 1]
[466, 47]
use continuousAt_extChartAt' I ys
𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type inst✝¹⁷ : Norm...
case right 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type ins...
Please generate a tactic in lean4 to solve the state. STATE: 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteS...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
HolomorphicAt.extChartAt
[448, 1]
[466, 47]
simp only [Function.comp, extChartAt, PartialHomeomorph.extend, PartialEquiv.coe_trans, PartialHomeomorph.toFun_eq_coe, ModelWithCorners.toPartialEquiv_coe, PartialHomeomorph.refl_partialEquiv, PartialEquiv.refl_source, PartialHomeomorph.singletonChartedSpace_chartAt_eq, modelWithCornersSelf_partialEquiv, Parti...
case right 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type ins...
case right 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type ins...
Please generate a tactic in lean4 to solve the state. STATE: case right 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ ...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
HolomorphicAt.extChartAt
[448, 1]
[466, 47]
have a : (chartAt A x).symm ≫ₕ chartAt A y ∈ analyticGroupoid I := by apply StructureGroupoid.compatible_of_mem_maximalAtlas exact (@StructureGroupoid.chart_mem_maximalAtlas _ _ _ _ _ (analyticGroupoid I) cm.toHasGroupoid x) exact (@StructureGroupoid.chart_mem_maximalAtlas _ _ _ _ _ (analyticGroupoid I) c...
case right 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type ins...
case right 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type ins...
Please generate a tactic in lean4 to solve the state. STATE: case right 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ ...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
HolomorphicAt.extChartAt
[448, 1]
[466, 47]
simp only [mem_analyticGroupoid_of_boundaryless, PartialHomeomorph.trans_symm_eq_symm_trans_symm, Function.comp, PartialHomeomorph.trans_apply] at a
case right 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type ins...
case right 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type ins...
Please generate a tactic in lean4 to solve the state. STATE: case right 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ ...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
HolomorphicAt.extChartAt
[448, 1]
[466, 47]
apply a.2
case right 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type ins...
case right.a 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type i...
Please generate a tactic in lean4 to solve the state. STATE: case right 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ ...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
HolomorphicAt.extChartAt
[448, 1]
[466, 47]
clear a
case right.a 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type i...
case right.a 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type i...
Please generate a tactic in lean4 to solve the state. STATE: case right.a 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
HolomorphicAt.extChartAt
[448, 1]
[466, 47]
use chartAt A y y
case right.a 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type i...
case h 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type inst✝¹⁷...
Please generate a tactic in lean4 to solve the state. STATE: case right.a 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
HolomorphicAt.extChartAt
[448, 1]
[466, 47]
aesop
case h 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type inst✝¹⁷...
no goals
Please generate a tactic in lean4 to solve the state. STATE: case h 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : Co...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
HolomorphicAt.extChartAt
[448, 1]
[466, 47]
apply StructureGroupoid.compatible_of_mem_maximalAtlas
𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type inst✝¹⁷ : Norm...
case he 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type inst✝¹...
Please generate a tactic in lean4 to solve the state. STATE: 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteS...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
HolomorphicAt.extChartAt
[448, 1]
[466, 47]
exact (@StructureGroupoid.chart_mem_maximalAtlas _ _ _ _ _ (analyticGroupoid I) cm.toHasGroupoid x)
case he 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type inst✝¹...
case he' 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type inst✝...
Please generate a tactic in lean4 to solve the state. STATE: case he 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : C...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
HolomorphicAt.extChartAt
[448, 1]
[466, 47]
exact (@StructureGroupoid.chart_mem_maximalAtlas _ _ _ _ _ (analyticGroupoid I) cm.toHasGroupoid y)
case he' 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type inst✝...
no goals
Please generate a tactic in lean4 to solve the state. STATE: case he' 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : ...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
HolomorphicAt.extChartAt_symm
[469, 1]
[487, 42]
rw [holomorphicAt_iff]
𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type inst✝¹⁷ : Norm...
𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type inst✝¹⁷ : Norm...
Please generate a tactic in lean4 to solve the state. STATE: 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteS...
https://github.com/girving/ray.git
0be790285dd0fce78913b0cb9bddaffa94bd25f9
Ray/AnalyticManifold/AnalyticManifold.lean
HolomorphicAt.extChartAt_symm
[469, 1]
[487, 42]
use continuousAt_extChartAt_symm'' I ys
𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type inst✝¹⁷ : Norm...
case right 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteSpace F inst✝¹⁸ : TopologicalSpace B G C : Type ins...
Please generate a tactic in lean4 to solve the state. STATE: 𝕜 : Type inst✝²⁶ : NontriviallyNormedField 𝕜 E A : Type inst✝²⁵ : NormedAddCommGroup E inst✝²⁴ : NormedSpace 𝕜 E inst✝²³ : CompleteSpace E inst✝²² : TopologicalSpace A F B : Type inst✝²¹ : NormedAddCommGroup F inst✝²⁰ : NormedSpace 𝕜 F inst✝¹⁹ : CompleteS...