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 | HolomorphicAt.eventually | [608, 1] | [624, 68] | apply (fa.continuousAt.eventually_mem ((isOpen_extChartAt_source J (f x)).mem_nhds
(mem_extChartAt_source J (f x)))).eventually_nhds.mp | 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.eventually | [608, 1] | [624, 68] | apply ((isOpen_extChartAt_source I x).eventually_mem (mem_extChartAt_source I x)).mp | 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.eventually | [608, 1] | [624, 68] | apply ((continuousAt_extChartAt I x).eventually
((isOpen_analyticAt _ _).eventually_mem (holomorphicAt_iff.mp fa).2)).mp | 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.eventually | [608, 1] | [624, 68] | refine eventually_of_forall fun y a m fm ↦ ?_ | 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.eventually | [608, 1] | [624, 68] | rw [mem_setOf] at 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
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.eventually | [608, 1] | [624, 68] | have h := a.holomorphicAt (modelWithCornersSelf 𝕜 E) (modelWithCornersSelf 𝕜 F) | 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.eventually | [608, 1] | [624, 68] | clear 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
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.eventually | [608, 1] | [624, 68] | have h' := (HolomorphicAt.extChartAt_symm (PartialEquiv.map_source _ fm.self_of_nhds)).comp_of_eq
(h.comp (HolomorphicAt.extChartAt m)) ?_ | 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 refine_2
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
... | 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.eventually | [608, 1] | [624, 68] | swap | case refine_2
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
... | case refine_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
... | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_2
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✝... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/AnalyticManifold.lean | HolomorphicAt.eventually | [608, 1] | [624, 68] | simp only [Function.comp, PartialEquiv.left_inv _ m] | case refine_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
... | case refine_2
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
... | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_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✝... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/AnalyticManifold.lean | HolomorphicAt.eventually | [608, 1] | [624, 68] | apply h'.congr | case refine_2
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
... | case refine_2
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
... | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_2
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✝... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/AnalyticManifold.lean | HolomorphicAt.eventually | [608, 1] | [624, 68] | clear h h' | case refine_2
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
... | case refine_2
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
... | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_2
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✝... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/AnalyticManifold.lean | HolomorphicAt.eventually | [608, 1] | [624, 68] | simp only [Function.comp] | case refine_2
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
... | case refine_2
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
... | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_2
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✝... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/AnalyticManifold.lean | HolomorphicAt.eventually | [608, 1] | [624, 68] | apply ((isOpen_extChartAt_source I x).eventually_mem m).mp | case refine_2
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
... | case refine_2
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
... | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_2
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✝... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/AnalyticManifold.lean | HolomorphicAt.eventually | [608, 1] | [624, 68] | refine fm.mp (eventually_of_forall fun z mf m ↦ ?_) | case refine_2
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
... | case refine_2
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
... | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_2
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✝... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/AnalyticManifold.lean | HolomorphicAt.eventually | [608, 1] | [624, 68] | simp only [PartialEquiv.left_inv _ m, PartialEquiv.left_inv _ mf] | case refine_2
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
... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_2
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✝... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/AnalyticManifold.lean | isOpen_holomorphicAt | [627, 1] | [628, 62] | rw [isOpen_iff_eventually] | 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 | isOpen_holomorphicAt | [627, 1] | [628, 62] | intro x fa | 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 | isOpen_holomorphicAt | [627, 1] | [628, 62] | exact fa.eventually | 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 | HasMFDerivAt.prod | [631, 1] | [636, 43] | simp only [HasMFDerivAt, ModelWithCorners.range_eq_univ, hasFDerivWithinAt_univ] 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 | HasMFDerivAt.prod | [631, 1] | [636, 43] | 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 | HasMFDerivAt.prod | [631, 1] | [636, 43] | exact fh.2.prod gh.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... | 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 | tangentSpace_prod | [639, 1] | [641, 27] | simp only [TangentSpace] | 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 | MDifferentiableAt.hasMFDerivAt_uncurry | [645, 1] | [686, 35] | set fst := ContinuousLinearMap.fst 𝕜 (TangentSpace J y) (TangentSpace K z) | 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 | MDifferentiableAt.hasMFDerivAt_uncurry | [645, 1] | [686, 35] | set snd := ContinuousLinearMap.snd 𝕜 (TangentSpace J y) (TangentSpace K z) | 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 | MDifferentiableAt.hasMFDerivAt_uncurry | [645, 1] | [686, 35] | generalize hdf : mfderiv (J.prod K) L (uncurry f) (y, z) = df | 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 | MDifferentiableAt.hasMFDerivAt_uncurry | [645, 1] | [686, 35] | have fh := fd.hasMFDerivAt | 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 | MDifferentiableAt.hasMFDerivAt_uncurry | [645, 1] | [686, 35] | rw [hdf] 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 | MDifferentiableAt.hasMFDerivAt_uncurry | [645, 1] | [686, 35] | suffices e : df = df0.comp fst + df1.comp snd by rw [e] at fh; exact 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 | MDifferentiableAt.hasMFDerivAt_uncurry | [645, 1] | [686, 35] | apply ContinuousLinearMap.ext | 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 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:
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 | MDifferentiableAt.hasMFDerivAt_uncurry | [645, 1] | [686, 35] | intro ⟨u, v⟩ | 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 | MDifferentiableAt.hasMFDerivAt_uncurry | [645, 1] | [686, 35] | simp only [Function.uncurry_apply_pair, ContinuousLinearMap.add_apply,
ContinuousLinearMap.comp_apply] | 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 | MDifferentiableAt.hasMFDerivAt_uncurry | [645, 1] | [686, 35] | have hu : ∀ u : TangentSpace J y, df (u, 0) = df0 u := by
intro u
have d : HasMFDerivAt J L (uncurry f ∘ fun x ↦ (x, z)) y
(df.comp ((ContinuousLinearMap.id 𝕜 (TangentSpace J y)).prod 0)) :=
fh.comp y ((hasMFDerivAt_id _ _).prod (hasMFDerivAt_const _ _ _ _))
simp only [hasMFDerivAt_unique fh0 d]
refi... | 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 | MDifferentiableAt.hasMFDerivAt_uncurry | [645, 1] | [686, 35] | have hv : ∀ v : TangentSpace K z, df (0, v) = df1 v := by
intro v
have d : HasMFDerivAt K L (uncurry f ∘ fun x ↦ (y, x)) z (df.comp
((0 : TangentSpace K z →L[𝕜] TangentSpace J y).prod
(ContinuousLinearMap.id 𝕜 (TangentSpace K z)))) :=
fh.comp z ((hasMFDerivAt_const _ _ _ _).prod (hasMFDerivAt_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... | 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 | MDifferentiableAt.hasMFDerivAt_uncurry | [645, 1] | [686, 35] | have e : (u, v) = (u, 0) + (0, v) := by simp only [Prod.mk_add_mk, add_zero, zero_add] | 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 | MDifferentiableAt.hasMFDerivAt_uncurry | [645, 1] | [686, 35] | nth_rw 1 [e] | 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 | MDifferentiableAt.hasMFDerivAt_uncurry | [645, 1] | [686, 35] | rw [map_add] | 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 | MDifferentiableAt.hasMFDerivAt_uncurry | [645, 1] | [686, 35] | exact congr_arg₂ _ (hu u) (hv v) | 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 | MDifferentiableAt.hasMFDerivAt_uncurry | [645, 1] | [686, 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 | MDifferentiableAt.hasMFDerivAt_uncurry | [645, 1] | [686, 35] | exact 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... | 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 | MDifferentiableAt.hasMFDerivAt_uncurry | [645, 1] | [686, 35] | intro u | 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 | MDifferentiableAt.hasMFDerivAt_uncurry | [645, 1] | [686, 35] | have d : HasMFDerivAt J L (uncurry f ∘ fun x ↦ (x, z)) y
(df.comp ((ContinuousLinearMap.id 𝕜 (TangentSpace J y)).prod 0)) :=
fh.comp y ((hasMFDerivAt_id _ _).prod (hasMFDerivAt_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... | 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 | MDifferentiableAt.hasMFDerivAt_uncurry | [645, 1] | [686, 35] | simp only [hasMFDerivAt_unique fh0 d] | 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 | MDifferentiableAt.hasMFDerivAt_uncurry | [645, 1] | [686, 35] | refine Eq.trans (congr_arg _ ?_) (ContinuousLinearMap.comp_apply _ _ _).symm | 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 | MDifferentiableAt.hasMFDerivAt_uncurry | [645, 1] | [686, 35] | refine Eq.trans ?_ (ContinuousLinearMap.prod_apply _ _ _).symm | 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 | MDifferentiableAt.hasMFDerivAt_uncurry | [645, 1] | [686, 35] | simp only [ContinuousLinearMap.zero_apply, Prod.mk.injEq, and_true] | 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 | MDifferentiableAt.hasMFDerivAt_uncurry | [645, 1] | [686, 35] | exact rfl | 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 | MDifferentiableAt.hasMFDerivAt_uncurry | [645, 1] | [686, 35] | intro v | 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 | MDifferentiableAt.hasMFDerivAt_uncurry | [645, 1] | [686, 35] | have d : HasMFDerivAt K L (uncurry f ∘ fun x ↦ (y, x)) z (df.comp
((0 : TangentSpace K z →L[𝕜] TangentSpace J y).prod
(ContinuousLinearMap.id 𝕜 (TangentSpace K z)))) :=
fh.comp z ((hasMFDerivAt_const _ _ _ _).prod (hasMFDerivAt_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... | 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 | MDifferentiableAt.hasMFDerivAt_uncurry | [645, 1] | [686, 35] | rw [hasMFDerivAt_unique fh1 d] | 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 | MDifferentiableAt.hasMFDerivAt_uncurry | [645, 1] | [686, 35] | refine Eq.trans (congr_arg _ ?_) (ContinuousLinearMap.comp_apply _ _ _).symm | 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 | MDifferentiableAt.hasMFDerivAt_uncurry | [645, 1] | [686, 35] | refine Eq.trans ?_ (ContinuousLinearMap.prod_apply _ _ _).symm | 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 | MDifferentiableAt.hasMFDerivAt_uncurry | [645, 1] | [686, 35] | simp only [Prod.mk.injEq] | 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 | MDifferentiableAt.hasMFDerivAt_uncurry | [645, 1] | [686, 35] | exact ⟨(ContinuousLinearMap.zero_apply _).symm, rfl⟩ | 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 | MDifferentiableAt.hasMFDerivAt_uncurry | [645, 1] | [686, 35] | simp only [Prod.mk_add_mk, add_zero, zero_add] | 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 | MDifferentiableAt.hasMFDerivAt_comp2 | [689, 1] | [701, 11] | have fh := (fd.hasMFDerivAt_uncurry fh0 fh1).comp x (gh.prod hh) | 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 | MDifferentiableAt.hasMFDerivAt_comp2 | [689, 1] | [701, 11] | simp only [ContinuousLinearMap.add_comp, ContinuousLinearMap.comp_assoc,
ContinuousLinearMap.fst_comp_prod, ContinuousLinearMap.snd_comp_prod] 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 | MDifferentiableAt.hasMFDerivAt_comp2 | [689, 1] | [701, 11] | exact 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... | 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 | hasMFDerivAt_iff_hasFDerivAt' | [705, 1] | [715, 51] | simp only [HasMFDerivAt, ModelWithCorners.range_eq_univ, hasFDerivWithinAt_univ,
writtenInExtChartAt, extChartAt_eq_refl, Function.comp, PartialEquiv.refl_coe,
PartialEquiv.refl_symm, id] | 𝕜 : Type
inst✝³⁴ : NontriviallyNormedField 𝕜
E A : Type
inst✝³³ : NormedAddCommGroup E
inst✝³² : NormedSpace 𝕜 E
inst✝³¹ : CompleteSpace E
inst✝³⁰ : TopologicalSpace A
F B : Type
inst✝²⁹ : NormedAddCommGroup F
inst✝²⁸ : NormedSpace 𝕜 F
inst✝²⁷ : CompleteSpace F
inst✝²⁶ : TopologicalSpace B
G C : Type
inst✝²⁵ : Norm... | 𝕜 : Type
inst✝³⁴ : NontriviallyNormedField 𝕜
E A : Type
inst✝³³ : NormedAddCommGroup E
inst✝³² : NormedSpace 𝕜 E
inst✝³¹ : CompleteSpace E
inst✝³⁰ : TopologicalSpace A
F B : Type
inst✝²⁹ : NormedAddCommGroup F
inst✝²⁸ : NormedSpace 𝕜 F
inst✝²⁷ : CompleteSpace F
inst✝²⁶ : TopologicalSpace B
G C : Type
inst✝²⁵ : Norm... | Please generate a tactic in lean4 to solve the state.
STATE:
𝕜 : Type
inst✝³⁴ : NontriviallyNormedField 𝕜
E A : Type
inst✝³³ : NormedAddCommGroup E
inst✝³² : NormedSpace 𝕜 E
inst✝³¹ : CompleteSpace E
inst✝³⁰ : TopologicalSpace A
F B : Type
inst✝²⁹ : NormedAddCommGroup F
inst✝²⁸ : NormedSpace 𝕜 F
inst✝²⁷ : CompleteS... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/AnalyticManifold.lean | hasMFDerivAt_iff_hasFDerivAt' | [705, 1] | [715, 51] | exact ⟨fun x ↦ x.2, fun d ↦ ⟨d.continuousAt, d⟩⟩ | 𝕜 : Type
inst✝³⁴ : NontriviallyNormedField 𝕜
E A : Type
inst✝³³ : NormedAddCommGroup E
inst✝³² : NormedSpace 𝕜 E
inst✝³¹ : CompleteSpace E
inst✝³⁰ : TopologicalSpace A
F B : Type
inst✝²⁹ : NormedAddCommGroup F
inst✝²⁸ : NormedSpace 𝕜 F
inst✝²⁷ : CompleteSpace F
inst✝²⁶ : TopologicalSpace B
G C : Type
inst✝²⁵ : Norm... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
𝕜 : Type
inst✝³⁴ : NontriviallyNormedField 𝕜
E A : Type
inst✝³³ : NormedAddCommGroup E
inst✝³² : NormedSpace 𝕜 E
inst✝³¹ : CompleteSpace E
inst✝³⁰ : TopologicalSpace A
F B : Type
inst✝²⁹ : NormedAddCommGroup F
inst✝²⁸ : NormedSpace 𝕜 F
inst✝²⁷ : CompleteS... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/AnalyticManifold.lean | HolomorphicOn.continuousOn_tangentMap | [719, 1] | [729, 87] | generalize ht : {x | HolomorphicAt I J f x} = t | 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 | HolomorphicOn.continuousOn_tangentMap | [719, 1] | [729, 87] | have o : IsOpen t := by rw [← ht]; exact isOpen_holomorphicAt | 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 | HolomorphicOn.continuousOn_tangentMap | [719, 1] | [729, 87] | have sub : s ⊆ t := by rw [← ht]; exact fa | 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 | HolomorphicOn.continuousOn_tangentMap | [719, 1] | [729, 87] | replace fa : HolomorphicOn I J f t := by
simp only [HolomorphicOn, mem_setOf_eq, imp_self, implies_true, ← ht] | 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 | HolomorphicOn.continuousOn_tangentMap | [719, 1] | [729, 87] | refine ContinuousOn.mono ?_ (preimage_mono sub) | 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 | HolomorphicOn.continuousOn_tangentMap | [719, 1] | [729, 87] | apply (fa.smoothOn.contMDiffOn.continuousOn_tangentMapWithin le_top o.uniqueMDiffOn).congr | 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 | HolomorphicOn.continuousOn_tangentMap | [719, 1] | [729, 87] | intro x m | 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 | HolomorphicOn.continuousOn_tangentMap | [719, 1] | [729, 87] | simp only [mem_preimage] at m | 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 | HolomorphicOn.continuousOn_tangentMap | [719, 1] | [729, 87] | rw [tangentMapWithin_eq_tangentMap (o.uniqueMDiffOn _ m) (fa _ m).mdifferentiableAt] | 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 | HolomorphicOn.continuousOn_tangentMap | [719, 1] | [729, 87] | rw [← ht] | 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 | HolomorphicOn.continuousOn_tangentMap | [719, 1] | [729, 87] | exact isOpen_holomorphicAt | 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 | HolomorphicOn.continuousOn_tangentMap | [719, 1] | [729, 87] | rw [← ht] | 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 | HolomorphicOn.continuousOn_tangentMap | [719, 1] | [729, 87] | exact fa | 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 | HolomorphicOn.continuousOn_tangentMap | [719, 1] | [729, 87] | simp only [HolomorphicOn, mem_setOf_eq, imp_self, implies_true, ← ht] | 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 | extChartAt_symm_map_nhds' | [757, 1] | [761, 66] | convert extChartAt_symm_map_nhds (mem_extChartAt_target I x) | 𝕜 : Type
inst✝²⁹ : NontriviallyNormedField 𝕜
E A : Type
inst✝²⁸ : NormedAddCommGroup E
inst✝²⁷ : NormedSpace 𝕜 E
inst✝²⁶ : CompleteSpace E
inst✝²⁵ : TopologicalSpace A
F B : Type
inst✝²⁴ : NormedAddCommGroup F
inst✝²³ : NormedSpace 𝕜 F
inst✝²² : CompleteSpace F
inst✝²¹ : TopologicalSpace B
G C : Type
inst✝²⁰ : Norm... | case h.e'_3.h.e'_3
𝕜 : Type
inst✝²⁹ : NontriviallyNormedField 𝕜
E A : Type
inst✝²⁸ : NormedAddCommGroup E
inst✝²⁷ : NormedSpace 𝕜 E
inst✝²⁶ : CompleteSpace E
inst✝²⁵ : TopologicalSpace A
F B : Type
inst✝²⁴ : NormedAddCommGroup F
inst✝²³ : NormedSpace 𝕜 F
inst✝²² : CompleteSpace F
inst✝²¹ : TopologicalSpace B
G C : ... | Please generate a tactic in lean4 to solve the state.
STATE:
𝕜 : Type
inst✝²⁹ : NontriviallyNormedField 𝕜
E A : Type
inst✝²⁸ : NormedAddCommGroup E
inst✝²⁷ : NormedSpace 𝕜 E
inst✝²⁶ : CompleteSpace E
inst✝²⁵ : TopologicalSpace A
F B : Type
inst✝²⁴ : NormedAddCommGroup F
inst✝²³ : NormedSpace 𝕜 F
inst✝²² : CompleteS... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/AnalyticManifold.lean | extChartAt_symm_map_nhds' | [757, 1] | [761, 66] | simp only [PartialEquiv.left_inv _ (mem_extChartAt_source I x)] | case h.e'_3.h.e'_3
𝕜 : Type
inst✝²⁹ : NontriviallyNormedField 𝕜
E A : Type
inst✝²⁸ : NormedAddCommGroup E
inst✝²⁷ : NormedSpace 𝕜 E
inst✝²⁶ : CompleteSpace E
inst✝²⁵ : TopologicalSpace A
F B : Type
inst✝²⁴ : NormedAddCommGroup F
inst✝²³ : NormedSpace 𝕜 F
inst✝²² : CompleteSpace F
inst✝²¹ : TopologicalSpace B
G C : ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_3.h.e'_3
𝕜 : Type
inst✝²⁹ : NontriviallyNormedField 𝕜
E A : Type
inst✝²⁸ : NormedAddCommGroup E
inst✝²⁷ : NormedSpace 𝕜 E
inst✝²⁶ : CompleteSpace E
inst✝²⁵ : TopologicalSpace A
F B : Type
inst✝²⁴ : NormedAddCommGroup F
inst✝²³ : NormedSpace 𝕜 F
... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/AnalyticManifold.lean | AnalyticManifold.punctured_nhds_neBot | [765, 1] | [775, 34] | have p := Module.punctured_nhds_neBot 𝕜 E (extChartAt I x x) | 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 | AnalyticManifold.punctured_nhds_neBot | [765, 1] | [775, 34] | simp only [← Filter.frequently_true_iff_neBot, frequently_nhdsWithin_iff, ←
extChartAt_symm_map_nhds' I x, Filter.frequently_map, true_and_iff,
mem_compl_singleton_iff] at p ⊢ | 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 | AnalyticManifold.punctured_nhds_neBot | [765, 1] | [775, 34] | apply p.mp | 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 | AnalyticManifold.punctured_nhds_neBot | [765, 1] | [775, 34] | apply ((isOpen_extChartAt_target I x).eventually_mem (mem_extChartAt_target I x)).mp | 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 | AnalyticManifold.punctured_nhds_neBot | [765, 1] | [775, 34] | refine eventually_of_forall fun y m 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 : 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 | AnalyticManifold.punctured_nhds_neBot | [765, 1] | [775, 34] | contrapose 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 : 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 | AnalyticManifold.punctured_nhds_neBot | [765, 1] | [775, 34] | simp only [not_not] at m 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 : 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 | AnalyticManifold.punctured_nhds_neBot | [765, 1] | [775, 34] | nth_rw 2 [← 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 : 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 | AnalyticManifold.punctured_nhds_neBot | [765, 1] | [775, 34] | rw [PartialEquiv.right_inv _ m] | 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... | no goals | 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 | mfderiv_comp' | [778, 1] | [790, 40] | apply mfderiv_comp | 𝕜✝ : Type
inst✝³⁹ : NontriviallyNormedField 𝕜✝
E✝ A : Type
inst✝³⁸ : NormedAddCommGroup E✝
inst✝³⁷ : NormedSpace 𝕜✝ E✝
inst✝³⁶ : CompleteSpace E✝
inst✝³⁵ : TopologicalSpace A
F B : Type
inst✝³⁴ : NormedAddCommGroup F
inst✝³³ : NormedSpace 𝕜✝ F
inst✝³² : CompleteSpace F
inst✝³¹ : TopologicalSpace B
G C : Type
inst✝³... | case hg
𝕜✝ : Type
inst✝³⁹ : NontriviallyNormedField 𝕜✝
E✝ A : Type
inst✝³⁸ : NormedAddCommGroup E✝
inst✝³⁷ : NormedSpace 𝕜✝ E✝
inst✝³⁶ : CompleteSpace E✝
inst✝³⁵ : TopologicalSpace A
F B : Type
inst✝³⁴ : NormedAddCommGroup F
inst✝³³ : NormedSpace 𝕜✝ F
inst✝³² : CompleteSpace F
inst✝³¹ : TopologicalSpace B
G C : Typ... | Please generate a tactic in lean4 to solve the state.
STATE:
𝕜✝ : Type
inst✝³⁹ : NontriviallyNormedField 𝕜✝
E✝ A : Type
inst✝³⁸ : NormedAddCommGroup E✝
inst✝³⁷ : NormedSpace 𝕜✝ E✝
inst✝³⁶ : CompleteSpace E✝
inst✝³⁵ : TopologicalSpace A
F B : Type
inst✝³⁴ : NormedAddCommGroup F
inst✝³³ : NormedSpace 𝕜✝ F
inst✝³² : C... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/AnalyticManifold.lean | mfderiv_comp' | [778, 1] | [790, 40] | repeat assumption | case hg
𝕜✝ : Type
inst✝³⁹ : NontriviallyNormedField 𝕜✝
E✝ A : Type
inst✝³⁸ : NormedAddCommGroup E✝
inst✝³⁷ : NormedSpace 𝕜✝ E✝
inst✝³⁶ : CompleteSpace E✝
inst✝³⁵ : TopologicalSpace A
F B : Type
inst✝³⁴ : NormedAddCommGroup F
inst✝³³ : NormedSpace 𝕜✝ F
inst✝³² : CompleteSpace F
inst✝³¹ : TopologicalSpace B
G C : Typ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case hg
𝕜✝ : Type
inst✝³⁹ : NontriviallyNormedField 𝕜✝
E✝ A : Type
inst✝³⁸ : NormedAddCommGroup E✝
inst✝³⁷ : NormedSpace 𝕜✝ E✝
inst✝³⁶ : CompleteSpace E✝
inst✝³⁵ : TopologicalSpace A
F B : Type
inst✝³⁴ : NormedAddCommGroup F
inst✝³³ : NormedSpace 𝕜✝ F
ins... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/AnalyticManifold.lean | mfderiv_comp' | [778, 1] | [790, 40] | assumption | case hf
𝕜✝ : Type
inst✝³⁹ : NontriviallyNormedField 𝕜✝
E✝ A : Type
inst✝³⁸ : NormedAddCommGroup E✝
inst✝³⁷ : NormedSpace 𝕜✝ E✝
inst✝³⁶ : CompleteSpace E✝
inst✝³⁵ : TopologicalSpace A
F B : Type
inst✝³⁴ : NormedAddCommGroup F
inst✝³³ : NormedSpace 𝕜✝ F
inst✝³² : CompleteSpace F
inst✝³¹ : TopologicalSpace B
G C : Typ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case hf
𝕜✝ : Type
inst✝³⁹ : NontriviallyNormedField 𝕜✝
E✝ A : Type
inst✝³⁸ : NormedAddCommGroup E✝
inst✝³⁷ : NormedSpace 𝕜✝ E✝
inst✝³⁶ : CompleteSpace E✝
inst✝³⁵ : TopologicalSpace A
F B : Type
inst✝³⁴ : NormedAddCommGroup F
inst✝³³ : NormedSpace 𝕜✝ F
ins... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/Bound.lean | Bound.pow_le_pow_right_of_le_one_or_one_le | [220, 1] | [225, 40] | rcases h with ⟨a1, nm⟩ | ⟨a0, a1, mn⟩ | α : Type
inst✝¹ : LinearOrder α
a✝ b c : α
R : Type
inst✝ : OrderedSemiring R
a : R
n m : ℕ
h : 1 ≤ a ∧ n ≤ m ∨ 0 ≤ a ∧ a ≤ 1 ∧ m ≤ n
⊢ a ^ n ≤ a ^ m | case inl.intro
α : Type
inst✝¹ : LinearOrder α
a✝ b c : α
R : Type
inst✝ : OrderedSemiring R
a : R
n m : ℕ
a1 : 1 ≤ a
nm : n ≤ m
⊢ a ^ n ≤ a ^ m
case inr.intro.intro
α : Type
inst✝¹ : LinearOrder α
a✝ b c : α
R : Type
inst✝ : OrderedSemiring R
a : R
n m : ℕ
a0 : 0 ≤ a
a1 : a ≤ 1
mn : m ≤ n
⊢ a ^ n ≤ a ^ m | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝¹ : LinearOrder α
a✝ b c : α
R : Type
inst✝ : OrderedSemiring R
a : R
n m : ℕ
h : 1 ≤ a ∧ n ≤ m ∨ 0 ≤ a ∧ a ≤ 1 ∧ m ≤ n
⊢ a ^ n ≤ a ^ m
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/Bound.lean | Bound.pow_le_pow_right_of_le_one_or_one_le | [220, 1] | [225, 40] | exact pow_le_pow_right a1 nm | case inl.intro
α : Type
inst✝¹ : LinearOrder α
a✝ b c : α
R : Type
inst✝ : OrderedSemiring R
a : R
n m : ℕ
a1 : 1 ≤ a
nm : n ≤ m
⊢ a ^ n ≤ a ^ m | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case inl.intro
α : Type
inst✝¹ : LinearOrder α
a✝ b c : α
R : Type
inst✝ : OrderedSemiring R
a : R
n m : ℕ
a1 : 1 ≤ a
nm : n ≤ m
⊢ a ^ n ≤ a ^ m
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/Bound.lean | Bound.pow_le_pow_right_of_le_one_or_one_le | [220, 1] | [225, 40] | exact pow_le_pow_of_le_one a0 a1 mn | case inr.intro.intro
α : Type
inst✝¹ : LinearOrder α
a✝ b c : α
R : Type
inst✝ : OrderedSemiring R
a : R
n m : ℕ
a0 : 0 ≤ a
a1 : a ≤ 1
mn : m ≤ n
⊢ a ^ n ≤ a ^ m | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.intro.intro
α : Type
inst✝¹ : LinearOrder α
a✝ b c : α
R : Type
inst✝ : OrderedSemiring R
a : R
n m : ℕ
a0 : 0 ≤ a
a1 : a ≤ 1
mn : m ≤ n
⊢ a ^ n ≤ a ^ m
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/Bound.lean | Bound.Real.rpow_le_rpow_of_exponent_le_or_ge | [227, 1] | [232, 52] | rcases h with ⟨x1, yz⟩ | ⟨x0, x1, zy⟩ | α : Type
inst✝ : LinearOrder α
a b c : α
x y z : ℝ
h : 1 ≤ x ∧ y ≤ z ∨ 0 < x ∧ x ≤ 1 ∧ z ≤ y
⊢ x ^ y ≤ x ^ z | case inl.intro
α : Type
inst✝ : LinearOrder α
a b c : α
x y z : ℝ
x1 : 1 ≤ x
yz : y ≤ z
⊢ x ^ y ≤ x ^ z
case inr.intro.intro
α : Type
inst✝ : LinearOrder α
a b c : α
x y z : ℝ
x0 : 0 < x
x1 : x ≤ 1
zy : z ≤ y
⊢ x ^ y ≤ x ^ z | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : LinearOrder α
a b c : α
x y z : ℝ
h : 1 ≤ x ∧ y ≤ z ∨ 0 < x ∧ x ≤ 1 ∧ z ≤ y
⊢ x ^ y ≤ x ^ z
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/Bound.lean | Bound.Real.rpow_le_rpow_of_exponent_le_or_ge | [227, 1] | [232, 52] | exact Real.rpow_le_rpow_of_exponent_le x1 yz | case inl.intro
α : Type
inst✝ : LinearOrder α
a b c : α
x y z : ℝ
x1 : 1 ≤ x
yz : y ≤ z
⊢ x ^ y ≤ x ^ z | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case inl.intro
α : Type
inst✝ : LinearOrder α
a b c : α
x y z : ℝ
x1 : 1 ≤ x
yz : y ≤ z
⊢ x ^ y ≤ x ^ z
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Tactic/Bound.lean | Bound.Real.rpow_le_rpow_of_exponent_le_or_ge | [227, 1] | [232, 52] | exact Real.rpow_le_rpow_of_exponent_ge x0 x1 zy | case inr.intro.intro
α : Type
inst✝ : LinearOrder α
a b c : α
x y z : ℝ
x0 : 0 < x
x1 : x ≤ 1
zy : z ≤ y
⊢ x ^ y ≤ x ^ z | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.intro.intro
α : Type
inst✝ : LinearOrder α
a b c : α
x y z : ℝ
x0 : 0 < x
x1 : x ≤ 1
zy : z ≤ y
⊢ x ^ y ≤ x ^ z
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multibrot/Specific.lean | exp_ofNat_lt | [14, 1] | [18, 84] | rw [←Real.exp_one_pow a] | a : ℕ
b : ℝ
a0 : autoParam (a ≠ 0) _auto✝
h0 : autoParam (2.7182818286 ^ a < b) _auto✝
⊢ (↑a).exp < b | a : ℕ
b : ℝ
a0 : autoParam (a ≠ 0) _auto✝
h0 : autoParam (2.7182818286 ^ a < b) _auto✝
⊢ exp 1 ^ a < b | Please generate a tactic in lean4 to solve the state.
STATE:
a : ℕ
b : ℝ
a0 : autoParam (a ≠ 0) _auto✝
h0 : autoParam (2.7182818286 ^ a < b) _auto✝
⊢ (↑a).exp < b
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multibrot/Specific.lean | exp_ofNat_lt | [14, 1] | [18, 84] | exact _root_.trans (pow_lt_pow_left Real.exp_one_lt_d9 (Real.exp_nonneg _) a0) h0 | a : ℕ
b : ℝ
a0 : autoParam (a ≠ 0) _auto✝
h0 : autoParam (2.7182818286 ^ a < b) _auto✝
⊢ exp 1 ^ a < b | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
a : ℕ
b : ℝ
a0 : autoParam (a ≠ 0) _auto✝
h0 : autoParam (2.7182818286 ^ a < b) _auto✝
⊢ exp 1 ^ a < b
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multibrot/Specific.lean | exp_neg_ofNat_lt | [20, 1] | [26, 13] | rw [Real.exp_neg, inv_lt, ←Real.exp_one_pow a] | a : ℕ
b : ℝ
a0 : autoParam (a ≠ 0) _auto✝
b0 : autoParam (0 < b) _auto✝
h0 : autoParam (b⁻¹ < 2.7182818283 ^ a) _auto✝
⊢ (-↑a).exp < b | a : ℕ
b : ℝ
a0 : autoParam (a ≠ 0) _auto✝
b0 : autoParam (0 < b) _auto✝
h0 : autoParam (b⁻¹ < 2.7182818283 ^ a) _auto✝
⊢ b⁻¹ < exp 1 ^ a
case ha
a : ℕ
b : ℝ
a0 : autoParam (a ≠ 0) _auto✝
b0 : autoParam (0 < b) _auto✝
h0 : autoParam (b⁻¹ < 2.7182818283 ^ a) _auto✝
⊢ 0 < (↑a).exp
case hb
a : ℕ
b : ℝ
a0 : autoParam (a ≠... | Please generate a tactic in lean4 to solve the state.
STATE:
a : ℕ
b : ℝ
a0 : autoParam (a ≠ 0) _auto✝
b0 : autoParam (0 < b) _auto✝
h0 : autoParam (b⁻¹ < 2.7182818283 ^ a) _auto✝
⊢ (-↑a).exp < b
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multibrot/Specific.lean | exp_neg_ofNat_lt | [20, 1] | [26, 13] | exact _root_.trans h0 (pow_lt_pow_left Real.exp_one_gt_d9 (by norm_num) a0) | a : ℕ
b : ℝ
a0 : autoParam (a ≠ 0) _auto✝
b0 : autoParam (0 < b) _auto✝
h0 : autoParam (b⁻¹ < 2.7182818283 ^ a) _auto✝
⊢ b⁻¹ < exp 1 ^ a | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
a : ℕ
b : ℝ
a0 : autoParam (a ≠ 0) _auto✝
b0 : autoParam (0 < b) _auto✝
h0 : autoParam (b⁻¹ < 2.7182818283 ^ a) _auto✝
⊢ b⁻¹ < exp 1 ^ a
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multibrot/Specific.lean | exp_neg_ofNat_lt | [20, 1] | [26, 13] | norm_num | a : ℕ
b : ℝ
a0 : autoParam (a ≠ 0) _auto✝
b0 : autoParam (0 < b) _auto✝
h0 : autoParam (b⁻¹ < 2.7182818283 ^ a) _auto✝
⊢ 0 ≤ 2.7182818283 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
a : ℕ
b : ℝ
a0 : autoParam (a ≠ 0) _auto✝
b0 : autoParam (0 < b) _auto✝
h0 : autoParam (b⁻¹ < 2.7182818283 ^ a) _auto✝
⊢ 0 ≤ 2.7182818283
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multibrot/Specific.lean | exp_neg_ofNat_lt | [20, 1] | [26, 13] | exact Real.exp_pos _ | case ha
a : ℕ
b : ℝ
a0 : autoParam (a ≠ 0) _auto✝
b0 : autoParam (0 < b) _auto✝
h0 : autoParam (b⁻¹ < 2.7182818283 ^ a) _auto✝
⊢ 0 < (↑a).exp | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case ha
a : ℕ
b : ℝ
a0 : autoParam (a ≠ 0) _auto✝
b0 : autoParam (0 < b) _auto✝
h0 : autoParam (b⁻¹ < 2.7182818283 ^ a) _auto✝
⊢ 0 < (↑a).exp
TACTIC:
|
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