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/Dynamics/Multiple.lean | not_local_inj_of_deriv_zero | [140, 1] | [167, 65] | exact ff | case intro.intro.intro.refine_3.intro.right
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : ℂ → ℂ
c : ℂ
f' : ℂ → ℂ := fun z => f (z + c) - f c
f0' : (fun z => f (z + c) - f c) 0 =... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.refine_3.intro.right
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : ℂ → ℂ
c : ℂ
f' : ℂ → ℂ := ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | not_local_inj_of_deriv_zero | [140, 1] | [167, 65] | rw [← sub_self c] | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : ℂ → ℂ
c : ℂ
f' : ℂ → ℂ := fun z => f (z + c) - f c
f0' : (fun z => f (z + c) - f c) 0 = 0
g : ℂ → ℂ
ga : AnalyticAt ℂ g 0
e : g 0 =... | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : ℂ → ℂ
c : ℂ
f' : ℂ → ℂ := fun z => f (z + c) - f c
f0' : (fun z => f (z + c) - f c) 0 = 0
g : ℂ → ℂ
ga : AnalyticAt ℂ g 0
e : g 0 =... | Please generate a tactic in lean4 to solve the state.
STATE:
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : ℂ → ℂ
c : ℂ
f' : ℂ → ℂ := fun z => f (z + c) - f c
f0' : (fun z => f (... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | not_local_inj_of_deriv_zero | [140, 1] | [167, 65] | exact continuousAt_id.sub continuousAt_const | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : ℂ → ℂ
c : ℂ
f' : ℂ → ℂ := fun z => f (z + c) - f c
f0' : (fun z => f (z + c) - f c) 0 = 0
g : ℂ → ℂ
ga : AnalyticAt ℂ g 0
e : g 0 =... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : ℂ → ℂ
c : ℂ
f' : ℂ → ℂ := fun z => f (z + c) - f c
f0' : (fun z => f (... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | not_local_inj_of_mfderiv_zero | [172, 1] | [225, 63] | generalize hg : (fun z ↦ extChartAt I (f c) (f ((extChartAt I c).symm z))) = g | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
fa : HolomorphicAt I I f c
df : mfderiv I I f c = 0
⊢ ∃ g, HolomorphicAt I I g c ∧ g c = c ∧ ∀ᶠ (z : S) in 𝓝[≠] c, g z... | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
fa : HolomorphicAt I I f c
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartAt I c... | Please generate a tactic in lean4 to solve the state.
STATE:
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
fa : HolomorphicAt I I f c
df : mfderiv I I f c = 0
⊢ ∃ g,... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | not_local_inj_of_mfderiv_zero | [172, 1] | [225, 63] | have dg : mfderiv I I g (extChartAt I c c) = 0 := by
have fd : MDifferentiableAt I I f ((extChartAt I c).symm (extChartAt I c c)) := by
rw [PartialEquiv.left_inv]; exact fa.mdifferentiableAt; apply mem_extChartAt_source
rw [← hg, ←Function.comp_def, mfderiv_comp _ (HolomorphicAt.extChartAt _).mdifferentiableAt ... | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
fa : HolomorphicAt I I f c
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartAt I c... | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
fa : HolomorphicAt I I f c
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartAt I c... | Please generate a tactic in lean4 to solve the state.
STATE:
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
fa : HolomorphicAt I I f c
df : mfderiv I I f c = 0
g : ℂ ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | not_local_inj_of_mfderiv_zero | [172, 1] | [225, 63] | simp only [holomorphicAt_iff, Function.comp, hg] at fa | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
fa : HolomorphicAt I I f c
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartAt I c... | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartAt I c).symm z))) = g
dg : mfderi... | Please generate a tactic in lean4 to solve the state.
STATE:
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
fa : HolomorphicAt I I f c
df : mfderiv I I f c = 0
g : ℂ ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | not_local_inj_of_mfderiv_zero | [172, 1] | [225, 63] | have dg' := fa.2.differentiableAt.mdifferentiableAt.hasMFDerivAt | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartAt I c).symm z))) = g
dg : mfderi... | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartAt I c).symm z))) = g
dg : mfderi... | Please generate a tactic in lean4 to solve the state.
STATE:
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extCha... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | not_local_inj_of_mfderiv_zero | [172, 1] | [225, 63] | rw [dg, hasMFDerivAt_iff_hasFDerivAt] at dg' | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartAt I c).symm z))) = g
dg : mfderi... | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartAt I c).symm z))) = g
dg : mfderi... | Please generate a tactic in lean4 to solve the state.
STATE:
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extCha... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | not_local_inj_of_mfderiv_zero | [172, 1] | [225, 63] | replace dg := dg'.hasDerivAt | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartAt I c).symm z))) = g
dg : mfderi... | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartAt I c).symm z))) = g
fa : Contin... | Please generate a tactic in lean4 to solve the state.
STATE:
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extCha... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | not_local_inj_of_mfderiv_zero | [172, 1] | [225, 63] | clear dg' | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartAt I c).symm z))) = g
fa : Contin... | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartAt I c).symm z))) = g
fa : Contin... | Please generate a tactic in lean4 to solve the state.
STATE:
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extCha... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | not_local_inj_of_mfderiv_zero | [172, 1] | [225, 63] | rcases not_local_inj_of_deriv_zero fa.2 dg with ⟨h, ha, h0, e⟩ | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartAt I c).symm z))) = g
fa : Contin... | case intro.intro.intro
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartAt I c).sy... | Please generate a tactic in lean4 to solve the state.
STATE:
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extCha... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | not_local_inj_of_mfderiv_zero | [172, 1] | [225, 63] | refine ⟨fun z ↦ (extChartAt I c).symm (h (extChartAt I c z)), ?_, ?_, ?_⟩ | case intro.intro.intro
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartAt I c).sy... | case intro.intro.intro.refine_1
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartA... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | not_local_inj_of_mfderiv_zero | [172, 1] | [225, 63] | have fd : MDifferentiableAt I I f ((extChartAt I c).symm (extChartAt I c c)) := by
rw [PartialEquiv.left_inv]; exact fa.mdifferentiableAt; apply mem_extChartAt_source | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
fa : HolomorphicAt I I f c
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartAt I c... | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
fa : HolomorphicAt I I f c
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartAt I c... | Please generate a tactic in lean4 to solve the state.
STATE:
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
fa : HolomorphicAt I I f c
df : mfderiv I I f c = 0
g : ℂ ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | not_local_inj_of_mfderiv_zero | [172, 1] | [225, 63] | rw [← hg, ←Function.comp_def, mfderiv_comp _ (HolomorphicAt.extChartAt _).mdifferentiableAt _,
←Function.comp_def, mfderiv_comp _ fd (HolomorphicAt.extChartAt_symm _).mdifferentiableAt,
PartialEquiv.left_inv, df, ContinuousLinearMap.zero_comp, ContinuousLinearMap.comp_zero] | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
fa : HolomorphicAt I I f c
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartAt I c... | case h
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
fa : HolomorphicAt I I f c
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChar... | Please generate a tactic in lean4 to solve the state.
STATE:
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
fa : HolomorphicAt I I f c
df : mfderiv I I f c = 0
g : ℂ ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | not_local_inj_of_mfderiv_zero | [172, 1] | [225, 63] | apply mem_extChartAt_source | case h
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
fa : HolomorphicAt I I f c
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChar... | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
fa : HolomorphicAt I I f c
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartAt I c... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
fa : HolomorphicAt I I f c
df : mfderiv I I f c = 0... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | not_local_inj_of_mfderiv_zero | [172, 1] | [225, 63] | apply mem_extChartAt_target | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
fa : HolomorphicAt I I f c
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartAt I c... | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
fa : HolomorphicAt I I f c
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartAt I c... | Please generate a tactic in lean4 to solve the state.
STATE:
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
fa : HolomorphicAt I I f c
df : mfderiv I I f c = 0
g : ℂ ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | not_local_inj_of_mfderiv_zero | [172, 1] | [225, 63] | rw [PartialEquiv.left_inv] | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
fa : HolomorphicAt I I f c
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartAt I c... | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
fa : HolomorphicAt I I f c
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartAt I c... | Please generate a tactic in lean4 to solve the state.
STATE:
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
fa : HolomorphicAt I I f c
df : mfderiv I I f c = 0
g : ℂ ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | not_local_inj_of_mfderiv_zero | [172, 1] | [225, 63] | apply mem_extChartAt_source | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
fa : HolomorphicAt I I f c
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartAt I c... | case h
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
fa : HolomorphicAt I I f c
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChar... | Please generate a tactic in lean4 to solve the state.
STATE:
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
fa : HolomorphicAt I I f c
df : mfderiv I I f c = 0
g : ℂ ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | not_local_inj_of_mfderiv_zero | [172, 1] | [225, 63] | apply mem_extChartAt_source | case h
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
fa : HolomorphicAt I I f c
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChar... | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
fa : HolomorphicAt I I f c
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartAt I c... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
fa : HolomorphicAt I I f c
df : mfderiv I I f c = 0... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | not_local_inj_of_mfderiv_zero | [172, 1] | [225, 63] | exact MDifferentiableAt.comp _ fd
(HolomorphicAt.extChartAt_symm (mem_extChartAt_target _ _)).mdifferentiableAt | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
fa : HolomorphicAt I I f c
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartAt I c... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
fa : HolomorphicAt I I f c
df : mfderiv I I f c = 0
g : ℂ ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | not_local_inj_of_mfderiv_zero | [172, 1] | [225, 63] | rw [PartialEquiv.left_inv] | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
fa : HolomorphicAt I I f c
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartAt I c... | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
fa : HolomorphicAt I I f c
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartAt I c... | Please generate a tactic in lean4 to solve the state.
STATE:
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
fa : HolomorphicAt I I f c
df : mfderiv I I f c = 0
g : ℂ ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | not_local_inj_of_mfderiv_zero | [172, 1] | [225, 63] | exact fa.mdifferentiableAt | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
fa : HolomorphicAt I I f c
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartAt I c... | case h
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
fa : HolomorphicAt I I f c
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChar... | Please generate a tactic in lean4 to solve the state.
STATE:
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
fa : HolomorphicAt I I f c
df : mfderiv I I f c = 0
g : ℂ ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | not_local_inj_of_mfderiv_zero | [172, 1] | [225, 63] | apply mem_extChartAt_source | case h
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
fa : HolomorphicAt I I f c
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChar... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
fa : HolomorphicAt I I f c
df : mfderiv I I f c = 0... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | not_local_inj_of_mfderiv_zero | [172, 1] | [225, 63] | apply (HolomorphicAt.extChartAt_symm (mem_extChartAt_target I c)).comp_of_eq | case intro.intro.intro.refine_1
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartA... | case intro.intro.intro.refine_1.gh
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extCha... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.refine_1
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | not_local_inj_of_mfderiv_zero | [172, 1] | [225, 63] | apply (ha.holomorphicAt I I).comp_of_eq
(HolomorphicAt.extChartAt (mem_extChartAt_source I c)) rfl | case intro.intro.intro.refine_1.gh
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extCha... | case intro.intro.intro.refine_1.e
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChar... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.refine_1.gh
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | not_local_inj_of_mfderiv_zero | [172, 1] | [225, 63] | exact h0 | case intro.intro.intro.refine_1.e
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChar... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.refine_1.e
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | not_local_inj_of_mfderiv_zero | [172, 1] | [225, 63] | simp only [h0, PartialEquiv.left_inv _ (mem_extChartAt_source I c)] | case intro.intro.intro.refine_2
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartA... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.refine_2
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | not_local_inj_of_mfderiv_zero | [172, 1] | [225, 63] | rw [eventually_nhdsWithin_iff] at e ⊢ | case intro.intro.intro.refine_3
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartA... | case intro.intro.intro.refine_3
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartA... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.refine_3
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | not_local_inj_of_mfderiv_zero | [172, 1] | [225, 63] | apply ((continuousAt_extChartAt I c).eventually e).mp | case intro.intro.intro.refine_3
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartA... | case intro.intro.intro.refine_3
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartA... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.refine_3
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | not_local_inj_of_mfderiv_zero | [172, 1] | [225, 63] | apply ((isOpen_extChartAt_source I c).eventually_mem (mem_extChartAt_source I c)).mp | case intro.intro.intro.refine_3
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartA... | case intro.intro.intro.refine_3
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartA... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.refine_3
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | not_local_inj_of_mfderiv_zero | [172, 1] | [225, 63] | have m2 : ∀ᶠ z in 𝓝 c, f z ∈ (extChartAt I (f c)).source :=
fa.1.eventually_mem (extChartAt_source_mem_nhds I _) | case intro.intro.intro.refine_3
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartA... | case intro.intro.intro.refine_3
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartA... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.refine_3
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | not_local_inj_of_mfderiv_zero | [172, 1] | [225, 63] | refine m1.mp (m2.mp (m3.mp (eventually_of_forall ?_))) | case intro.intro.intro.refine_3
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartA... | case intro.intro.intro.refine_3
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartA... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.refine_3
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | not_local_inj_of_mfderiv_zero | [172, 1] | [225, 63] | simp only [mem_compl_singleton_iff] | case intro.intro.intro.refine_3
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartA... | case intro.intro.intro.refine_3
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartA... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.refine_3
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | not_local_inj_of_mfderiv_zero | [172, 1] | [225, 63] | intro z m3 m2 m1 m0 even zc | case intro.intro.intro.refine_3
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartA... | case intro.intro.intro.refine_3
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartA... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.refine_3
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | not_local_inj_of_mfderiv_zero | [172, 1] | [225, 63] | rcases even ((PartialEquiv.injOn _).ne m0 (mem_extChartAt_source I c) zc) with ⟨hz, gh⟩ | case intro.intro.intro.refine_3
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartA... | case intro.intro.intro.refine_3.intro
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(ext... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.refine_3
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | not_local_inj_of_mfderiv_zero | [172, 1] | [225, 63] | constructor | case intro.intro.intro.refine_3.intro
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(ext... | case intro.intro.intro.refine_3.intro.left
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.refine_3.intro
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | not_local_inj_of_mfderiv_zero | [172, 1] | [225, 63] | refine ContinuousAt.eventually_mem ?_ (extChartAt_target_mem_nhds' I ?_) | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartAt I c).symm z))) = g
fa : Contin... | case refine_1
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartAt I c).symm z))) =... | Please generate a tactic in lean4 to solve the state.
STATE:
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extCha... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | not_local_inj_of_mfderiv_zero | [172, 1] | [225, 63] | exact ha.continuousAt.comp_of_eq (continuousAt_extChartAt I c) rfl | case refine_1
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartAt I c).symm z))) =... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_1
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | not_local_inj_of_mfderiv_zero | [172, 1] | [225, 63] | rw [h0] | case refine_2
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartAt I c).symm z))) =... | case refine_2
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartAt I c).symm z))) =... | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_2
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | not_local_inj_of_mfderiv_zero | [172, 1] | [225, 63] | exact mem_extChartAt_target I c | case refine_2
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartAt I c).symm z))) =... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_2
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | not_local_inj_of_mfderiv_zero | [172, 1] | [225, 63] | refine ContinuousAt.eventually_mem ?_ (extChartAt_source_mem_nhds' I ?_) | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartAt I c).symm z))) = g
fa : Contin... | case refine_1
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartAt I c).symm z))) =... | Please generate a tactic in lean4 to solve the state.
STATE:
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extCha... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | not_local_inj_of_mfderiv_zero | [172, 1] | [225, 63] | apply fa.1.comp_of_eq | case refine_1
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartAt I c).symm z))) =... | case refine_1.hf
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartAt I c).symm z))... | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_1
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | not_local_inj_of_mfderiv_zero | [172, 1] | [225, 63] | apply (continuousAt_extChartAt_symm I _).comp_of_eq | case refine_1.hf
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartAt I c).symm z))... | case refine_1.hf.hf
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartAt I c).symm ... | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_1.hf
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | not_local_inj_of_mfderiv_zero | [172, 1] | [225, 63] | apply ha.continuousAt.comp_of_eq | case refine_1.hf.hf
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartAt I c).symm ... | case refine_1.hf.hf.hf
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartAt I c).sy... | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_1.hf.hf
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | not_local_inj_of_mfderiv_zero | [172, 1] | [225, 63] | exact continuousAt_extChartAt I _ | case refine_1.hf.hf.hf
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartAt I c).sy... | case refine_1.hf.hf.hy
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartAt I c).sy... | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_1.hf.hf.hf
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | not_local_inj_of_mfderiv_zero | [172, 1] | [225, 63] | rfl | case refine_1.hf.hf.hy
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartAt I c).sy... | case refine_1.hf.hy
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartAt I c).symm ... | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_1.hf.hf.hy
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | not_local_inj_of_mfderiv_zero | [172, 1] | [225, 63] | exact h0 | case refine_1.hf.hy
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartAt I c).symm ... | case refine_1.hy
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartAt I c).symm z))... | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_1.hf.hy
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | not_local_inj_of_mfderiv_zero | [172, 1] | [225, 63] | rw [h0, PartialEquiv.left_inv _ (mem_extChartAt_source I _)] | case refine_1.hy
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartAt I c).symm z))... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_1.hy
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | not_local_inj_of_mfderiv_zero | [172, 1] | [225, 63] | rw [h0, PartialEquiv.left_inv _ (mem_extChartAt_source I _)] | case refine_2
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartAt I c).symm z))) =... | case refine_2
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartAt I c).symm z))) =... | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_2
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | not_local_inj_of_mfderiv_zero | [172, 1] | [225, 63] | apply mem_extChartAt_source | case refine_2
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (↑(extChartAt I c).symm z))) =... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_2
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | not_local_inj_of_mfderiv_zero | [172, 1] | [225, 63] | nth_rw 2 [← PartialEquiv.left_inv _ m0] | case intro.intro.intro.refine_3.intro.left
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (... | case intro.intro.intro.refine_3.intro.left
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.refine_3.intro.left
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | not_local_inj_of_mfderiv_zero | [172, 1] | [225, 63] | rw [(PartialEquiv.injOn _).ne_iff] | case intro.intro.intro.refine_3.intro.left
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (... | case intro.intro.intro.refine_3.intro.left
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.refine_3.intro.left
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | not_local_inj_of_mfderiv_zero | [172, 1] | [225, 63] | exact hz | case intro.intro.intro.refine_3.intro.left
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f (... | case intro.intro.intro.refine_3.intro.left.hx
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.refine_3.intro.left
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | not_local_inj_of_mfderiv_zero | [172, 1] | [225, 63] | rw [PartialEquiv.symm_source] | case intro.intro.intro.refine_3.intro.left.hx
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (... | case intro.intro.intro.refine_3.intro.left.hx
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.refine_3.intro.left.hx
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | not_local_inj_of_mfderiv_zero | [172, 1] | [225, 63] | exact m1 | case intro.intro.intro.refine_3.intro.left.hx
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (... | case intro.intro.intro.refine_3.intro.left.hy
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.refine_3.intro.left.hx
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | not_local_inj_of_mfderiv_zero | [172, 1] | [225, 63] | rw [PartialEquiv.symm_source] | case intro.intro.intro.refine_3.intro.left.hy
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (... | case intro.intro.intro.refine_3.intro.left.hy
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.refine_3.intro.left.hy
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | not_local_inj_of_mfderiv_zero | [172, 1] | [225, 63] | exact PartialEquiv.map_source _ m0 | case intro.intro.intro.refine_3.intro.left.hy
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.refine_3.intro.left.hy
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | not_local_inj_of_mfderiv_zero | [172, 1] | [225, 63] | simp only [← hg] at gh | case intro.intro.intro.refine_3.intro.right
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f ... | case intro.intro.intro.refine_3.intro.right
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f ... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.refine_3.intro.right
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | not_local_inj_of_mfderiv_zero | [172, 1] | [225, 63] | rw [PartialEquiv.left_inv _ m0] at gh | case intro.intro.intro.refine_3.intro.right
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f ... | case intro.intro.intro.refine_3.intro.right
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f ... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.refine_3.intro.right
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | not_local_inj_of_mfderiv_zero | [172, 1] | [225, 63] | rw [(PartialEquiv.injOn _).eq_iff m3 m2] at gh | case intro.intro.intro.refine_3.intro.right
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f ... | case intro.intro.intro.refine_3.intro.right
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f ... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.refine_3.intro.right
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | not_local_inj_of_mfderiv_zero | [172, 1] | [225, 63] | exact gh | case intro.intro.intro.refine_3.intro.right
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I I f c = 0
g : ℂ → ℂ
hg : (fun z => ↑(extChartAt I (f c)) (f ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.refine_3.intro.right
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
c : S
df : mfderiv I... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | Set.InjOn.mfderiv_ne_zero | [228, 1] | [237, 29] | contrapose inj | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
s : Set S
inj : InjOn f s
so : IsOpen s
c : S
m : c ∈ s
fa : HolomorphicAt I I f c
⊢ mfderiv I I f c ≠ 0 | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
s : Set S
so : IsOpen s
c : S
m : c ∈ s
fa : HolomorphicAt I I f c
inj : ¬mfderiv I I f c ≠ 0
⊢ ¬InjOn f s | Please generate a tactic in lean4 to solve the state.
STATE:
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
s : Set S
inj : InjOn f s
so : IsOpen s
c : S
m : c ∈ s
fa : Hol... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | Set.InjOn.mfderiv_ne_zero | [228, 1] | [237, 29] | simp only [not_not, InjOn, not_forall] at inj ⊢ | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
s : Set S
so : IsOpen s
c : S
m : c ∈ s
fa : HolomorphicAt I I f c
inj : ¬mfderiv I I f c ≠ 0
⊢ ¬InjOn f s | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
s : Set S
so : IsOpen s
c : S
m : c ∈ s
fa : HolomorphicAt I I f c
inj : mfderiv I I f c = 0
⊢ ∃ x, ∃ (_ : x ∈ s), ∃ x_1, ∃ (... | Please generate a tactic in lean4 to solve the state.
STATE:
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
s : Set S
so : IsOpen s
c : S
m : c ∈ s
fa : HolomorphicAt I I f... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | Set.InjOn.mfderiv_ne_zero | [228, 1] | [237, 29] | rcases not_local_inj_of_mfderiv_zero fa inj with ⟨g, ga, gc, fg⟩ | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
s : Set S
so : IsOpen s
c : S
m : c ∈ s
fa : HolomorphicAt I I f c
inj : mfderiv I I f c = 0
⊢ ∃ x, ∃ (_ : x ∈ s), ∃ x_1, ∃ (... | case intro.intro.intro
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
s : Set S
so : IsOpen s
c : S
m : c ∈ s
fa : HolomorphicAt I I f c
inj : mfderiv I I f c = 0
g : S → S... | Please generate a tactic in lean4 to solve the state.
STATE:
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
s : Set S
so : IsOpen s
c : S
m : c ∈ s
fa : HolomorphicAt I I f... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | Set.InjOn.mfderiv_ne_zero | [228, 1] | [237, 29] | have gm : ∀ᶠ z in 𝓝 c, g z ∈ s :=
ga.continuousAt.eventually_mem (so.mem_nhds (by simp only [gc, m])) | case intro.intro.intro
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
s : Set S
so : IsOpen s
c : S
m : c ∈ s
fa : HolomorphicAt I I f c
inj : mfderiv I I f c = 0
g : S → S... | case intro.intro.intro
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
s : Set S
so : IsOpen s
c : S
m : c ∈ s
fa : HolomorphicAt I I f c
inj : mfderiv I I f c = 0
g : S → S... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
s : Set S
so : IsOpen s
c : S
m : c ∈ s
f... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | Set.InjOn.mfderiv_ne_zero | [228, 1] | [237, 29] | replace fg := fg.and (((so.eventually_mem m).and gm).filter_mono nhdsWithin_le_nhds) | case intro.intro.intro
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
s : Set S
so : IsOpen s
c : S
m : c ∈ s
fa : HolomorphicAt I I f c
inj : mfderiv I I f c = 0
g : S → S... | case intro.intro.intro
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
s : Set S
so : IsOpen s
c : S
m : c ∈ s
fa : HolomorphicAt I I f c
inj : mfderiv I I f c = 0
g : S → S... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
s : Set S
so : IsOpen s
c : S
m : c ∈ s
f... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | Set.InjOn.mfderiv_ne_zero | [228, 1] | [237, 29] | rcases @Filter.Eventually.exists _ _ _ (AnalyticManifold.punctured_nhds_neBot I c) fg
with ⟨z, ⟨gz, fg⟩, zs, gs⟩ | case intro.intro.intro
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
s : Set S
so : IsOpen s
c : S
m : c ∈ s
fa : HolomorphicAt I I f c
inj : mfderiv I I f c = 0
g : S → S... | case intro.intro.intro.intro.intro.intro.intro
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
s : Set S
so : IsOpen s
c : S
m : c ∈ s
fa : HolomorphicAt I I f c
inj : mfder... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
s : Set S
so : IsOpen s
c : S
m : c ∈ s
f... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | Set.InjOn.mfderiv_ne_zero | [228, 1] | [237, 29] | use g z, gs, z, zs, fg, gz | case intro.intro.intro.intro.intro.intro.intro
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
s : Set S
so : IsOpen s
c : S
m : c ∈ s
fa : HolomorphicAt I I f c
inj : mfder... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.intro.intro.intro.intro
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
s : Set S
so : Is... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/Multiple.lean | Set.InjOn.mfderiv_ne_zero | [228, 1] | [237, 29] | simp only [gc, m] | S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
s : Set S
so : IsOpen s
c : S
m : c ∈ s
fa : HolomorphicAt I I f c
inj : mfderiv I I f c = 0
g : S → S
ga : HolomorphicAt I I... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
inst✝³ : AnalyticManifold I S
T : Type
inst✝² : TopologicalSpace T
inst✝¹ : ChartedSpace ℂ T
inst✝ : AnalyticManifold I T
f : S → T
s : Set S
so : IsOpen s
c : S
m : c ∈ s
fa : HolomorphicAt I I f... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Holomorphic.lean | differentiable_iff_analytic2 | [36, 1] | [55, 37] | constructor | E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℂ E
inst✝ : CompleteSpace E
o : IsOpen s
⊢ Diffe... | case mp
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℂ E
inst✝ : CompleteSpace E
o : IsOpen s... | Please generate a tactic in lean4 to solve the state.
STATE:
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : NormedAddCommGroup E
inst✝¹ :... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Holomorphic.lean | differentiable_iff_analytic2 | [36, 1] | [55, 37] | intro d | case mp
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℂ E
inst✝ : CompleteSpace E
o : IsOpen s... | case mp
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℂ E
inst✝ : CompleteSpace E
o : IsOpen s... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : NormedAddCommGroup E
... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Holomorphic.lean | differentiable_iff_analytic2 | [36, 1] | [55, 37] | apply osgood o d.continuousOn | case mp
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℂ E
inst✝ : CompleteSpace E
o : IsOpen s... | case mp.fa0
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℂ E
inst✝ : CompleteSpace E
o : IsOp... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : NormedAddCommGroup E
... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Holomorphic.lean | differentiable_iff_analytic2 | [36, 1] | [55, 37] | intro z0 z1 zs | case mp.fa0
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℂ E
inst✝ : CompleteSpace E
o : IsOp... | case mp.fa0
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℂ E
inst✝ : CompleteSpace E
o : IsOp... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp.fa0
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : NormedAddCommGrou... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Holomorphic.lean | differentiable_iff_analytic2 | [36, 1] | [55, 37] | rcases Metric.isOpen_iff.mp o (z0, z1) zs with ⟨r, rp, rs⟩ | case mp.fa0
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℂ E
inst✝ : CompleteSpace E
o : IsOp... | case mp.fa0.intro.intro
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℂ E
inst✝ : CompleteSpac... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp.fa0
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : NormedAddCommGrou... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Holomorphic.lean | differentiable_iff_analytic2 | [36, 1] | [55, 37] | have d0 : DifferentiableOn ℂ (fun z0 ↦ f (z0, z1)) (ball z0 r) := by
apply DifferentiableOn.comp d
exact DifferentiableOn.prod differentiableOn_id (differentiableOn_const _)
intro z0 z0s; apply rs; simp at z0s ⊢; assumption | case mp.fa0.intro.intro
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℂ E
inst✝ : CompleteSpac... | case mp.fa0.intro.intro
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℂ E
inst✝ : CompleteSpac... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp.fa0.intro.intro
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : Norme... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Holomorphic.lean | differentiable_iff_analytic2 | [36, 1] | [55, 37] | exact (analyticOn_iff_differentiableOn isOpen_ball).mpr d0 z0 (Metric.mem_ball_self rp) | case mp.fa0.intro.intro
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℂ E
inst✝ : CompleteSpac... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mp.fa0.intro.intro
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : Norme... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Holomorphic.lean | differentiable_iff_analytic2 | [36, 1] | [55, 37] | apply DifferentiableOn.comp d | E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℂ E
inst✝ : CompleteSpace E
o : IsOpen s
d : Dif... | case hf
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℂ E
inst✝ : CompleteSpace E
o : IsOpen s... | Please generate a tactic in lean4 to solve the state.
STATE:
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : NormedAddCommGroup E
inst✝¹ :... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Holomorphic.lean | differentiable_iff_analytic2 | [36, 1] | [55, 37] | exact DifferentiableOn.prod differentiableOn_id (differentiableOn_const _) | case hf
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℂ E
inst✝ : CompleteSpace E
o : IsOpen s... | case st
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℂ E
inst✝ : CompleteSpace E
o : IsOpen s... | Please generate a tactic in lean4 to solve the state.
STATE:
case hf
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : NormedAddCommGroup E
... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Holomorphic.lean | differentiable_iff_analytic2 | [36, 1] | [55, 37] | intro z0 z0s | case st
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℂ E
inst✝ : CompleteSpace E
o : IsOpen s... | case st
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℂ E
inst✝ : CompleteSpace E
o : IsOpen s... | Please generate a tactic in lean4 to solve the state.
STATE:
case st
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : NormedAddCommGroup E
... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Holomorphic.lean | differentiable_iff_analytic2 | [36, 1] | [55, 37] | apply rs | case st
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℂ E
inst✝ : CompleteSpace E
o : IsOpen s... | case st.a
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℂ E
inst✝ : CompleteSpace E
o : IsOpen... | Please generate a tactic in lean4 to solve the state.
STATE:
case st
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : NormedAddCommGroup E
... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Holomorphic.lean | differentiable_iff_analytic2 | [36, 1] | [55, 37] | simp at z0s ⊢ | case st.a
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℂ E
inst✝ : CompleteSpace E
o : IsOpen... | case st.a
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℂ E
inst✝ : CompleteSpace E
o : IsOpen... | Please generate a tactic in lean4 to solve the state.
STATE:
case st.a
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : NormedAddCommGroup ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Holomorphic.lean | differentiable_iff_analytic2 | [36, 1] | [55, 37] | assumption | case st.a
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℂ E
inst✝ : CompleteSpace E
o : IsOpen... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case st.a
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : NormedAddCommGroup ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Holomorphic.lean | differentiable_iff_analytic2 | [36, 1] | [55, 37] | intro z0 z1 zs | case mp.fa1
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℂ E
inst✝ : CompleteSpace E
o : IsOp... | case mp.fa1
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℂ E
inst✝ : CompleteSpace E
o : IsOp... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp.fa1
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : NormedAddCommGrou... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Holomorphic.lean | differentiable_iff_analytic2 | [36, 1] | [55, 37] | rcases Metric.isOpen_iff.mp o (z0, z1) zs with ⟨r, rp, rs⟩ | case mp.fa1
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℂ E
inst✝ : CompleteSpace E
o : IsOp... | case mp.fa1.intro.intro
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℂ E
inst✝ : CompleteSpac... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp.fa1
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : NormedAddCommGrou... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Holomorphic.lean | differentiable_iff_analytic2 | [36, 1] | [55, 37] | have d1 : DifferentiableOn ℂ (fun z1 ↦ f (z0, z1)) (ball z1 r) := by
apply DifferentiableOn.comp d
exact DifferentiableOn.prod (differentiableOn_const _) differentiableOn_id
intro z1 z1s; apply rs; simp at z1s ⊢; assumption | case mp.fa1.intro.intro
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℂ E
inst✝ : CompleteSpac... | case mp.fa1.intro.intro
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℂ E
inst✝ : CompleteSpac... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp.fa1.intro.intro
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : Norme... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Holomorphic.lean | differentiable_iff_analytic2 | [36, 1] | [55, 37] | exact (analyticOn_iff_differentiableOn isOpen_ball).mpr d1 z1 (Metric.mem_ball_self rp) | case mp.fa1.intro.intro
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℂ E
inst✝ : CompleteSpac... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mp.fa1.intro.intro
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : Norme... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Holomorphic.lean | differentiable_iff_analytic2 | [36, 1] | [55, 37] | apply DifferentiableOn.comp d | E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℂ E
inst✝ : CompleteSpace E
o : IsOpen s
d : Dif... | case hf
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℂ E
inst✝ : CompleteSpace E
o : IsOpen s... | Please generate a tactic in lean4 to solve the state.
STATE:
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : NormedAddCommGroup E
inst✝¹ :... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Holomorphic.lean | differentiable_iff_analytic2 | [36, 1] | [55, 37] | exact DifferentiableOn.prod (differentiableOn_const _) differentiableOn_id | case hf
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℂ E
inst✝ : CompleteSpace E
o : IsOpen s... | case st
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℂ E
inst✝ : CompleteSpace E
o : IsOpen s... | Please generate a tactic in lean4 to solve the state.
STATE:
case hf
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : NormedAddCommGroup E
... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Holomorphic.lean | differentiable_iff_analytic2 | [36, 1] | [55, 37] | intro z1 z1s | case st
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℂ E
inst✝ : CompleteSpace E
o : IsOpen s... | case st
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℂ E
inst✝ : CompleteSpace E
o : IsOpen s... | Please generate a tactic in lean4 to solve the state.
STATE:
case st
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : NormedAddCommGroup E
... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Holomorphic.lean | differentiable_iff_analytic2 | [36, 1] | [55, 37] | apply rs | case st
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℂ E
inst✝ : CompleteSpace E
o : IsOpen s... | case st.a
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℂ E
inst✝ : CompleteSpace E
o : IsOpen... | Please generate a tactic in lean4 to solve the state.
STATE:
case st
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : NormedAddCommGroup E
... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Holomorphic.lean | differentiable_iff_analytic2 | [36, 1] | [55, 37] | simp at z1s ⊢ | case st.a
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℂ E
inst✝ : CompleteSpace E
o : IsOpen... | case st.a
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℂ E
inst✝ : CompleteSpace E
o : IsOpen... | Please generate a tactic in lean4 to solve the state.
STATE:
case st.a
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : NormedAddCommGroup ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Holomorphic.lean | differentiable_iff_analytic2 | [36, 1] | [55, 37] | assumption | case st.a
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℂ E
inst✝ : CompleteSpace E
o : IsOpen... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case st.a
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : NormedAddCommGroup ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Holomorphic.lean | differentiable_iff_analytic2 | [36, 1] | [55, 37] | exact fun a ↦ a.differentiableOn | case mpr
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℂ E
inst✝ : CompleteSpace E
o : IsOpen ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
s : Set (ℂ × ℂ)
inst✝² : NormedAddCommGroup E... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Holomorphic.lean | contDiffAt_iff_analytic_at2 | [58, 1] | [66, 45] | constructor | E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
x : ℂ × ℂ
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℂ E
inst✝ : CompleteSpace E
n : ℕ∞
n1 : 1 ≤ n
⊢ ContDi... | case mp
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
x : ℂ × ℂ
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℂ E
inst✝ : CompleteSpace E
n : ℕ∞
n1 : 1 ≤ n
... | Please generate a tactic in lean4 to solve the state.
STATE:
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
x : ℂ × ℂ
inst✝² : NormedAddCommGroup E
inst✝¹ : Norme... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Holomorphic.lean | contDiffAt_iff_analytic_at2 | [58, 1] | [66, 45] | intro d | case mp
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
x : ℂ × ℂ
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℂ E
inst✝ : CompleteSpace E
n : ℕ∞
n1 : 1 ≤ n
... | case mp
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
x : ℂ × ℂ
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℂ E
inst✝ : CompleteSpace E
n : ℕ∞
n1 : 1 ≤ n
... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
x : ℂ × ℂ
inst✝² : NormedAddCommGroup E
inst✝¹... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Holomorphic.lean | contDiffAt_iff_analytic_at2 | [58, 1] | [66, 45] | rcases d.contDiffOn n1 with ⟨u, un, d⟩ | case mp
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
x : ℂ × ℂ
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℂ E
inst✝ : CompleteSpace E
n : ℕ∞
n1 : 1 ≤ n
... | case mp.intro.intro
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
x : ℂ × ℂ
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℂ E
inst✝ : CompleteSpace E
n : ℕ∞... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
x : ℂ × ℂ
inst✝² : NormedAddCommGroup E
inst✝¹... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Holomorphic.lean | contDiffAt_iff_analytic_at2 | [58, 1] | [66, 45] | rcases mem_nhds_iff.mp un with ⟨v, uv, vo, vx⟩ | case mp.intro.intro
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
x : ℂ × ℂ
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℂ E
inst✝ : CompleteSpace E
n : ℕ∞... | case mp.intro.intro.intro.intro.intro
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
x : ℂ × ℂ
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℂ E
inst✝ : Comp... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp.intro.intro
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
x : ℂ × ℂ
inst✝² : NormedAddCommGr... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Holomorphic.lean | contDiffAt_iff_analytic_at2 | [58, 1] | [66, 45] | refine (differentiable_iff_analytic2 vo).mp ?_ _ vx | case mp.intro.intro.intro.intro.intro
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
x : ℂ × ℂ
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℂ E
inst✝ : Comp... | case mp.intro.intro.intro.intro.intro
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
x : ℂ × ℂ
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℂ E
inst✝ : Comp... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp.intro.intro.intro.intro.intro
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
x : ℂ × ℂ
inst✝²... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Holomorphic.lean | contDiffAt_iff_analytic_at2 | [58, 1] | [66, 45] | exact (d.mono uv).differentiableOn (by norm_num) | case mp.intro.intro.intro.intro.intro
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
x : ℂ × ℂ
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℂ E
inst✝ : Comp... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mp.intro.intro.intro.intro.intro
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
x : ℂ × ℂ
inst✝²... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Holomorphic.lean | contDiffAt_iff_analytic_at2 | [58, 1] | [66, 45] | norm_num | E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
x : ℂ × ℂ
inst✝² : NormedAddCommGroup E
inst✝¹ : NormedSpace ℂ E
inst✝ : CompleteSpace E
n : ℕ∞
n1 : 1 ≤ n
d✝ : Con... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E✝ : Type
inst✝⁸ : NormedAddCommGroup E✝
inst✝⁷ : NormedSpace ℂ E✝
inst✝⁶ : CompleteSpace E✝
F : Type
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace ℂ F
inst✝³ : CompleteSpace F
E : Type
f : ℂ × ℂ → E
x : ℂ × ℂ
inst✝² : NormedAddCommGroup E
inst✝¹ : Norme... |
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