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/Analytic/Uniform.lean | uniform_analytic_lim | [189, 1] | [270, 21] | generalize hMp : M.sum (fun k : β β¦ p k fun _ β¦ y) = Mp | case intro.intro.intro.intro.intro
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), C... | case intro.intro.intro.intro.intro
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), C... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.intro.intro
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Uniform.lean | uniform_analytic_lim | [189, 1] | [270, 21] | rw [hMp] at dppr | case intro.intro.intro.intro.intro
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), C... | case intro.intro.intro.intro.intro
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), C... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.intro.intro
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Uniform.lean | uniform_analytic_lim | [189, 1] | [270, 21] | generalize hMpr : M.sum (fun k β¦ pr n k fun _ β¦ y) = Mpr | case intro.intro.intro.intro.intro
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), C... | case intro.intro.intro.intro.intro
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), C... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.intro.intro
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Uniform.lean | uniform_analytic_lim | [189, 1] | [270, 21] | rw [hMpr] at dpf dppr | case intro.intro.intro.intro.intro
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), C... | case intro.intro.intro.intro.intro
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), C... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.intro.intro
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Uniform.lean | uniform_analytic_lim | [189, 1] | [270, 21] | calc dist Mp (g (c + y))
_ β€ dist Mp (f n (c + y)) + dist (f n (c + y)) (g (c + y)) := dist_triangle _ _ _
_ β€ dist Mp Mpr + dist Mpr (f n (c + y)) + d := by bound
_ β€ e / 4 + d + d := by bound
_ = e / 4 + 2 * (1 - a) * (e / 4) := by rw [β d4]; ring
_ β€ e / 4 + 2 * (1 - 0) * (e / 4) := by bound
_ = 3 / 4 * ... | case intro.intro.intro.intro.intro
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), C... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.intro.intro
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Uniform.lean | uniform_analytic_lim | [189, 1] | [270, 21] | intro n | I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
o : IsOpen s
h : β (n : I), AnalyticOn β (f n) s
u : TendstoUniformlyOn f g atTop s
c : β
hc : c β s
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
hb : β (n : I), AnalyticOn β (f n) (closedBall c βr)
pr : I β FormalMultilinearSeries β β β :=... | I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
o : IsOpen s
h : β (n : I), AnalyticOn β (f n) s
u : TendstoUniformlyOn f g atTop s
c : β
hc : c β s
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
hb : β (n : I), AnalyticOn β (f n) (closedBall c βr)
pr : I β FormalMultilinearSeries β β β :=... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
o : IsOpen s
h : β (n : I), AnalyticOn β (f n) s
u : TendstoUniformlyOn f g atTop s
c : β
hc : c β s
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
hb : β (n : I), AnalyticOn β (f n... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Uniform.lean | uniform_analytic_lim | [189, 1] | [270, 21] | have cs := cauchy_on_cball_radius rp (hb n) | I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
o : IsOpen s
h : β (n : I), AnalyticOn β (f n) s
u : TendstoUniformlyOn f g atTop s
c : β
hc : c β s
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
hb : β (n : I), AnalyticOn β (f n) (closedBall c βr)
pr : I β FormalMultilinearSeries β β β :=... | I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
o : IsOpen s
h : β (n : I), AnalyticOn β (f n) s
u : TendstoUniformlyOn f g atTop s
c : β
hc : c β s
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
hb : β (n : I), AnalyticOn β (f n) (closedBall c βr)
pr : I β FormalMultilinearSeries β β β :=... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
o : IsOpen s
h : β (n : I), AnalyticOn β (f n) s
u : TendstoUniformlyOn f g atTop s
c : β
hc : c β s
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
hb : β (n : I), AnalyticOn β (f n... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Uniform.lean | uniform_analytic_lim | [189, 1] | [270, 21] | have pn : pr n = cauchyPowerSeries (f n) c r := rfl | I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
o : IsOpen s
h : β (n : I), AnalyticOn β (f n) s
u : TendstoUniformlyOn f g atTop s
c : β
hc : c β s
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
hb : β (n : I), AnalyticOn β (f n) (closedBall c βr)
pr : I β FormalMultilinearSeries β β β :=... | I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
o : IsOpen s
h : β (n : I), AnalyticOn β (f n) s
u : TendstoUniformlyOn f g atTop s
c : β
hc : c β s
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
hb : β (n : I), AnalyticOn β (f n) (closedBall c βr)
pr : I β FormalMultilinearSeries β β β :=... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
o : IsOpen s
h : β (n : I), AnalyticOn β (f n) s
u : TendstoUniformlyOn f g atTop s
c : β
hc : c β s
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
hb : β (n : I), AnalyticOn β (f n... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Uniform.lean | uniform_analytic_lim | [189, 1] | [270, 21] | rw [β pn] at cs | I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
o : IsOpen s
h : β (n : I), AnalyticOn β (f n) s
u : TendstoUniformlyOn f g atTop s
c : β
hc : c β s
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
hb : β (n : I), AnalyticOn β (f n) (closedBall c βr)
pr : I β FormalMultilinearSeries β β β :=... | I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
o : IsOpen s
h : β (n : I), AnalyticOn β (f n) s
u : TendstoUniformlyOn f g atTop s
c : β
hc : c β s
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
hb : β (n : I), AnalyticOn β (f n) (closedBall c βr)
pr : I β FormalMultilinearSeries β β β :=... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
o : IsOpen s
h : β (n : I), AnalyticOn β (f n) s
u : TendstoUniformlyOn f g atTop s
c : β
hc : c β s
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
hb : β (n : I), AnalyticOn β (f n... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Uniform.lean | uniform_analytic_lim | [189, 1] | [270, 21] | exact cs | I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
o : IsOpen s
h : β (n : I), AnalyticOn β (f n) s
u : TendstoUniformlyOn f g atTop s
c : β
hc : c β s
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
hb : β (n : I), AnalyticOn β (f n) (closedBall c βr)
pr : I β FormalMultilinearSeries β β β :=... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
o : IsOpen s
h : β (n : I), AnalyticOn β (f n) s
u : TendstoUniformlyOn f g atTop s
c : β
hc : c β s
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
hb : β (n : I), AnalyticOn β (f n... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Uniform.lean | uniform_analytic_lim | [189, 1] | [270, 21] | bound | I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
u : TendstoUniformlyOn f g atTop s
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), C... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
u : TendstoUniformlyOn f g atTop s
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Uniform.lean | uniform_analytic_lim | [189, 1] | [270, 21] | bound | I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
u : TendstoUniformlyOn f g atTop s
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), C... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
u : TendstoUniformlyOn f g atTop s
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Uniform.lean | uniform_analytic_lim | [189, 1] | [270, 21] | rw [β d4] | I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
u : TendstoUniformlyOn f g atTop s
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), C... | I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
u : TendstoUniformlyOn f g atTop s
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), C... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
u : TendstoUniformlyOn f g atTop s
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Uniform.lean | uniform_analytic_lim | [189, 1] | [270, 21] | bound | I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
u : TendstoUniformlyOn f g atTop s
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), C... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
u : TendstoUniformlyOn f g atTop s
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Uniform.lean | uniform_analytic_lim | [189, 1] | [270, 21] | apply le_of_lt | I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), ContinuousOn (f n) (closedBall c βr)... | case a
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), ContinuousOn (f n) (closedBal... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Uniform.lean | uniform_analytic_lim | [189, 1] | [270, 21] | rw [dist_comm] | case a
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), ContinuousOn (f n) (closedBal... | case a
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), ContinuousOn (f n) (closedBal... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Uniform.lean | uniform_analytic_lim | [189, 1] | [270, 21] | refine hn (c + y) ?_ | case a
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), ContinuousOn (f n) (closedBal... | case a
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), ContinuousOn (f n) (closedBal... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Uniform.lean | uniform_analytic_lim | [189, 1] | [270, 21] | apply cb | case a
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), ContinuousOn (f n) (closedBal... | case a.a
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), ContinuousOn (f n) (closedB... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Uniform.lean | uniform_analytic_lim | [189, 1] | [270, 21] | simp | case a.a
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), ContinuousOn (f n) (closedB... | case a.a
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), ContinuousOn (f n) (closedB... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.a
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Uniform.lean | uniform_analytic_lim | [189, 1] | [270, 21] | exact yr.le | case a.a
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), ContinuousOn (f n) (closedB... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a.a
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Uniform.lean | uniform_analytic_lim | [189, 1] | [270, 21] | trans M.sum fun k : β β¦ dist (p k fun _ β¦ y) (pr n k fun _ β¦ y) | I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), ContinuousOn (f n) (closedBall c βr)... | I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), ContinuousOn (f n) (closedBall c βr)... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Uniform.lean | uniform_analytic_lim | [189, 1] | [270, 21] | apply dist_sum_sum_le M (fun k : β β¦ p k fun _ β¦ y) fun k : β β¦ pr n k fun _ β¦ y | I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), ContinuousOn (f n) (closedBall c βr)... | I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), ContinuousOn (f n) (closedBall c βr)... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Uniform.lean | uniform_analytic_lim | [189, 1] | [270, 21] | trans M.sum fun k β¦ a ^ k * d | I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), ContinuousOn (f n) (closedBall c βr)... | I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), ContinuousOn (f n) (closedBall c βr)... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Uniform.lean | uniform_analytic_lim | [189, 1] | [270, 21] | apply Finset.sum_le_sum | I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), ContinuousOn (f n) (closedBall c βr)... | case h
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), ContinuousOn (f n) (closedBal... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Uniform.lean | uniform_analytic_lim | [189, 1] | [270, 21] | intro k _ | case h
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), ContinuousOn (f n) (closedBal... | case h
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), ContinuousOn (f n) (closedBal... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Uniform.lean | uniform_analytic_lim | [189, 1] | [270, 21] | have hak : a ^ k = abs y ^ k * rβ»ΒΉ ^ k := by
calc (abs y / r) ^ k
_ = (abs y * rβ»ΒΉ) ^ k := by rw [div_eq_mul_inv, NNReal.coe_inv]
_ = abs y ^ k * rβ»ΒΉ ^ k := mul_pow _ _ _ | case h
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), ContinuousOn (f n) (closedBal... | case h
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), ContinuousOn (f n) (closedBal... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Uniform.lean | uniform_analytic_lim | [189, 1] | [270, 21] | rw [hak] | case h
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), ContinuousOn (f n) (closedBal... | case h
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), ContinuousOn (f n) (closedBal... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Uniform.lean | uniform_analytic_lim | [189, 1] | [270, 21] | generalize hd' : d.toNNReal = d' | case h
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), ContinuousOn (f n) (closedBal... | case h
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), ContinuousOn (f n) (closedBal... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Uniform.lean | uniform_analytic_lim | [189, 1] | [270, 21] | have dd : (d' : β) = d := by rw [β hd']; exact Real.coe_toNNReal d dp.le | case h
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), ContinuousOn (f n) (closedBal... | case h
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), ContinuousOn (f n) (closedBal... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Uniform.lean | uniform_analytic_lim | [189, 1] | [270, 21] | have hcb : β z, z β closedBall c r β abs (g z - f n z) β€ d' := by
intro z zb; exact _root_.trans (hn z (cb zb)).le (le_of_eq dd.symm) | case h
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), ContinuousOn (f n) (closedBal... | case h
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), ContinuousOn (f n) (closedBal... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Uniform.lean | uniform_analytic_lim | [189, 1] | [270, 21] | exact _root_.trans (cauchy_dist k y rp cg (cf n) hcb)
(mul_le_mul_of_nonneg_left (le_of_eq dd) (by bound)) | case h
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), ContinuousOn (f n) (closedBal... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Uniform.lean | uniform_analytic_lim | [189, 1] | [270, 21] | calc (abs y / r) ^ k
_ = (abs y * rβ»ΒΉ) ^ k := by rw [div_eq_mul_inv, NNReal.coe_inv]
_ = abs y ^ k * rβ»ΒΉ ^ k := mul_pow _ _ _ | I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), ContinuousOn (f n) (closedBall c βr)... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Uniform.lean | uniform_analytic_lim | [189, 1] | [270, 21] | rw [div_eq_mul_inv, NNReal.coe_inv] | I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), ContinuousOn (f n) (closedBall c βr)... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Uniform.lean | uniform_analytic_lim | [189, 1] | [270, 21] | rw [β hd'] | I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), ContinuousOn (f n) (closedBall c βr)... | I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), ContinuousOn (f n) (closedBall c βr)... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Uniform.lean | uniform_analytic_lim | [189, 1] | [270, 21] | exact Real.coe_toNNReal d dp.le | I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), ContinuousOn (f n) (closedBall c βr)... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Uniform.lean | uniform_analytic_lim | [189, 1] | [270, 21] | intro z zb | I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), ContinuousOn (f n) (closedBall c βr)... | I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), ContinuousOn (f n) (closedBall c βr)... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Uniform.lean | uniform_analytic_lim | [189, 1] | [270, 21] | exact _root_.trans (hn z (cb zb)).le (le_of_eq dd.symm) | I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), ContinuousOn (f n) (closedBall c βr)... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Uniform.lean | uniform_analytic_lim | [189, 1] | [270, 21] | bound | I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), ContinuousOn (f n) (closedBall c βr)... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Uniform.lean | uniform_analytic_lim | [189, 1] | [270, 21] | have pgb : (M.sum fun k β¦ a ^ k) β€ (1 - a)β»ΒΉ := partial_geometric_bound M a0 a1 | I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), ContinuousOn (f n) (closedBall c βr)... | I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), ContinuousOn (f n) (closedBall c βr)... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Uniform.lean | uniform_analytic_lim | [189, 1] | [270, 21] | calc
(M.sum fun k β¦ a ^ k * d) = (M.sum fun k β¦ a ^ k) * d := by rw [β Finset.sum_mul]
_ β€ (1 - a)β»ΒΉ * d := by bound
_ = (1 - a)β»ΒΉ * ((1 - a) * (e / 4)) := by rw [β d4]
_ = (1 - a) * (1 - a)β»ΒΉ * (e / 4) := by ring
_ = 1 * (e / 4) := by rw [mul_inv_cancel a1p.ne']
_ = e / 4 := by ring | I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), ContinuousOn (f n) (closedBall c βr)... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Uniform.lean | uniform_analytic_lim | [189, 1] | [270, 21] | rw [β Finset.sum_mul] | I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), ContinuousOn (f n) (closedBall c βr)... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Uniform.lean | uniform_analytic_lim | [189, 1] | [270, 21] | bound | I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), ContinuousOn (f n) (closedBall c βr)... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Uniform.lean | uniform_analytic_lim | [189, 1] | [270, 21] | rw [β d4] | I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), ContinuousOn (f n) (closedBall c βr)... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Uniform.lean | uniform_analytic_lim | [189, 1] | [270, 21] | ring | I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), ContinuousOn (f n) (closedBall c βr)... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Uniform.lean | uniform_analytic_lim | [189, 1] | [270, 21] | rw [mul_inv_cancel a1p.ne'] | I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), ContinuousOn (f n) (closedBall c βr)... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Uniform.lean | uniform_analytic_lim | [189, 1] | [270, 21] | ring | I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), ContinuousOn (f n) (closedBall c βr)... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Uniform.lean | uniform_analytic_lim | [189, 1] | [270, 21] | bound | I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), ContinuousOn (f n) (closedBall c βr)... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Uniform.lean | uniform_analytic_lim | [189, 1] | [270, 21] | bound | I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), ContinuousOn (f n) (closedBall c βr)... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Uniform.lean | uniform_analytic_lim | [189, 1] | [270, 21] | rw [β d4] | I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), ContinuousOn (f n) (closedBall c βr)... | I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), ContinuousOn (f n) (closedBall c βr)... | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Uniform.lean | uniform_analytic_lim | [189, 1] | [270, 21] | ring | I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), ContinuousOn (f n) (closedBall c βr)... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Uniform.lean | uniform_analytic_lim | [189, 1] | [270, 21] | bound | I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), ContinuousOn (f n) (closedBall c βr)... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Uniform.lean | uniform_analytic_lim | [189, 1] | [270, 21] | ring | I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), ContinuousOn (f n) (closedBall c βr)... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Uniform.lean | uniform_analytic_lim | [189, 1] | [270, 21] | norm_num | I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), ContinuousOn (f n) (closedBall c βr)... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Analytic/Uniform.lean | uniform_analytic_lim | [189, 1] | [270, 21] | simp | I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr n) c βr
cf : β (n : I), ContinuousOn (f n) (closedBall c βr)... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
I : Type
instβΒΉ : Lattice I
instβ : Nonempty I
f : I β β β β
g : β β β
s : Set β
c : β
r : ββ₯0
cb : closedBall c βr β s
rp : 0 < r
pr : I β FormalMultilinearSeries β β β := fun n => cauchyPowerSeries (f n) c βr
hpf : β (n : I), HasFPowerSeriesOnBall (f n) (pr... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Pow.lean | pow_mul_nat | [7, 1] | [17, 10] | by_cases z0 : z = 0 | z w : β
n : β
β’ (z ^ w) ^ n = z ^ (w * βn) | case pos
z w : β
n : β
z0 : z = 0
β’ (z ^ w) ^ n = z ^ (w * βn)
case neg
z w : β
n : β
z0 : Β¬z = 0
β’ (z ^ w) ^ n = z ^ (w * βn) | Please generate a tactic in lean4 to solve the state.
STATE:
z w : β
n : β
β’ (z ^ w) ^ n = z ^ (w * βn)
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Pow.lean | pow_mul_nat | [7, 1] | [17, 10] | simp only [Complex.cpow_def_of_ne_zero z0, β Complex.exp_nat_mul] | case neg
z w : β
n : β
z0 : Β¬z = 0
β’ (z ^ w) ^ n = z ^ (w * βn) | case neg
z w : β
n : β
z0 : Β¬z = 0
β’ (βn * (z.log * w)).exp = (z.log * (w * βn)).exp | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
z w : β
n : β
z0 : Β¬z = 0
β’ (z ^ w) ^ n = z ^ (w * βn)
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Pow.lean | pow_mul_nat | [7, 1] | [17, 10] | ring_nf | case neg
z w : β
n : β
z0 : Β¬z = 0
β’ (βn * (z.log * w)).exp = (z.log * (w * βn)).exp | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
z w : β
n : β
z0 : Β¬z = 0
β’ (βn * (z.log * w)).exp = (z.log * (w * βn)).exp
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Pow.lean | pow_mul_nat | [7, 1] | [17, 10] | rw [z0] | case pos
z w : β
n : β
z0 : z = 0
β’ (z ^ w) ^ n = z ^ (w * βn) | case pos
z w : β
n : β
z0 : z = 0
β’ (0 ^ w) ^ n = 0 ^ (w * βn) | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
z w : β
n : β
z0 : z = 0
β’ (z ^ w) ^ n = z ^ (w * βn)
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Pow.lean | pow_mul_nat | [7, 1] | [17, 10] | by_cases w0 : w = 0 | case pos
z w : β
n : β
z0 : z = 0
β’ (0 ^ w) ^ n = 0 ^ (w * βn) | case pos
z w : β
n : β
z0 : z = 0
w0 : w = 0
β’ (0 ^ w) ^ n = 0 ^ (w * βn)
case neg
z w : β
n : β
z0 : z = 0
w0 : Β¬w = 0
β’ (0 ^ w) ^ n = 0 ^ (w * βn) | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
z w : β
n : β
z0 : z = 0
β’ (0 ^ w) ^ n = 0 ^ (w * βn)
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Pow.lean | pow_mul_nat | [7, 1] | [17, 10] | by_cases n0 : n = 0 | case neg
z w : β
n : β
z0 : z = 0
w0 : Β¬w = 0
β’ (0 ^ w) ^ n = 0 ^ (w * βn) | case pos
z w : β
n : β
z0 : z = 0
w0 : Β¬w = 0
n0 : n = 0
β’ (0 ^ w) ^ n = 0 ^ (w * βn)
case neg
z w : β
n : β
z0 : z = 0
w0 : Β¬w = 0
n0 : Β¬n = 0
β’ (0 ^ w) ^ n = 0 ^ (w * βn) | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
z w : β
n : β
z0 : z = 0
w0 : Β¬w = 0
β’ (0 ^ w) ^ n = 0 ^ (w * βn)
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Pow.lean | pow_mul_nat | [7, 1] | [17, 10] | have wn0 : w * n β 0 := mul_ne_zero w0 (Nat.cast_ne_zero.mpr n0) | case neg
z w : β
n : β
z0 : z = 0
w0 : Β¬w = 0
n0 : Β¬n = 0
β’ (0 ^ w) ^ n = 0 ^ (w * βn) | case neg
z w : β
n : β
z0 : z = 0
w0 : Β¬w = 0
n0 : Β¬n = 0
wn0 : w * βn β 0
β’ (0 ^ w) ^ n = 0 ^ (w * βn) | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
z w : β
n : β
z0 : z = 0
w0 : Β¬w = 0
n0 : Β¬n = 0
β’ (0 ^ w) ^ n = 0 ^ (w * βn)
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Pow.lean | pow_mul_nat | [7, 1] | [17, 10] | rw [Complex.zero_cpow w0] | case neg
z w : β
n : β
z0 : z = 0
w0 : Β¬w = 0
n0 : Β¬n = 0
wn0 : w * βn β 0
β’ (0 ^ w) ^ n = 0 ^ (w * βn) | case neg
z w : β
n : β
z0 : z = 0
w0 : Β¬w = 0
n0 : Β¬n = 0
wn0 : w * βn β 0
β’ 0 ^ n = 0 ^ (w * βn) | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
z w : β
n : β
z0 : z = 0
w0 : Β¬w = 0
n0 : Β¬n = 0
wn0 : w * βn β 0
β’ (0 ^ w) ^ n = 0 ^ (w * βn)
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Pow.lean | pow_mul_nat | [7, 1] | [17, 10] | rw [Complex.zero_cpow wn0] | case neg
z w : β
n : β
z0 : z = 0
w0 : Β¬w = 0
n0 : Β¬n = 0
wn0 : w * βn β 0
β’ 0 ^ n = 0 ^ (w * βn) | case neg
z w : β
n : β
z0 : z = 0
w0 : Β¬w = 0
n0 : Β¬n = 0
wn0 : w * βn β 0
β’ 0 ^ n = 0 | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
z w : β
n : β
z0 : z = 0
w0 : Β¬w = 0
n0 : Β¬n = 0
wn0 : w * βn β 0
β’ 0 ^ n = 0 ^ (w * βn)
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Pow.lean | pow_mul_nat | [7, 1] | [17, 10] | exact zero_pow n0 | case neg
z w : β
n : β
z0 : z = 0
w0 : Β¬w = 0
n0 : Β¬n = 0
wn0 : w * βn β 0
β’ 0 ^ n = 0 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
z w : β
n : β
z0 : z = 0
w0 : Β¬w = 0
n0 : Β¬n = 0
wn0 : w * βn β 0
β’ 0 ^ n = 0
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Pow.lean | pow_mul_nat | [7, 1] | [17, 10] | rw [w0] | case pos
z w : β
n : β
z0 : z = 0
w0 : w = 0
β’ (0 ^ w) ^ n = 0 ^ (w * βn) | case pos
z w : β
n : β
z0 : z = 0
w0 : w = 0
β’ (0 ^ 0) ^ n = 0 ^ (0 * βn) | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
z w : β
n : β
z0 : z = 0
w0 : w = 0
β’ (0 ^ w) ^ n = 0 ^ (w * βn)
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Pow.lean | pow_mul_nat | [7, 1] | [17, 10] | simp | case pos
z w : β
n : β
z0 : z = 0
w0 : w = 0
β’ (0 ^ 0) ^ n = 0 ^ (0 * βn) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
z w : β
n : β
z0 : z = 0
w0 : w = 0
β’ (0 ^ 0) ^ n = 0 ^ (0 * βn)
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Pow.lean | pow_mul_nat | [7, 1] | [17, 10] | rw [n0] | case pos
z w : β
n : β
z0 : z = 0
w0 : Β¬w = 0
n0 : n = 0
β’ (0 ^ w) ^ n = 0 ^ (w * βn) | case pos
z w : β
n : β
z0 : z = 0
w0 : Β¬w = 0
n0 : n = 0
β’ (0 ^ w) ^ 0 = 0 ^ (w * β0) | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
z w : β
n : β
z0 : z = 0
w0 : Β¬w = 0
n0 : n = 0
β’ (0 ^ w) ^ n = 0 ^ (w * βn)
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Pow.lean | pow_mul_nat | [7, 1] | [17, 10] | simp | case pos
z w : β
n : β
z0 : z = 0
w0 : Β¬w = 0
n0 : n = 0
β’ (0 ^ w) ^ 0 = 0 ^ (w * β0) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
z w : β
n : β
z0 : z = 0
w0 : Β¬w = 0
n0 : n = 0
β’ (0 ^ w) ^ 0 = 0 ^ (w * β0)
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Mandelbrot.lean | approx_bad_potential_image | [60, 1] | [75, 9] | rw [potential_image, bad_potential_image] | c : β Γ β
n : β
r : Floating
β’ potential_image βc β approx (bad_potential_image n r c) | c : β Γ β
n : β
r : Floating
β’ (let p := potential 2 ββc;
let t := p ^ 16;
lerp t βclear βoutside) β
approx
(let c := Box.ofRat c;
let p := c.potential c n r;
let t := p.1.sqr.sqr.sqr.sqr;
let i := lerp t clear' outside';
i.quantize) | Please generate a tactic in lean4 to solve the state.
STATE:
c : β Γ β
n : β
r : Floating
β’ potential_image βc β approx (bad_potential_image n r c)
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Mandelbrot.lean | approx_bad_potential_image | [60, 1] | [75, 9] | have e : β p : β, p^16 = (((p^2)^2)^2)^2 := by intro p; rw [βpow_mul, βpow_mul, βpow_mul] | c : β Γ β
n : β
r : Floating
β’ (let p := potential 2 ββc;
let t := p ^ 16;
lerp t βclear βoutside) β
approx
(let c := Box.ofRat c;
let p := c.potential c n r;
let t := p.1.sqr.sqr.sqr.sqr;
let i := lerp t clear' outside';
i.quantize) | c : β Γ β
n : β
r : Floating
e : β (p : β), p ^ 16 = (((p ^ 2) ^ 2) ^ 2) ^ 2
β’ (let p := potential 2 ββc;
let t := p ^ 16;
lerp t βclear βoutside) β
approx
(let c := Box.ofRat c;
let p := c.potential c n r;
let t := p.1.sqr.sqr.sqr.sqr;
let i := lerp t clear' outside';
i.quanti... | Please generate a tactic in lean4 to solve the state.
STATE:
c : β Γ β
n : β
r : Floating
β’ (let p := potential 2 ββc;
let t := p ^ 16;
lerp t βclear βoutside) β
approx
(let c := Box.ofRat c;
let p := c.potential c n r;
let t := p.1.sqr.sqr.sqr.sqr;
let i := lerp t clear' outside';
... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Mandelbrot.lean | approx_bad_potential_image | [60, 1] | [75, 9] | simp only [far', outside', clear', green', e] | c : β Γ β
n : β
r : Floating
e : β (p : β), p ^ 16 = (((p ^ 2) ^ 2) ^ 2) ^ 2
β’ (let p := potential 2 ββc;
let t := p ^ 16;
lerp t βclear βoutside) β
approx
(let c := Box.ofRat c;
let p := c.potential c n r;
let t := p.1.sqr.sqr.sqr.sqr;
let i := lerp t clear' outside';
i.quanti... | c : β Γ β
n : β
r : Floating
e : β (p : β), p ^ 16 = (((p ^ 2) ^ 2) ^ 2) ^ 2
β’ lerp ((((potential 2 ββc ^ 2) ^ 2) ^ 2) ^ 2) βclear βoutside β
approx (lerp ((Box.ofRat c).potential (Box.ofRat c) n r).1.sqr.sqr.sqr.sqr clear.ofRat outside.ofRat).quantize | Please generate a tactic in lean4 to solve the state.
STATE:
c : β Γ β
n : β
r : Floating
e : β (p : β), p ^ 16 = (((p ^ 2) ^ 2) ^ 2) ^ 2
β’ (let p := potential 2 ββc;
let t := p ^ 16;
lerp t βclear βoutside) β
approx
(let c := Box.ofRat c;
let p := c.potential c n r;
let t := p.1.sqr.sqr.s... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Mandelbrot.lean | approx_bad_potential_image | [60, 1] | [75, 9] | apply Color.mem_approx_quantize | c : β Γ β
n : β
r : Floating
e : β (p : β), p ^ 16 = (((p ^ 2) ^ 2) ^ 2) ^ 2
β’ lerp ((((potential 2 ββc ^ 2) ^ 2) ^ 2) ^ 2) βclear βoutside β
approx (lerp ((Box.ofRat c).potential (Box.ofRat c) n r).1.sqr.sqr.sqr.sqr clear.ofRat outside.ofRat).quantize | case cm
c : β Γ β
n : β
r : Floating
e : β (p : β), p ^ 16 = (((p ^ 2) ^ 2) ^ 2) ^ 2
β’ lerp ((((potential 2 ββc ^ 2) ^ 2) ^ 2) ^ 2) βclear βoutside β
approx (lerp ((Box.ofRat c).potential (Box.ofRat c) n r).1.sqr.sqr.sqr.sqr clear.ofRat outside.ofRat) | Please generate a tactic in lean4 to solve the state.
STATE:
c : β Γ β
n : β
r : Floating
e : β (p : β), p ^ 16 = (((p ^ 2) ^ 2) ^ 2) ^ 2
β’ lerp ((((potential 2 ββc ^ 2) ^ 2) ^ 2) ^ 2) βclear βoutside β
approx (lerp ((Box.ofRat c).potential (Box.ofRat c) n r).1.sqr.sqr.sqr.sqr clear.ofRat outside.ofRat).quantize
TA... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Mandelbrot.lean | approx_bad_potential_image | [60, 1] | [75, 9] | apply mem_approx_lerp | case cm
c : β Γ β
n : β
r : Floating
e : β (p : β), p ^ 16 = (((p ^ 2) ^ 2) ^ 2) ^ 2
β’ lerp ((((potential 2 ββc ^ 2) ^ 2) ^ 2) ^ 2) βclear βoutside β
approx (lerp ((Box.ofRat c).potential (Box.ofRat c) n r).1.sqr.sqr.sqr.sqr clear.ofRat outside.ofRat) | case cm.tm
c : β Γ β
n : β
r : Floating
e : β (p : β), p ^ 16 = (((p ^ 2) ^ 2) ^ 2) ^ 2
β’ (((potential 2 ββc ^ 2) ^ 2) ^ 2) ^ 2 β approx ((Box.ofRat c).potential (Box.ofRat c) n r).1.sqr.sqr.sqr.sqr
case cm.xm
c : β Γ β
n : β
r : Floating
e : β (p : β), p ^ 16 = (((p ^ 2) ^ 2) ^ 2) ^ 2
β’ βclear β approx clear.ofRat
c... | Please generate a tactic in lean4 to solve the state.
STATE:
case cm
c : β Γ β
n : β
r : Floating
e : β (p : β), p ^ 16 = (((p ^ 2) ^ 2) ^ 2) ^ 2
β’ lerp ((((potential 2 ββc ^ 2) ^ 2) ^ 2) ^ 2) βclear βoutside β
approx (lerp ((Box.ofRat c).potential (Box.ofRat c) n r).1.sqr.sqr.sqr.sqr clear.ofRat outside.ofRat)
TAC... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Mandelbrot.lean | approx_bad_potential_image | [60, 1] | [75, 9] | intro p | c : β Γ β
n : β
r : Floating
β’ β (p : β), p ^ 16 = (((p ^ 2) ^ 2) ^ 2) ^ 2 | c : β Γ β
n : β
r : Floating
p : β
β’ p ^ 16 = (((p ^ 2) ^ 2) ^ 2) ^ 2 | Please generate a tactic in lean4 to solve the state.
STATE:
c : β Γ β
n : β
r : Floating
β’ β (p : β), p ^ 16 = (((p ^ 2) ^ 2) ^ 2) ^ 2
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Mandelbrot.lean | approx_bad_potential_image | [60, 1] | [75, 9] | rw [βpow_mul, βpow_mul, βpow_mul] | c : β Γ β
n : β
r : Floating
p : β
β’ p ^ 16 = (((p ^ 2) ^ 2) ^ 2) ^ 2 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
c : β Γ β
n : β
r : Floating
p : β
β’ p ^ 16 = (((p ^ 2) ^ 2) ^ 2) ^ 2
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Mandelbrot.lean | approx_bad_potential_image | [60, 1] | [75, 9] | apply Interval.mem_approx_sqr | case cm.tm
c : β Γ β
n : β
r : Floating
e : β (p : β), p ^ 16 = (((p ^ 2) ^ 2) ^ 2) ^ 2
β’ (((potential 2 ββc ^ 2) ^ 2) ^ 2) ^ 2 β approx ((Box.ofRat c).potential (Box.ofRat c) n r).1.sqr.sqr.sqr.sqr | case cm.tm.ax
c : β Γ β
n : β
r : Floating
e : β (p : β), p ^ 16 = (((p ^ 2) ^ 2) ^ 2) ^ 2
β’ ((potential 2 ββc ^ 2) ^ 2) ^ 2 β approx ((Box.ofRat c).potential (Box.ofRat c) n r).1.sqr.sqr.sqr | Please generate a tactic in lean4 to solve the state.
STATE:
case cm.tm
c : β Γ β
n : β
r : Floating
e : β (p : β), p ^ 16 = (((p ^ 2) ^ 2) ^ 2) ^ 2
β’ (((potential 2 ββc ^ 2) ^ 2) ^ 2) ^ 2 β approx ((Box.ofRat c).potential (Box.ofRat c) n r).1.sqr.sqr.sqr.sqr
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Mandelbrot.lean | approx_bad_potential_image | [60, 1] | [75, 9] | apply Interval.mem_approx_sqr | case cm.tm.ax
c : β Γ β
n : β
r : Floating
e : β (p : β), p ^ 16 = (((p ^ 2) ^ 2) ^ 2) ^ 2
β’ ((potential 2 ββc ^ 2) ^ 2) ^ 2 β approx ((Box.ofRat c).potential (Box.ofRat c) n r).1.sqr.sqr.sqr | case cm.tm.ax.ax
c : β Γ β
n : β
r : Floating
e : β (p : β), p ^ 16 = (((p ^ 2) ^ 2) ^ 2) ^ 2
β’ (potential 2 ββc ^ 2) ^ 2 β approx ((Box.ofRat c).potential (Box.ofRat c) n r).1.sqr.sqr | Please generate a tactic in lean4 to solve the state.
STATE:
case cm.tm.ax
c : β Γ β
n : β
r : Floating
e : β (p : β), p ^ 16 = (((p ^ 2) ^ 2) ^ 2) ^ 2
β’ ((potential 2 ββc ^ 2) ^ 2) ^ 2 β approx ((Box.ofRat c).potential (Box.ofRat c) n r).1.sqr.sqr.sqr
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Mandelbrot.lean | approx_bad_potential_image | [60, 1] | [75, 9] | apply Interval.mem_approx_sqr | case cm.tm.ax.ax
c : β Γ β
n : β
r : Floating
e : β (p : β), p ^ 16 = (((p ^ 2) ^ 2) ^ 2) ^ 2
β’ (potential 2 ββc ^ 2) ^ 2 β approx ((Box.ofRat c).potential (Box.ofRat c) n r).1.sqr.sqr | case cm.tm.ax.ax.ax
c : β Γ β
n : β
r : Floating
e : β (p : β), p ^ 16 = (((p ^ 2) ^ 2) ^ 2) ^ 2
β’ potential 2 ββc ^ 2 β approx ((Box.ofRat c).potential (Box.ofRat c) n r).1.sqr | Please generate a tactic in lean4 to solve the state.
STATE:
case cm.tm.ax.ax
c : β Γ β
n : β
r : Floating
e : β (p : β), p ^ 16 = (((p ^ 2) ^ 2) ^ 2) ^ 2
β’ (potential 2 ββc ^ 2) ^ 2 β approx ((Box.ofRat c).potential (Box.ofRat c) n r).1.sqr.sqr
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Mandelbrot.lean | approx_bad_potential_image | [60, 1] | [75, 9] | apply Interval.mem_approx_sqr | case cm.tm.ax.ax.ax
c : β Γ β
n : β
r : Floating
e : β (p : β), p ^ 16 = (((p ^ 2) ^ 2) ^ 2) ^ 2
β’ potential 2 ββc ^ 2 β approx ((Box.ofRat c).potential (Box.ofRat c) n r).1.sqr | case cm.tm.ax.ax.ax.ax
c : β Γ β
n : β
r : Floating
e : β (p : β), p ^ 16 = (((p ^ 2) ^ 2) ^ 2) ^ 2
β’ potential 2 ββc β approx ((Box.ofRat c).potential (Box.ofRat c) n r).1 | Please generate a tactic in lean4 to solve the state.
STATE:
case cm.tm.ax.ax.ax
c : β Γ β
n : β
r : Floating
e : β (p : β), p ^ 16 = (((p ^ 2) ^ 2) ^ 2) ^ 2
β’ potential 2 ββc ^ 2 β approx ((Box.ofRat c).potential (Box.ofRat c) n r).1.sqr
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Mandelbrot.lean | approx_bad_potential_image | [60, 1] | [75, 9] | mono | case cm.tm.ax.ax.ax.ax
c : β Γ β
n : β
r : Floating
e : β (p : β), p ^ 16 = (((p ^ 2) ^ 2) ^ 2) ^ 2
β’ potential 2 ββc β approx ((Box.ofRat c).potential (Box.ofRat c) n r).1 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case cm.tm.ax.ax.ax.ax
c : β Γ β
n : β
r : Floating
e : β (p : β), p ^ 16 = (((p ^ 2) ^ 2) ^ 2) ^ 2
β’ potential 2 ββc β approx ((Box.ofRat c).potential (Box.ofRat c) n r).1
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Mandelbrot.lean | approx_bad_potential_image | [60, 1] | [75, 9] | mono | case cm.xm
c : β Γ β
n : β
r : Floating
e : β (p : β), p ^ 16 = (((p ^ 2) ^ 2) ^ 2) ^ 2
β’ βclear β approx clear.ofRat | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case cm.xm
c : β Γ β
n : β
r : Floating
e : β (p : β), p ^ 16 = (((p ^ 2) ^ 2) ^ 2) ^ 2
β’ βclear β approx clear.ofRat
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Mandelbrot.lean | approx_bad_potential_image | [60, 1] | [75, 9] | mono | case cm.ym
c : β Γ β
n : β
r : Floating
e : β (p : β), p ^ 16 = (((p ^ 2) ^ 2) ^ 2) ^ 2
β’ βoutside β approx outside.ofRat | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case cm.ym
c : β Γ β
n : β
r : Floating
e : β (p : β), p ^ 16 = (((p ^ 2) ^ 2) ^ 2) ^ 2
β’ βoutside β approx outside.ofRat
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Pow.lean | pow_mul_nat | [7, 1] | [17, 10] | by_cases z0 : z = 0 | z w : β
n : β
β’ (z ^ w) ^ n = z ^ (w * βn) | case pos
z w : β
n : β
z0 : z = 0
β’ (z ^ w) ^ n = z ^ (w * βn)
case neg
z w : β
n : β
z0 : Β¬z = 0
β’ (z ^ w) ^ n = z ^ (w * βn) | Please generate a tactic in lean4 to solve the state.
STATE:
z w : β
n : β
β’ (z ^ w) ^ n = z ^ (w * βn)
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Pow.lean | pow_mul_nat | [7, 1] | [17, 10] | simp only [Complex.cpow_def_of_ne_zero z0, β Complex.exp_nat_mul] | case neg
z w : β
n : β
z0 : Β¬z = 0
β’ (z ^ w) ^ n = z ^ (w * βn) | case neg
z w : β
n : β
z0 : Β¬z = 0
β’ (βn * (z.log * w)).exp = (z.log * (w * βn)).exp | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
z w : β
n : β
z0 : Β¬z = 0
β’ (z ^ w) ^ n = z ^ (w * βn)
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Pow.lean | pow_mul_nat | [7, 1] | [17, 10] | ring_nf | case neg
z w : β
n : β
z0 : Β¬z = 0
β’ (βn * (z.log * w)).exp = (z.log * (w * βn)).exp | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
z w : β
n : β
z0 : Β¬z = 0
β’ (βn * (z.log * w)).exp = (z.log * (w * βn)).exp
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Pow.lean | pow_mul_nat | [7, 1] | [17, 10] | rw [z0] | case pos
z w : β
n : β
z0 : z = 0
β’ (z ^ w) ^ n = z ^ (w * βn) | case pos
z w : β
n : β
z0 : z = 0
β’ (0 ^ w) ^ n = 0 ^ (w * βn) | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
z w : β
n : β
z0 : z = 0
β’ (z ^ w) ^ n = z ^ (w * βn)
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Pow.lean | pow_mul_nat | [7, 1] | [17, 10] | by_cases w0 : w = 0 | case pos
z w : β
n : β
z0 : z = 0
β’ (0 ^ w) ^ n = 0 ^ (w * βn) | case pos
z w : β
n : β
z0 : z = 0
w0 : w = 0
β’ (0 ^ w) ^ n = 0 ^ (w * βn)
case neg
z w : β
n : β
z0 : z = 0
w0 : Β¬w = 0
β’ (0 ^ w) ^ n = 0 ^ (w * βn) | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
z w : β
n : β
z0 : z = 0
β’ (0 ^ w) ^ n = 0 ^ (w * βn)
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Pow.lean | pow_mul_nat | [7, 1] | [17, 10] | by_cases n0 : n = 0 | case neg
z w : β
n : β
z0 : z = 0
w0 : Β¬w = 0
β’ (0 ^ w) ^ n = 0 ^ (w * βn) | case pos
z w : β
n : β
z0 : z = 0
w0 : Β¬w = 0
n0 : n = 0
β’ (0 ^ w) ^ n = 0 ^ (w * βn)
case neg
z w : β
n : β
z0 : z = 0
w0 : Β¬w = 0
n0 : Β¬n = 0
β’ (0 ^ w) ^ n = 0 ^ (w * βn) | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
z w : β
n : β
z0 : z = 0
w0 : Β¬w = 0
β’ (0 ^ w) ^ n = 0 ^ (w * βn)
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Pow.lean | pow_mul_nat | [7, 1] | [17, 10] | have wn0 : w * n β 0 := mul_ne_zero w0 (Nat.cast_ne_zero.mpr n0) | case neg
z w : β
n : β
z0 : z = 0
w0 : Β¬w = 0
n0 : Β¬n = 0
β’ (0 ^ w) ^ n = 0 ^ (w * βn) | case neg
z w : β
n : β
z0 : z = 0
w0 : Β¬w = 0
n0 : Β¬n = 0
wn0 : w * βn β 0
β’ (0 ^ w) ^ n = 0 ^ (w * βn) | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
z w : β
n : β
z0 : z = 0
w0 : Β¬w = 0
n0 : Β¬n = 0
β’ (0 ^ w) ^ n = 0 ^ (w * βn)
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Pow.lean | pow_mul_nat | [7, 1] | [17, 10] | rw [Complex.zero_cpow w0] | case neg
z w : β
n : β
z0 : z = 0
w0 : Β¬w = 0
n0 : Β¬n = 0
wn0 : w * βn β 0
β’ (0 ^ w) ^ n = 0 ^ (w * βn) | case neg
z w : β
n : β
z0 : z = 0
w0 : Β¬w = 0
n0 : Β¬n = 0
wn0 : w * βn β 0
β’ 0 ^ n = 0 ^ (w * βn) | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
z w : β
n : β
z0 : z = 0
w0 : Β¬w = 0
n0 : Β¬n = 0
wn0 : w * βn β 0
β’ (0 ^ w) ^ n = 0 ^ (w * βn)
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Pow.lean | pow_mul_nat | [7, 1] | [17, 10] | rw [Complex.zero_cpow wn0] | case neg
z w : β
n : β
z0 : z = 0
w0 : Β¬w = 0
n0 : Β¬n = 0
wn0 : w * βn β 0
β’ 0 ^ n = 0 ^ (w * βn) | case neg
z w : β
n : β
z0 : z = 0
w0 : Β¬w = 0
n0 : Β¬n = 0
wn0 : w * βn β 0
β’ 0 ^ n = 0 | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
z w : β
n : β
z0 : z = 0
w0 : Β¬w = 0
n0 : Β¬n = 0
wn0 : w * βn β 0
β’ 0 ^ n = 0 ^ (w * βn)
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Pow.lean | pow_mul_nat | [7, 1] | [17, 10] | exact zero_pow n0 | case neg
z w : β
n : β
z0 : z = 0
w0 : Β¬w = 0
n0 : Β¬n = 0
wn0 : w * βn β 0
β’ 0 ^ n = 0 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
z w : β
n : β
z0 : z = 0
w0 : Β¬w = 0
n0 : Β¬n = 0
wn0 : w * βn β 0
β’ 0 ^ n = 0
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Pow.lean | pow_mul_nat | [7, 1] | [17, 10] | rw [w0] | case pos
z w : β
n : β
z0 : z = 0
w0 : w = 0
β’ (0 ^ w) ^ n = 0 ^ (w * βn) | case pos
z w : β
n : β
z0 : z = 0
w0 : w = 0
β’ (0 ^ 0) ^ n = 0 ^ (0 * βn) | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
z w : β
n : β
z0 : z = 0
w0 : w = 0
β’ (0 ^ w) ^ n = 0 ^ (w * βn)
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Pow.lean | pow_mul_nat | [7, 1] | [17, 10] | simp | case pos
z w : β
n : β
z0 : z = 0
w0 : w = 0
β’ (0 ^ 0) ^ n = 0 ^ (0 * βn) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
z w : β
n : β
z0 : z = 0
w0 : w = 0
β’ (0 ^ 0) ^ n = 0 ^ (0 * βn)
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Pow.lean | pow_mul_nat | [7, 1] | [17, 10] | rw [n0] | case pos
z w : β
n : β
z0 : z = 0
w0 : Β¬w = 0
n0 : n = 0
β’ (0 ^ w) ^ n = 0 ^ (w * βn) | case pos
z w : β
n : β
z0 : z = 0
w0 : Β¬w = 0
n0 : n = 0
β’ (0 ^ w) ^ 0 = 0 ^ (w * β0) | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
z w : β
n : β
z0 : z = 0
w0 : Β¬w = 0
n0 : n = 0
β’ (0 ^ w) ^ n = 0 ^ (w * βn)
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Pow.lean | pow_mul_nat | [7, 1] | [17, 10] | simp | case pos
z w : β
n : β
z0 : z = 0
w0 : Β¬w = 0
n0 : n = 0
β’ (0 ^ w) ^ 0 = 0 ^ (w * β0) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
z w : β
n : β
z0 : z = 0
w0 : Β¬w = 0
n0 : n = 0
β’ (0 ^ w) ^ 0 = 0 ^ (w * β0)
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNearM.lean | attracts_shift | [48, 1] | [50, 60] | simp only [Attracts, β Function.iterate_add_apply] | S : Type
instββ΄ : TopologicalSpace S
instβΒ³ : CompactSpace S
instβΒ² : T3Space S
instβΒΉ : ChartedSpace β S
instβ : AnalyticManifold I S
fβ : β β S β S
c : β
aβ zβ : S
d n : β
f : S β S
z a : S
k : β
β’ Attracts f (f^[k] z) a β Attracts f z a | S : Type
instββ΄ : TopologicalSpace S
instβΒ³ : CompactSpace S
instβΒ² : T3Space S
instβΒΉ : ChartedSpace β S
instβ : AnalyticManifold I S
fβ : β β S β S
c : β
aβ zβ : S
d n : β
f : S β S
z a : S
k : β
β’ Tendsto (fun n => f^[n + k] z) atTop (π a) β Tendsto (fun n => f^[n] z) atTop (π a) | Please generate a tactic in lean4 to solve the state.
STATE:
S : Type
instββ΄ : TopologicalSpace S
instβΒ³ : CompactSpace S
instβΒ² : T3Space S
instβΒΉ : ChartedSpace β S
instβ : AnalyticManifold I S
fβ : β β S β S
c : β
aβ zβ : S
d n : β
f : S β S
z a : S
k : β
β’ Attracts f (f^[k] z) a β Attracts f z a
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNearM.lean | attracts_shift | [48, 1] | [50, 60] | apply @Filter.tendsto_add_atTop_iff_nat _ fun n β¦ f^[n] z | S : Type
instββ΄ : TopologicalSpace S
instβΒ³ : CompactSpace S
instβΒ² : T3Space S
instβΒΉ : ChartedSpace β S
instβ : AnalyticManifold I S
fβ : β β S β S
c : β
aβ zβ : S
d n : β
f : S β S
z a : S
k : β
β’ Tendsto (fun n => f^[n + k] z) atTop (π a) β Tendsto (fun n => f^[n] z) atTop (π a) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
S : Type
instββ΄ : TopologicalSpace S
instβΒ³ : CompactSpace S
instβΒ² : T3Space S
instβΒΉ : ChartedSpace β S
instβ : AnalyticManifold I S
fβ : β β S β S
c : β
aβ zβ : S
d n : β
f : S β S
z a : S
k : β
β’ Tendsto (fun n => f^[n + k] z) atTop (π a) β Tendsto (fun ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNearM.lean | Super.dp | [69, 1] | [69, 74] | norm_num | S : Type
instββ΄ : TopologicalSpace S
instβΒ³ : CompactSpace S
instβΒ² : T3Space S
instβΒΉ : ChartedSpace β S
instβ : AnalyticManifold I S
f : β β S β S
c : β
a z : S
d n : β
s : Super f d a
β’ 0 < 1 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
S : Type
instββ΄ : TopologicalSpace S
instβΒ³ : CompactSpace S
instβΒ² : T3Space S
instβΒΉ : ChartedSpace β S
instβ : AnalyticManifold I S
f : β β S β S
c : β
a z : S
d n : β
s : Super f d a
β’ 0 < 1
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Dynamics/BottcherNearM.lean | Super.d1 | [71, 1] | [71, 80] | norm_num | S : Type
instββ΄ : TopologicalSpace S
instβΒ³ : CompactSpace S
instβΒ² : T3Space S
instβΒΉ : ChartedSpace β S
instβ : AnalyticManifold I S
f : β β S β S
c : β
a z : S
d n : β
s : Super f d a
β’ 1 < 2 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
S : Type
instββ΄ : TopologicalSpace S
instβΒ³ : CompactSpace S
instβΒ² : T3Space S
instβΒΉ : ChartedSpace β S
instβ : AnalyticManifold I S
f : β β S β S
c : β
a z : S
d n : β
s : Super f d a
β’ 1 < 2
TACTIC:
|
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