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/Render/Potential.lean | Box.approx_potential_large | [132, 1] | [151, 9] | linarith | c' z' : ℂ
z : Box
cz : Complex.abs c' ≤ Complex.abs z'
z6 : 6 ≤ Complex.abs z'
zm : z' ∈ approx z
⊢ 0 < Complex.abs z' | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
c' z' : ℂ
z : Box
cz : Complex.abs c' ≤ Complex.abs z'
z6 : 6 ≤ Complex.abs z'
zm : z' ∈ approx z
⊢ 0 < Complex.abs z'
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Potential.lean | Box.mem_approx_potential | [153, 1] | [212, 46] | set s := superF 2 | c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
⊢ ⋯.potential c' ↑z' ∈ approx (c.potential z n r).1 | c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
⊢ s.potential c' ↑z' ∈ approx (c.potential z n r).1 | Please generate a tactic in lean4 to solve the state.
STATE:
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
⊢ ⋯.potential c' ↑z' ∈ approx (c.potential z n r).1
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Potential.lean | Box.mem_approx_potential | [153, 1] | [212, 46] | rw [Box.potential] | c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
⊢ s.potential c' ↑z' ∈ approx (c.potential z n r).1 | c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
⊢ s.potential c' ↑z' ∈
approx
(let cs := c.normSq.hi;
let i := iterate c z (cs.max 9) n;
match i.exit with
| Exit.nan => (nan, PotentialMode.nan)
| Exit.lar... | Please generate a tactic in lean4 to solve the state.
STATE:
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
⊢ s.potential c' ↑z' ∈ approx (c.potential z n r).1
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Potential.lean | Box.mem_approx_potential | [153, 1] | [212, 46] | generalize hcs : (normSq c).hi = cs | c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
⊢ s.potential c' ↑z' ∈
approx
(let cs := c.normSq.hi;
let i := iterate c z (cs.max 9) n;
match i.exit with
| Exit.nan => (nan, PotentialMode.nan)
| Exit.lar... | c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
⊢ s.potential c' ↑z' ∈
approx
(let cs := cs;
let i := iterate c z (cs.max 9) n;
match i.exit with
| Exit.nan => (nan, Potential... | Please generate a tactic in lean4 to solve the state.
STATE:
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
⊢ s.potential c' ↑z' ∈
approx
(let cs := c.normSq.hi;
let i := iterate c z (cs.max 9) n;
match i.exit with
... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Potential.lean | Box.mem_approx_potential | [153, 1] | [212, 46] | generalize hi : iterate c z (cs.max 9) n = i | c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
⊢ s.potential c' ↑z' ∈
approx
(let cs := cs;
let i := iterate c z (cs.max 9) n;
match i.exit with
| Exit.nan => (nan, Potential... | c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
⊢ s.potential c' ↑z' ∈
approx
(let cs := cs;
let i := iterate c z (cs.max 9) n;
match i.exit... | Please generate a tactic in lean4 to solve the state.
STATE:
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
⊢ s.potential c' ↑z' ∈
approx
(let cs := cs;
let i := iterate c z (cs.max 9) n;
... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Potential.lean | Box.mem_approx_potential | [153, 1] | [212, 46] | by_cases csn : cs = nan | c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
⊢ s.potential c' ↑z' ∈
approx
(let cs := cs;
let i := iterate c z (cs.max 9) n;
match i.exit... | case pos
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
csn : cs = nan
⊢ s.potential c' ↑z' ∈
approx
(let cs := cs;
let i := iterate c z (cs.max 9)... | Please generate a tactic in lean4 to solve the state.
STATE:
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
⊢ s.potential c' ↑z' ∈
approx
(let cs := cs;
... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Potential.lean | Box.mem_approx_potential | [153, 1] | [212, 46] | simp only [hi, Interval.hi_eq_nan, Floating.val_lt_val] | case neg
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
csn : ¬cs = nan
⊢ s.potential c' ↑z' ∈
approx
(let cs := cs;
let i := iterate c z (cs.max 9... | case neg
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
csn : ¬cs = nan
⊢ s.potential c' ↑z' ∈
approx
(match i.exit with
| Exit.nan => (nan, Potent... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
csn : ¬cs = nan
⊢ s.potential c' ↑z' ∈
appro... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Potential.lean | Box.mem_approx_potential | [153, 1] | [212, 46] | generalize hie : i.exit = ie | case neg
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
csn : ¬cs = nan
⊢ s.potential c' ↑z' ∈
approx
(match i.exit with
| Exit.nan => (nan, Potent... | case neg
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
csn : ¬cs = nan
ie : Exit
hie : i.exit = ie
⊢ s.potential c' ↑z' ∈
approx
(match ie with
| ... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
csn : ¬cs = nan
⊢ s.potential c' ↑z' ∈
appro... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Potential.lean | Box.mem_approx_potential | [153, 1] | [212, 46] | induction ie | case neg
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
csn : ¬cs = nan
ie : Exit
hie : i.exit = ie
⊢ s.potential c' ↑z' ∈
approx
(match ie with
| ... | case neg.count
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
csn : ¬cs = nan
hie : i.exit = Exit.count
⊢ s.potential c' ↑z' ∈
approx
(match Exit.count wit... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
csn : ¬cs = nan
ie : Exit
hie : i.exit = ie
⊢ s.... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Potential.lean | Box.mem_approx_potential | [153, 1] | [212, 46] | simp only [csn, Floating.nan_max, iterate_nan, Interval.approx_nan, mem_univ] | case pos
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
csn : cs = nan
⊢ s.potential c' ↑z' ∈
approx
(let cs := cs;
let i := iterate c z (cs.max 9)... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
csn : cs = nan
⊢ s.potential c' ↑z' ∈
approx... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Potential.lean | Box.mem_approx_potential | [153, 1] | [212, 46] | generalize hzs : (normSq i.z) = zs | case neg.count
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
csn : ¬cs = nan
hie : i.exit = Exit.count
⊢ s.potential c' ↑z' ∈
approx
(match Exit.count wit... | case neg.count
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
csn : ¬cs = nan
hie : i.exit = Exit.count
zs : Interval
hzs : i.z.normSq = zs
⊢ s.potential c' ↑z' ∈
... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.count
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
csn : ¬cs = nan
hie : i.exit = Exit.count
... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Potential.lean | Box.mem_approx_potential | [153, 1] | [212, 46] | by_cases bad : zs = nan ∨ (16 : Floating).val < zs.hi.val ∨ (16 : Floating).val < cs.val | case neg.count
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
csn : ¬cs = nan
hie : i.exit = Exit.count
zs : Interval
hzs : i.z.normSq = zs
⊢ s.potential c' ↑z' ∈
... | case pos
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
csn : ¬cs = nan
hie : i.exit = Exit.count
zs : Interval
hzs : i.z.normSq = zs
bad : zs = nan ∨ 16.val < zs.hi... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.count
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
csn : ¬cs = nan
hie : i.exit = Exit.count
... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Potential.lean | Box.mem_approx_potential | [153, 1] | [212, 46] | simp only [Floating.val_lt_val, bad, ↓reduceIte, Interval.approx_nan, mem_univ] | case pos
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
csn : ¬cs = nan
hie : i.exit = Exit.count
zs : Interval
hzs : i.z.normSq = zs
bad : zs = nan ∨ 16.val < zs.hi... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
csn : ¬cs = nan
hie : i.exit = Exit.count
zs : I... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Potential.lean | Box.mem_approx_potential | [153, 1] | [212, 46] | simp only [bad, ↓reduceIte] | case neg
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
csn : ¬cs = nan
hie : i.exit = Exit.count
zs : Interval
hzs : i.z.normSq = zs
bad : ¬(zs = nan ∨ 16.val < zs.... | case neg
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
csn : ¬cs = nan
hie : i.exit = Exit.count
zs : Interval
hzs : i.z.normSq = zs
bad : ¬(zs = nan ∨ 16.val < zs.... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
csn : ¬cs = nan
hie : i.exit = Exit.count
zs : I... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Potential.lean | Box.mem_approx_potential | [153, 1] | [212, 46] | simp only [not_or, not_lt, ←hzs] at bad | case neg
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
csn : ¬cs = nan
hie : i.exit = Exit.count
zs : Interval
hzs : i.z.normSq = zs
bad : ¬(zs = nan ∨ 16.val < zs.... | case neg
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
csn : ¬cs = nan
hie : i.exit = Exit.count
zs : Interval
hzs : i.z.normSq = zs
bad : ¬i.z.normSq = nan ∧ i.z.n... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
csn : ¬cs = nan
hie : i.exit = Exit.count
zs : I... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Potential.lean | Box.mem_approx_potential | [153, 1] | [212, 46] | rcases bad with ⟨zsn, z4, c4⟩ | case neg
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
csn : ¬cs = nan
hie : i.exit = Exit.count
zs : Interval
hzs : i.z.normSq = zs
bad : ¬i.z.normSq = nan ∧ i.z.n... | case neg.intro.intro
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
csn : ¬cs = nan
hie : i.exit = Exit.count
zs : Interval
hzs : i.z.normSq = zs
zsn : ¬i.z.normSq =... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
csn : ¬cs = nan
hie : i.exit = Exit.count
zs : I... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Potential.lean | Box.mem_approx_potential | [153, 1] | [212, 46] | rw [Floating.val_ofNat] at c4 z4 | case neg.intro.intro
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
csn : ¬cs = nan
hie : i.exit = Exit.count
zs : Interval
hzs : i.z.normSq = zs
zsn : ¬i.z.normSq =... | case neg.intro.intro
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
csn : ¬cs = nan
hie : i.exit = Exit.count
zs : Interval
hzs : i.z.normSq = zs
zsn : ¬i.z.normSq =... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.intro.intro
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
csn : ¬cs = nan
hie : i.exit = Exit.... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Potential.lean | Box.mem_approx_potential | [153, 1] | [212, 46] | simp only [← hcs, Nat.cast_ofNat, Interval.hi_eq_nan] at c4 z4 csn zsn | case neg.intro.intro
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
csn : ¬cs = nan
hie : i.exit = Exit.count
zs : Interval
hzs : i.z.normSq = zs
zsn : ¬i.z.normSq =... | case neg.intro.intro
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
hie : i.exit = Exit.count
zs : Interval
hzs : i.z.normSq = zs
zsn : ¬i.z.normSq = nan
z4 : i.z.no... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.intro.intro
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
csn : ¬cs = nan
hie : i.exit = Exit.... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Potential.lean | Box.mem_approx_potential | [153, 1] | [212, 46] | apply Interval.mem_approx_iter_sqrt' s.potential_nonneg | case neg.intro.intro
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
hie : i.exit = Exit.count
zs : Interval
hzs : i.z.normSq = zs
zsn : ¬i.z.normSq = nan
z4 : i.z.no... | case neg.intro.intro
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
hie : i.exit = Exit.count
zs : Interval
hzs : i.z.normSq = zs
zsn : ¬i.z.normSq = nan
z4 : i.z.no... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.intro.intro
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
hie : i.exit = Exit.count
zs : Inter... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Potential.lean | Box.mem_approx_potential | [153, 1] | [212, 46] | simp only [←s.potential_eqn_iter, f_f'_iter] | case neg.intro.intro
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
hie : i.exit = Exit.count
zs : Interval
hzs : i.z.normSq = zs
zsn : ¬i.z.normSq = nan
z4 : i.z.no... | case neg.intro.intro
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
hie : i.exit = Exit.count
zs : Interval
hzs : i.z.normSq = zs
zsn : ¬i.z.normSq = nan
z4 : i.z.no... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.intro.intro
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
hie : i.exit = Exit.count
zs : Inter... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Potential.lean | Box.mem_approx_potential | [153, 1] | [212, 46] | generalize hw' : (f' 2 c')^[i.n] z' = w' | case neg.intro.intro
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
hie : i.exit = Exit.count
zs : Interval
hzs : i.z.normSq = zs
zsn : ¬i.z.normSq = nan
z4 : i.z.no... | case neg.intro.intro
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
hie : i.exit = Exit.count
zs : Interval
hzs : i.z.normSq = zs
zsn : ¬i.z.normSq = nan
z4 : i.z.no... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.intro.intro
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
hie : i.exit = Exit.count
zs : Inter... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Potential.lean | Box.mem_approx_potential | [153, 1] | [212, 46] | have le4 : Real.sqrt 16 ≤ 4 := by rw [Real.sqrt_le_iff]; norm_num | case neg.intro.intro
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
hie : i.exit = Exit.count
zs : Interval
hzs : i.z.normSq = zs
zsn : ¬i.z.normSq = nan
z4 : i.z.no... | case neg.intro.intro
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
hie : i.exit = Exit.count
zs : Interval
hzs : i.z.normSq = zs
zsn : ¬i.z.normSq = nan
z4 : i.z.no... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.intro.intro
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
hie : i.exit = Exit.count
zs : Inter... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Potential.lean | Box.mem_approx_potential | [153, 1] | [212, 46] | apply approx_potential_small | case neg.intro.intro
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
hie : i.exit = Exit.count
zs : Interval
hzs : i.z.normSq = zs
zsn : ¬i.z.normSq = nan
z4 : i.z.no... | case neg.intro.intro.c4
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
hie : i.exit = Exit.count
zs : Interval
hzs : i.z.normSq = zs
zsn : ¬i.z.normSq = nan
z4 : i.z... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.intro.intro
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
hie : i.exit = Exit.count
zs : Inter... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Potential.lean | Box.mem_approx_potential | [153, 1] | [212, 46] | rw [Real.sqrt_le_iff] | c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
hie : i.exit = Exit.count
zs : Interval
hzs : i.z.normSq = zs
zsn : ¬i.z.normSq = nan
z4 : i.z.normSq.hi.val ≤ 16
c4 :... | c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
hie : i.exit = Exit.count
zs : Interval
hzs : i.z.normSq = zs
zsn : ¬i.z.normSq = nan
z4 : i.z.normSq.hi.val ≤ 16
c4 :... | Please generate a tactic in lean4 to solve the state.
STATE:
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
hie : i.exit = Exit.count
zs : Interval
hzs : i.z.normSq ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Potential.lean | Box.mem_approx_potential | [153, 1] | [212, 46] | norm_num | c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
hie : i.exit = Exit.count
zs : Interval
hzs : i.z.normSq = zs
zsn : ¬i.z.normSq = nan
z4 : i.z.normSq.hi.val ≤ 16
c4 :... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
hie : i.exit = Exit.count
zs : Interval
hzs : i.z.normSq ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Potential.lean | Box.mem_approx_potential | [153, 1] | [212, 46] | exact le_trans (Box.abs_le_sqrt_normSq cm csn) (le_trans (Real.sqrt_le_sqrt c4) le4) | case neg.intro.intro.c4
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
hie : i.exit = Exit.count
zs : Interval
hzs : i.z.normSq = zs
zsn : ¬i.z.normSq = nan
z4 : i.z... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.intro.intro.c4
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
hie : i.exit = Exit.count
zs : In... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Potential.lean | Box.mem_approx_potential | [153, 1] | [212, 46] | refine le_trans (Box.abs_le_sqrt_normSq ?_ zsn) (le_trans (Real.sqrt_le_sqrt z4) le4) | case neg.intro.intro.z4
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
hie : i.exit = Exit.count
zs : Interval
hzs : i.z.normSq = zs
zsn : ¬i.z.normSq = nan
z4 : i.z... | case neg.intro.intro.z4
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
hie : i.exit = Exit.count
zs : Interval
hzs : i.z.normSq = zs
zsn : ¬i.z.normSq = nan
z4 : i.z... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.intro.intro.z4
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
hie : i.exit = Exit.count
zs : In... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Potential.lean | Box.mem_approx_potential | [153, 1] | [212, 46] | rw [←hw', ←hi] | case neg.intro.intro.z4
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
hie : i.exit = Exit.count
zs : Interval
hzs : i.z.normSq = zs
zsn : ¬i.z.normSq = nan
z4 : i.z... | case neg.intro.intro.z4
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
hie : i.exit = Exit.count
zs : Interval
hzs : i.z.normSq = zs
zsn : ¬i.z.normSq = nan
z4 : i.z... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.intro.intro.z4
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
hie : i.exit = Exit.count
zs : In... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Potential.lean | Box.mem_approx_potential | [153, 1] | [212, 46] | exact mem_approx_iterate cm zm _ | case neg.intro.intro.z4
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
hie : i.exit = Exit.count
zs : Interval
hzs : i.z.normSq = zs
zsn : ¬i.z.normSq = nan
z4 : i.z... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.intro.intro.z4
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
hie : i.exit = Exit.count
zs : In... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Potential.lean | Box.mem_approx_potential | [153, 1] | [212, 46] | generalize hj : iterate c i.z ((r.mul r true).max (cs.max 36)) 1000 = j | case neg.large
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
csn : ¬cs = nan
hie : i.exit = Exit.large
⊢ s.potential c' ↑z' ∈
approx
(match Exit.large wit... | case neg.large
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
csn : ¬cs = nan
hie : i.exit = Exit.large
j : Iter
hj : iterate c i.z ((r.mul r true).max (cs.max 36)) ... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.large
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
csn : ¬cs = nan
hie : i.exit = Exit.large
... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Potential.lean | Box.mem_approx_potential | [153, 1] | [212, 46] | simp only [hj] | case neg.large
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
csn : ¬cs = nan
hie : i.exit = Exit.large
j : Iter
hj : iterate c i.z ((r.mul r true).max (cs.max 36)) ... | case neg.large
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
csn : ¬cs = nan
hie : i.exit = Exit.large
j : Iter
hj : iterate c i.z ((r.mul r true).max (cs.max 36)) ... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.large
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
csn : ¬cs = nan
hie : i.exit = Exit.large
... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Potential.lean | Box.mem_approx_potential | [153, 1] | [212, 46] | generalize hje : j.exit = je | case neg.large
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
csn : ¬cs = nan
hie : i.exit = Exit.large
j : Iter
hj : iterate c i.z ((r.mul r true).max (cs.max 36)) ... | case neg.large
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
csn : ¬cs = nan
hie : i.exit = Exit.large
j : Iter
hj : iterate c i.z ((r.mul r true).max (cs.max 36)) ... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.large
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
csn : ¬cs = nan
hie : i.exit = Exit.large
... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Potential.lean | Box.mem_approx_potential | [153, 1] | [212, 46] | induction je | case neg.large
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
csn : ¬cs = nan
hie : i.exit = Exit.large
j : Iter
hj : iterate c i.z ((r.mul r true).max (cs.max 36)) ... | case neg.large.count
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
csn : ¬cs = nan
hie : i.exit = Exit.large
j : Iter
hj : iterate c i.z ((r.mul r true).max (cs.max... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.large
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
csn : ¬cs = nan
hie : i.exit = Exit.large
... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Potential.lean | Box.mem_approx_potential | [153, 1] | [212, 46] | simp only [Interval.approx_nan, mem_univ] | case neg.large.count
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
csn : ¬cs = nan
hie : i.exit = Exit.large
j : Iter
hj : iterate c i.z ((r.mul r true).max (cs.max... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.large.count
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
csn : ¬cs = nan
hie : i.exit = Exit.... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Potential.lean | Box.mem_approx_potential | [153, 1] | [212, 46] | simp only | case neg.large.large
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
csn : ¬cs = nan
hie : i.exit = Exit.large
j : Iter
hj : iterate c i.z ((r.mul r true).max (cs.max... | case neg.large.large
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
csn : ¬cs = nan
hie : i.exit = Exit.large
j : Iter
hj : iterate c i.z ((r.mul r true).max (cs.max... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.large.large
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
csn : ¬cs = nan
hie : i.exit = Exit.... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Potential.lean | Box.mem_approx_potential | [153, 1] | [212, 46] | generalize hn : i.n + j.n = n | case neg.large.large
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
csn : ¬cs = nan
hie : i.exit = Exit.large
j : Iter
hj : iterate c i.z ((r.mul r true).max (cs.max... | case neg.large.large
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
csn : ¬cs = nan
hie : i.exit = Exit.large
j : Iter
hj : iterate c i.z ((r.mul r true).max (cs.m... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.large.large
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
csn : ¬cs = nan
hie : i.exit = Exit.... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Potential.lean | Box.mem_approx_potential | [153, 1] | [212, 46] | apply Interval.mem_approx_iter_sqrt' s.potential_nonneg | case neg.large.large
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
csn : ¬cs = nan
hie : i.exit = Exit.large
j : Iter
hj : iterate c i.z ((r.mul r true).max (cs.m... | case neg.large.large
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
csn : ¬cs = nan
hie : i.exit = Exit.large
j : Iter
hj : iterate c i.z ((r.mul r true).max (cs.m... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.large.large
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
csn : ¬cs = nan
hie : i.exit = Exi... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Potential.lean | Box.mem_approx_potential | [153, 1] | [212, 46] | simp only [←s.potential_eqn_iter, f_f'_iter, ←hj] at hje ⊢ | case neg.large.large
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
csn : ¬cs = nan
hie : i.exit = Exit.large
j : Iter
hj : iterate c i.z ((r.mul r true).max (cs.m... | case neg.large.large
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
csn : ¬cs = nan
hie : i.exit = Exit.large
j : Iter
hj : iterate c i.z ((r.mul r true).max (cs.m... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.large.large
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
csn : ¬cs = nan
hie : i.exit = Exi... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Potential.lean | Box.mem_approx_potential | [153, 1] | [212, 46] | generalize hw' : (f' 2 c')^[n] z' = w' | case neg.large.large
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
csn : ¬cs = nan
hie : i.exit = Exit.large
j : Iter
hj : iterate c i.z ((r.mul r true).max (cs.m... | case neg.large.large
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
csn : ¬cs = nan
hie : i.exit = Exit.large
j : Iter
hj : iterate c i.z ((r.mul r true).max (cs.m... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.large.large
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
csn : ¬cs = nan
hie : i.exit = Exi... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Potential.lean | Box.mem_approx_potential | [153, 1] | [212, 46] | have izm : (f' 2 c')^[i.n] z' ∈ approx i.z := by rw [←hi]; exact mem_approx_iterate cm zm _ | case neg.large.large
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
csn : ¬cs = nan
hie : i.exit = Exit.large
j : Iter
hj : iterate c i.z ((r.mul r true).max (cs.m... | case neg.large.large
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
csn : ¬cs = nan
hie : i.exit = Exit.large
j : Iter
hj : iterate c i.z ((r.mul r true).max (cs.m... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.large.large
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
csn : ¬cs = nan
hie : i.exit = Exi... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Potential.lean | Box.mem_approx_potential | [153, 1] | [212, 46] | have jl := iterate_large cm izm hje | case neg.large.large
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
csn : ¬cs = nan
hie : i.exit = Exit.large
j : Iter
hj : iterate c i.z ((r.mul r true).max (cs.m... | case neg.large.large
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
csn : ¬cs = nan
hie : i.exit = Exit.large
j : Iter
hj : iterate c i.z ((r.mul r true).max (cs.m... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.large.large
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
csn : ¬cs = nan
hie : i.exit = Exi... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Potential.lean | Box.mem_approx_potential | [153, 1] | [212, 46] | have jrn := ne_nan_of_iterate (hje.trans_ne (by decide)) | case neg.large.large
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
csn : ¬cs = nan
hie : i.exit = Exit.large
j : Iter
hj : iterate c i.z ((r.mul r true).max (cs.m... | case neg.large.large
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
csn : ¬cs = nan
hie : i.exit = Exit.large
j : Iter
hj : iterate c i.z ((r.mul r true).max (cs.m... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.large.large
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
csn : ¬cs = nan
hie : i.exit = Exi... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Potential.lean | Box.mem_approx_potential | [153, 1] | [212, 46] | simp only [hj, ← Function.iterate_add_apply, add_comm _ i.n, hn, hw'] at jl | case neg.large.large
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
csn : ¬cs = nan
hie : i.exit = Exit.large
j : Iter
hj : iterate c i.z ((r.mul r true).max (cs.m... | case neg.large.large
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
csn : ¬cs = nan
hie : i.exit = Exit.large
j : Iter
hj : iterate c i.z ((r.mul r true).max (cs.m... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.large.large
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
csn : ¬cs = nan
hie : i.exit = Exi... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Potential.lean | Box.mem_approx_potential | [153, 1] | [212, 46] | simp only [ne_eq, Floating.max_eq_nan, not_or] at jrn | case neg.large.large
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
csn : ¬cs = nan
hie : i.exit = Exit.large
j : Iter
hj : iterate c i.z ((r.mul r true).max (cs.m... | case neg.large.large
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
csn : ¬cs = nan
hie : i.exit = Exit.large
j : Iter
hj : iterate c i.z ((r.mul r true).max (cs.m... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.large.large
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
csn : ¬cs = nan
hie : i.exit = Exi... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Potential.lean | Box.mem_approx_potential | [153, 1] | [212, 46] | rw [Floating.val_max jrn.1 (Floating.max_ne_nan.mpr jrn.2),
Floating.val_max jrn.2.1 jrn.2.2, max_lt_iff, max_lt_iff, Floating.val_ofNat,
Nat.cast_eq_ofNat] at jl | case neg.large.large
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
csn : ¬cs = nan
hie : i.exit = Exit.large
j : Iter
hj : iterate c i.z ((r.mul r true).max (cs.m... | case neg.large.large
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
csn : ¬cs = nan
hie : i.exit = Exit.large
j : Iter
hj : iterate c i.z ((r.mul r true).max (cs.m... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.large.large
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
csn : ¬cs = nan
hie : i.exit = Exi... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Potential.lean | Box.mem_approx_potential | [153, 1] | [212, 46] | apply approx_potential_large | case neg.large.large
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
csn : ¬cs = nan
hie : i.exit = Exit.large
j : Iter
hj : iterate c i.z ((r.mul r true).max (cs.m... | case neg.large.large.cz
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
csn : ¬cs = nan
hie : i.exit = Exit.large
j : Iter
hj : iterate c i.z ((r.mul r true).max (c... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.large.large
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
csn : ¬cs = nan
hie : i.exit = Exi... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Potential.lean | Box.mem_approx_potential | [153, 1] | [212, 46] | rw [←hi] | c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
csn : ¬cs = nan
hie : i.exit = Exit.large
j : Iter
hj : iterate c i.z ((r.mul r true).max (cs.max 36)) 1000 = j
n : ... | c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
csn : ¬cs = nan
hie : i.exit = Exit.large
j : Iter
hj : iterate c i.z ((r.mul r true).max (cs.max 36)) 1000 = j
n : ... | Please generate a tactic in lean4 to solve the state.
STATE:
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
csn : ¬cs = nan
hie : i.exit = Exit.large
j : Iter
hj :... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Potential.lean | Box.mem_approx_potential | [153, 1] | [212, 46] | exact mem_approx_iterate cm zm _ | c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
csn : ¬cs = nan
hie : i.exit = Exit.large
j : Iter
hj : iterate c i.z ((r.mul r true).max (cs.max 36)) 1000 = j
n : ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
csn : ¬cs = nan
hie : i.exit = Exit.large
j : Iter
hj :... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Potential.lean | Box.mem_approx_potential | [153, 1] | [212, 46] | decide | c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
csn : ¬cs = nan
hie : i.exit = Exit.large
j : Iter
hj : iterate c i.z ((r.mul r true).max (cs.max 36)) 1000 = j
n : ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
csn : ¬cs = nan
hie : i.exit = Exit.large
j : Iter
hj :... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Potential.lean | Box.mem_approx_potential | [153, 1] | [212, 46] | refine le_trans ?_ (le_trans (Real.sqrt_le_sqrt jl.2.1.le) ?_) | case neg.large.large.cz
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
csn : ¬cs = nan
hie : i.exit = Exit.large
j : Iter
hj : iterate c i.z ((r.mul r true).max (c... | case neg.large.large.cz.refine_1
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
csn : ¬cs = nan
hie : i.exit = Exit.large
j : Iter
hj : iterate c i.z ((r.mul r tru... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.large.large.cz
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
csn : ¬cs = nan
hie : i.exit = ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Potential.lean | Box.mem_approx_potential | [153, 1] | [212, 46] | simp only [← hcs, Interval.hi_eq_nan] at csn ⊢ | case neg.large.large.cz.refine_1
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
csn : ¬cs = nan
hie : i.exit = Exit.large
j : Iter
hj : iterate c i.z ((r.mul r tru... | case neg.large.large.cz.refine_1
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
hie : i.exit = Exit.large
j : Iter
hj : iterate c i.z ((r.mul r true).max (cs.max 3... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.large.large.cz.refine_1
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
csn : ¬cs = nan
hie : ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Potential.lean | Box.mem_approx_potential | [153, 1] | [212, 46] | exact abs_le_sqrt_normSq cm csn | case neg.large.large.cz.refine_1
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
hie : i.exit = Exit.large
j : Iter
hj : iterate c i.z ((r.mul r true).max (cs.max 3... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.large.large.cz.refine_1
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
hie : i.exit = Exit.la... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Potential.lean | Box.mem_approx_potential | [153, 1] | [212, 46] | simp only [apply_nonneg, Real.sqrt_sq, le_refl] | case neg.large.large.cz.refine_2
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
csn : ¬cs = nan
hie : i.exit = Exit.large
j : Iter
hj : iterate c i.z ((r.mul r tru... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.large.large.cz.refine_2
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
csn : ¬cs = nan
hie : ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Potential.lean | Box.mem_approx_potential | [153, 1] | [212, 46] | refine le_trans ?_ (le_trans (Real.sqrt_le_sqrt jl.2.2.le) ?_) | case neg.large.large.z6
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
csn : ¬cs = nan
hie : i.exit = Exit.large
j : Iter
hj : iterate c i.z ((r.mul r true).max (c... | case neg.large.large.z6.refine_1
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
csn : ¬cs = nan
hie : i.exit = Exit.large
j : Iter
hj : iterate c i.z ((r.mul r tru... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.large.large.z6
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
csn : ¬cs = nan
hie : i.exit = ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Potential.lean | Box.mem_approx_potential | [153, 1] | [212, 46] | have e : (36 : ℝ) = 6 ^ 2 := by norm_num | case neg.large.large.z6.refine_1
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
csn : ¬cs = nan
hie : i.exit = Exit.large
j : Iter
hj : iterate c i.z ((r.mul r tru... | case neg.large.large.z6.refine_1
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
csn : ¬cs = nan
hie : i.exit = Exit.large
j : Iter
hj : iterate c i.z ((r.mul r tru... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.large.large.z6.refine_1
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
csn : ¬cs = nan
hie : ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Potential.lean | Box.mem_approx_potential | [153, 1] | [212, 46] | rw [e, Real.sqrt_sq (by norm_num)] | case neg.large.large.z6.refine_1
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
csn : ¬cs = nan
hie : i.exit = Exit.large
j : Iter
hj : iterate c i.z ((r.mul r tru... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.large.large.z6.refine_1
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
csn : ¬cs = nan
hie : ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Potential.lean | Box.mem_approx_potential | [153, 1] | [212, 46] | norm_num | c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
csn : ¬cs = nan
hie : i.exit = Exit.large
j : Iter
hj : iterate c i.z ((r.mul r true).max (cs.max 36)) 1000 = j
n : ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
csn : ¬cs = nan
hie : i.exit = Exit.large
j : Iter
hj :... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Potential.lean | Box.mem_approx_potential | [153, 1] | [212, 46] | norm_num | c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
csn : ¬cs = nan
hie : i.exit = Exit.large
j : Iter
hj : iterate c i.z ((r.mul r true).max (cs.max 36)) 1000 = j
n : ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
csn : ¬cs = nan
hie : i.exit = Exit.large
j : Iter
hj :... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Potential.lean | Box.mem_approx_potential | [153, 1] | [212, 46] | simp only [apply_nonneg, Real.sqrt_sq, le_refl] | case neg.large.large.z6.refine_2
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
csn : ¬cs = nan
hie : i.exit = Exit.large
j : Iter
hj : iterate c i.z ((r.mul r tru... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.large.large.z6.refine_2
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
csn : ¬cs = nan
hie : ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Potential.lean | Box.mem_approx_potential | [153, 1] | [212, 46] | rw [←hw', ←hn, add_comm _ j.n, Function.iterate_add_apply, ←hj] | case neg.large.large.zm
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
csn : ¬cs = nan
hie : i.exit = Exit.large
j : Iter
hj : iterate c i.z ((r.mul r true).max (c... | case neg.large.large.zm
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
csn : ¬cs = nan
hie : i.exit = Exit.large
j : Iter
hj : iterate c i.z ((r.mul r true).max (c... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.large.large.zm
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
csn : ¬cs = nan
hie : i.exit = ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Potential.lean | Box.mem_approx_potential | [153, 1] | [212, 46] | exact mem_approx_iterate cm izm _ | case neg.large.large.zm
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
csn : ¬cs = nan
hie : i.exit = Exit.large
j : Iter
hj : iterate c i.z ((r.mul r true).max (c... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.large.large.zm
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n✝ : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n✝ = i
csn : ¬cs = nan
hie : i.exit = ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Potential.lean | Box.mem_approx_potential | [153, 1] | [212, 46] | simp only [Interval.approx_nan, mem_univ] | case neg.large.nan
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
csn : ¬cs = nan
hie : i.exit = Exit.large
j : Iter
hj : iterate c i.z ((r.mul r true).max (cs.max 3... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.large.nan
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
csn : ¬cs = nan
hie : i.exit = Exit.la... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Potential.lean | Box.mem_approx_potential | [153, 1] | [212, 46] | simp only [Interval.approx_nan, mem_univ] | case neg.nan
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
csn : ¬cs = nan
hie : i.exit = Exit.nan
⊢ s.potential c' ↑z' ∈
approx
(match Exit.nan with
... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.nan
c' z' : ℂ
c z : Box
cm : c' ∈ approx c
zm : z' ∈ approx z
n : ℕ
r : Floating
s : Super (f 2) 2 OnePoint.infty := superF 2
cs : Floating
hcs : c.normSq.hi = cs
i : Iter
hi : iterate c z (cs.max 9) n = i
csn : ¬cs = nan
hie : i.exit = Exit.nan
⊢ s.... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Potential.lean | Box.mem_approx_potential' | [214, 1] | [217, 83] | simp only [_root_.potential, RiemannSphere.fill_coe, mem_approx_potential cm cm] | c' : ℂ
c : Box
cm : c' ∈ approx c
n : ℕ
r : Floating
⊢ _root_.potential 2 ↑c' ∈ approx (c.potential c n r).1 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
c' : ℂ
c : Box
cm : c' ∈ approx c
n : ℕ
r : Floating
⊢ _root_.potential 2 ↑c' ∈ approx (c.potential c n r).1
TACTIC:
|
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/OpenMapping.lean | nontrivial_local_of_global | [46, 1] | [61, 29] | have fh : HolomorphicOn I I f (closedBall z r) := fun _ m ↦ (fa _ m).holomorphicAt I I | X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticManifold 𝓘(ℂ... | X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticManifold 𝓘(ℂ... | Please generate a tactic in lean4 to solve the state.
STATE:
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : Topologica... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/OpenMapping.lean | nontrivial_local_of_global | [46, 1] | [61, 29] | have zs : z ∈ closedBall z r := mem_closedBall_self rp.le | X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticManifold 𝓘(ℂ... | X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticManifold 𝓘(ℂ... | Please generate a tactic in lean4 to solve the state.
STATE:
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : Topologica... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/OpenMapping.lean | nontrivial_local_of_global | [46, 1] | [61, 29] | use fh _ zs | X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticManifold 𝓘(ℂ... | case nonconst
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : Analyti... | Please generate a tactic in lean4 to solve the state.
STATE:
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : Topologica... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/OpenMapping.lean | nontrivial_local_of_global | [46, 1] | [61, 29] | contrapose ef | case nonconst
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : Analyti... | case nonconst
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : Analyti... | Please generate a tactic in lean4 to solve the state.
STATE:
case nonconst
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/OpenMapping.lean | nontrivial_local_of_global | [46, 1] | [61, 29] | simp only [Filter.not_frequently, not_not] at ef | case nonconst
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : Analyti... | case nonconst
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : Analyti... | Please generate a tactic in lean4 to solve the state.
STATE:
case nonconst
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/OpenMapping.lean | nontrivial_local_of_global | [46, 1] | [61, 29] | simp only [not_forall, not_le] | case nonconst
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : Analyti... | case nonconst
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : Analyti... | Please generate a tactic in lean4 to solve the state.
STATE:
case nonconst
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/OpenMapping.lean | nontrivial_local_of_global | [46, 1] | [61, 29] | have zrs : z + r ∈ sphere z r := by
simp only [mem_sphere, Complex.dist_eq, add_sub_cancel_left, Complex.abs_ofReal, abs_of_pos rp] | case nonconst
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : Analyti... | case nonconst
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : Analyti... | Please generate a tactic in lean4 to solve the state.
STATE:
case nonconst
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/OpenMapping.lean | nontrivial_local_of_global | [46, 1] | [61, 29] | use z + r, zrs | case nonconst
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : Analyti... | case h
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticManifo... | Please generate a tactic in lean4 to solve the state.
STATE:
case nonconst
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/OpenMapping.lean | nontrivial_local_of_global | [46, 1] | [61, 29] | simp only [fh.const_of_locally_const' zs (convex_closedBall z r).isPreconnected ef (z + r)
(Metric.sphere_subset_closedBall zrs),
sub_self, norm_zero, ep] | case h
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticManifo... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : Top... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/OpenMapping.lean | nontrivial_local_of_global | [46, 1] | [61, 29] | simp only [mem_sphere, Complex.dist_eq, add_sub_cancel_left, Complex.abs_ofReal, abs_of_pos rp] | X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticManifold 𝓘(ℂ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : Topologica... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/OpenMapping.lean | AnalyticOn.ball_subset_image_closedBall_param | [65, 1] | [101, 101] | have fn : ∀ d, d ∈ u → ∃ᶠ w in 𝓝 z, f d w ≠ f d z := by
refine fun d m ↦ (nontrivial_local_of_global (fa.along_snd.mono ?_) rp ep (ef d m)).nonconst
simp only [← closedBall_prod_same, mem_prod_eq, setOf_mem_eq, iff_true_iff.mpr m,
true_and_iff, subset_refl] | X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticManifold 𝓘(ℂ... | X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticManifold 𝓘(ℂ... | Please generate a tactic in lean4 to solve the state.
STATE:
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : Topologica... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/OpenMapping.lean | AnalyticOn.ball_subset_image_closedBall_param | [65, 1] | [101, 101] | have op : ∀ d, d ∈ u → ball (f d z) (e / 2) ⊆ f d '' closedBall z r := by
intro d du; refine DiffContOnCl.ball_subset_image_closedBall ?_ rp (ef d du) (fn d du)
have e : f d = uncurry f ∘ fun w ↦ (d, w) := rfl
rw [e]; apply DifferentiableOn.diffContOnCl; apply AnalyticOn.differentiableOn
refine fa.comp (analyti... | X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticManifold 𝓘(ℂ... | X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticManifold 𝓘(ℂ... | Please generate a tactic in lean4 to solve the state.
STATE:
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : Topologica... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/OpenMapping.lean | AnalyticOn.ball_subset_image_closedBall_param | [65, 1] | [101, 101] | rcases Metric.continuousAt_iff.mp
(fa (c, z) (mk_mem_prod (mem_of_mem_nhds un) (mem_closedBall_self rp.le))).continuousAt
(e / 4) (by linarith) with
⟨s, sp, sh⟩ | X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticManifold 𝓘(ℂ... | case intro.intro
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : Anal... | Please generate a tactic in lean4 to solve the state.
STATE:
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : Topologica... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/OpenMapping.lean | AnalyticOn.ball_subset_image_closedBall_param | [65, 1] | [101, 101] | rw [mem_nhds_prod_iff] | case intro.intro
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : Anal... | case intro.intro
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : Anal... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
in... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/OpenMapping.lean | AnalyticOn.ball_subset_image_closedBall_param | [65, 1] | [101, 101] | refine ⟨u ∩ ball c s, Filter.inter_mem un (Metric.ball_mem_nhds c (by linarith)), ?_⟩ | case intro.intro
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : Anal... | case intro.intro
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : Anal... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
in... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/OpenMapping.lean | AnalyticOn.ball_subset_image_closedBall_param | [65, 1] | [101, 101] | use ball (f c z) (e / 4), Metric.ball_mem_nhds _ (by linarith) | case intro.intro
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : Anal... | case right
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticMa... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
in... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/OpenMapping.lean | AnalyticOn.ball_subset_image_closedBall_param | [65, 1] | [101, 101] | intro ⟨d, w⟩ m | case right
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticMa... | case right
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticMa... | Please generate a tactic in lean4 to solve the state.
STATE:
case right
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ :... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/OpenMapping.lean | AnalyticOn.ball_subset_image_closedBall_param | [65, 1] | [101, 101] | simp only [mem_inter_iff, mem_prod_eq, mem_image, @mem_ball _ _ c, lt_min_iff] at m op ⊢ | case right
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticMa... | case right
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticMa... | Please generate a tactic in lean4 to solve the state.
STATE:
case right
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ :... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/OpenMapping.lean | AnalyticOn.ball_subset_image_closedBall_param | [65, 1] | [101, 101] | have wm : w ∈ ball (f d z) (e / 2) := by
simp only [mem_ball] at m ⊢
specialize @sh ⟨d, z⟩; simp only [Prod.dist_eq, dist_self, Function.uncurry] at sh
specialize sh (max_lt m.1.2 sp); rw [dist_comm] at sh
calc dist w (f d z)
_ ≤ dist w (f c z) + dist (f c z) (f d z) := by bound
_ < e / 4 + dist (f c z)... | case right
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticMa... | case right
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticMa... | Please generate a tactic in lean4 to solve the state.
STATE:
case right
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ :... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/OpenMapping.lean | AnalyticOn.ball_subset_image_closedBall_param | [65, 1] | [101, 101] | specialize op d m.1.1 wm | case right
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticMa... | case right
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticMa... | Please generate a tactic in lean4 to solve the state.
STATE:
case right
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ :... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/OpenMapping.lean | AnalyticOn.ball_subset_image_closedBall_param | [65, 1] | [101, 101] | rcases (mem_image _ _ _).mp op with ⟨y, yr, yw⟩ | case right
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticMa... | case right.intro.intro
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu ... | Please generate a tactic in lean4 to solve the state.
STATE:
case right
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ :... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/OpenMapping.lean | AnalyticOn.ball_subset_image_closedBall_param | [65, 1] | [101, 101] | use⟨d, y⟩ | case right.intro.intro
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu ... | case h
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticManifo... | Please generate a tactic in lean4 to solve the state.
STATE:
case right.intro.intro
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : T... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/OpenMapping.lean | AnalyticOn.ball_subset_image_closedBall_param | [65, 1] | [101, 101] | simp only [mem_prod_eq, Prod.ext_iff, yw, and_true_iff, eq_self_iff_true, true_and_iff, yr, m.1.1] | case h
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticManifo... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : Top... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/OpenMapping.lean | AnalyticOn.ball_subset_image_closedBall_param | [65, 1] | [101, 101] | refine fun d m ↦ (nontrivial_local_of_global (fa.along_snd.mono ?_) rp ep (ef d m)).nonconst | X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticManifold 𝓘(ℂ... | X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticManifold 𝓘(ℂ... | Please generate a tactic in lean4 to solve the state.
STATE:
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : Topologica... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/OpenMapping.lean | AnalyticOn.ball_subset_image_closedBall_param | [65, 1] | [101, 101] | simp only [← closedBall_prod_same, mem_prod_eq, setOf_mem_eq, iff_true_iff.mpr m,
true_and_iff, subset_refl] | X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticManifold 𝓘(ℂ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : Topologica... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/OpenMapping.lean | AnalyticOn.ball_subset_image_closedBall_param | [65, 1] | [101, 101] | intro d du | X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticManifold 𝓘(ℂ... | X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticManifold 𝓘(ℂ... | Please generate a tactic in lean4 to solve the state.
STATE:
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : Topologica... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/OpenMapping.lean | AnalyticOn.ball_subset_image_closedBall_param | [65, 1] | [101, 101] | refine DiffContOnCl.ball_subset_image_closedBall ?_ rp (ef d du) (fn d du) | X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticManifold 𝓘(ℂ... | X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticManifold 𝓘(ℂ... | Please generate a tactic in lean4 to solve the state.
STATE:
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : Topologica... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/OpenMapping.lean | AnalyticOn.ball_subset_image_closedBall_param | [65, 1] | [101, 101] | have e : f d = uncurry f ∘ fun w ↦ (d, w) := rfl | X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticManifold 𝓘(ℂ... | X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticManifold 𝓘(ℂ... | Please generate a tactic in lean4 to solve the state.
STATE:
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : Topologica... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/OpenMapping.lean | AnalyticOn.ball_subset_image_closedBall_param | [65, 1] | [101, 101] | rw [e] | X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticManifold 𝓘(ℂ... | X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticManifold 𝓘(ℂ... | Please generate a tactic in lean4 to solve the state.
STATE:
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : Topologica... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/OpenMapping.lean | AnalyticOn.ball_subset_image_closedBall_param | [65, 1] | [101, 101] | apply DifferentiableOn.diffContOnCl | X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticManifold 𝓘(ℂ... | case h
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticManifo... | Please generate a tactic in lean4 to solve the state.
STATE:
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : Topologica... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/OpenMapping.lean | AnalyticOn.ball_subset_image_closedBall_param | [65, 1] | [101, 101] | apply AnalyticOn.differentiableOn | case h
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticManifo... | case h.h
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticMani... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : Top... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/OpenMapping.lean | AnalyticOn.ball_subset_image_closedBall_param | [65, 1] | [101, 101] | refine fa.comp (analyticOn_const.prod (analyticOn_id _)) ?_ | case h.h
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticMani... | case h.h
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticMani... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : T... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/OpenMapping.lean | AnalyticOn.ball_subset_image_closedBall_param | [65, 1] | [101, 101] | intro w wr | case h.h
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticMani... | case h.h
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticMani... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : T... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/OpenMapping.lean | AnalyticOn.ball_subset_image_closedBall_param | [65, 1] | [101, 101] | simp only [closure_ball _ rp.ne'] at wr | case h.h
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticMani... | case h.h
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticMani... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : T... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/OpenMapping.lean | AnalyticOn.ball_subset_image_closedBall_param | [65, 1] | [101, 101] | simp only [← closedBall_prod_same, mem_prod_eq, du, wr, true_and_iff, du] | case h.h
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticMani... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : T... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/AnalyticManifold/OpenMapping.lean | AnalyticOn.ball_subset_image_closedBall_param | [65, 1] | [101, 101] | linarith | X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : TopologicalSpace U
inst✝ : ChartedSpace ℂ U
cmu : AnalyticManifold 𝓘(ℂ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
X : Type
inst✝⁶ : TopologicalSpace X
S : Type
inst✝⁵ : TopologicalSpace S
inst✝⁴ : ChartedSpace ℂ S
cms : AnalyticManifold 𝓘(ℂ, ℂ) S
T : Type
inst✝³ : TopologicalSpace T
inst✝² : ChartedSpace ℂ T
cmt : AnalyticManifold 𝓘(ℂ, ℂ) T
U : Type
inst✝¹ : Topologica... |
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