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/Misc/Measure.lean | mean_squeeze | [222, 1] | [281, 33] | have mb : m < b := by
calc (b + f x) / 2
_ < (b + b) / 2 := (div_lt_div_right (by norm_num)).mpr (by bound)
_ = b := by ring | case intro.intro.intro.intro
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpac... | case intro.intro.intro.intro
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpac... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.intro
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | mean_squeeze | [222, 1] | [281, 33] | have i0 : ∫ x in s \ t, f x ≤ (vs - vt) * b := by
have df : volume (s \ t) < ⊤ := lt_of_le_of_lt (measure_mono (Set.diff_subset _ _)) sn.finite
have dm : MeasurableSet (s \ t) := MeasurableSet.diff sn.measurable tm
have fb := @setIntegral_mono_on _ _ volume f (fun _ ↦ b) (s \ t)
(fi.mono (Set.diff_subset _ _)... | case intro.intro.intro.intro
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpac... | case intro.intro.intro.intro
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpac... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.intro
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | mean_squeeze | [222, 1] | [281, 33] | have i1 : ∫ x in t, f x ≤ vt * m := by
have fm := @setIntegral_mono_on _ _ volume f (fun _ ↦ m) t (fi.mono ts (le_refl _))
(integrableOn_const.mpr (Or.inr tf)) tm ?_
simp at fm; exact fm
intro y yt
rw [← ht] at yt; simp at ht yt
specialize he y yt.left yt.right
simp [Real.dist_eq] at he
calc f y
_... | case intro.intro.intro.intro
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpac... | case intro.intro.intro.intro
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpac... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.intro
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | mean_squeeze | [222, 1] | [281, 33] | calc (∫ x : X in s \ t, f x) + ∫ x : X in t, f x
_ ≤ (vs - vt) * b + vt * m := by bound
_ = vs * b - vt * (b - m) := by ring
_ < vs * b - 0 := (sub_lt_sub_left (by bound) _)
_ = b * vs := by ring | case intro.intro.intro.intro
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpac... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.intro
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | mean_squeeze | [222, 1] | [281, 33] | calc (b + f x) / 2
_ < (b + b) / 2 := (div_lt_div_right (by norm_num)).mpr (by bound)
_ = b := by ring | E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type
inst✝³ : Measure... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | mean_squeeze | [222, 1] | [281, 33] | norm_num | E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type
inst✝³ : Measure... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | mean_squeeze | [222, 1] | [281, 33] | bound | E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type
inst✝³ : Measure... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | mean_squeeze | [222, 1] | [281, 33] | ring | E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type
inst✝³ : Measure... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | mean_squeeze | [222, 1] | [281, 33] | have df : volume (s \ t) < ⊤ := lt_of_le_of_lt (measure_mono (Set.diff_subset _ _)) sn.finite | E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type
inst✝³ : Measure... | E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type
inst✝³ : Measure... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | mean_squeeze | [222, 1] | [281, 33] | have dm : MeasurableSet (s \ t) := MeasurableSet.diff sn.measurable tm | E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type
inst✝³ : Measure... | E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type
inst✝³ : Measure... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | mean_squeeze | [222, 1] | [281, 33] | have fb := @setIntegral_mono_on _ _ volume f (fun _ ↦ b) (s \ t)
(fi.mono (Set.diff_subset _ _) (le_refl _)) (integrableOn_const.mpr (Or.inr df)) dm ?_ | E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type
inst✝³ : Measure... | case refine_2
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type
in... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | mean_squeeze | [222, 1] | [281, 33] | simp [measure_diff ts tm (lt_top_iff_ne_top.mp tf),
ENNReal.toReal_sub_of_le (measure_mono ts) (lt_top_iff_ne_top.mp sn.finite)] at fb | case refine_2
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type
in... | case refine_2
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type
in... | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_2
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpa... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | mean_squeeze | [222, 1] | [281, 33] | exact fb | case refine_2
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type
in... | case refine_1
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type
in... | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_2
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpa... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | mean_squeeze | [222, 1] | [281, 33] | intro y yd | case refine_1
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type
in... | case refine_1
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type
in... | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_1
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpa... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | mean_squeeze | [222, 1] | [281, 33] | simp at yd | case refine_1
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type
in... | case refine_1
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type
in... | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_1
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpa... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | mean_squeeze | [222, 1] | [281, 33] | exact hi y yd.left | case refine_1
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type
in... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_1
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpa... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | mean_squeeze | [222, 1] | [281, 33] | have fm := @setIntegral_mono_on _ _ volume f (fun _ ↦ m) t (fi.mono ts (le_refl _))
(integrableOn_const.mpr (Or.inr tf)) tm ?_ | E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type
inst✝³ : Measure... | case refine_2
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type
in... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | mean_squeeze | [222, 1] | [281, 33] | simp at fm | case refine_2
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type
in... | case refine_2
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type
in... | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_2
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpa... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | mean_squeeze | [222, 1] | [281, 33] | exact fm | case refine_2
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type
in... | case refine_1
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type
in... | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_2
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpa... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | mean_squeeze | [222, 1] | [281, 33] | intro y yt | case refine_1
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type
in... | case refine_1
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type
in... | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_1
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpa... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | mean_squeeze | [222, 1] | [281, 33] | rw [← ht] at yt | case refine_1
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type
in... | case refine_1
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type
in... | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_1
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpa... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | mean_squeeze | [222, 1] | [281, 33] | simp at ht yt | case refine_1
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type
in... | case refine_1
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type
in... | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_1
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpa... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | mean_squeeze | [222, 1] | [281, 33] | specialize he y yt.left yt.right | case refine_1
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type
in... | case refine_1
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type
in... | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_1
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpa... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | mean_squeeze | [222, 1] | [281, 33] | simp [Real.dist_eq] at he | case refine_1
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type
in... | case refine_1
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type
in... | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_1
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpa... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | mean_squeeze | [222, 1] | [281, 33] | calc f y
_ = f x + (f y - f x) := by ring
_ ≤ f x + |f y - f x| := by bound
_ ≤ f x + (b - f x) / 2 := by bound
_ = (b + f x) / 2 := by ring | case refine_1
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type
in... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_1
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpa... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | mean_squeeze | [222, 1] | [281, 33] | ring | E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type
inst✝³ : Measure... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | mean_squeeze | [222, 1] | [281, 33] | bound | E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type
inst✝³ : Measure... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | mean_squeeze | [222, 1] | [281, 33] | bound | E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type
inst✝³ : Measure... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | mean_squeeze | [222, 1] | [281, 33] | ring | E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type
inst✝³ : Measure... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | mean_squeeze | [222, 1] | [281, 33] | bound | E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type
inst✝³ : Measure... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | mean_squeeze | [222, 1] | [281, 33] | ring | E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type
inst✝³ : Measure... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | mean_squeeze | [222, 1] | [281, 33] | bound | E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type
inst✝³ : Measure... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | mean_squeeze | [222, 1] | [281, 33] | ring | E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type
inst✝³ : Measure... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | mean_squeeze | [222, 1] | [281, 33] | rw [disjoint_comm] | case intro.intro.intro.intro.hst
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : Borel... | case intro.intro.intro.intro.hst
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : Borel... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.intro.hst
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | mean_squeeze | [222, 1] | [281, 33] | exact Set.disjoint_sdiff_right | case intro.intro.intro.intro.hst
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : Borel... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.intro.hst
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | mean_squeeze | [222, 1] | [281, 33] | exact tm | case intro.intro.intro.intro.ht
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelS... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.intro.ht
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
i... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | mean_squeeze | [222, 1] | [281, 33] | exact fi.mono (Set.diff_subset _ _) (le_refl _) | case intro.intro.intro.intro.hfs
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : Borel... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.intro.hfs
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | mean_squeeze | [222, 1] | [281, 33] | exact fi.mono ts (le_refl _) | case intro.intro.intro.intro.hft
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : Borel... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.intro.hft
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | ContinuousOn.intervalIntegral | [283, 1] | [305, 17] | rcases ((sc.prod isCompact_Icc).bddAbove_image fc.norm).exists_ge 0 with ⟨c, _, fb⟩ | E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type
inst✝³ : Measure... | case intro.intro
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | ContinuousOn.intervalIntegral | [283, 1] | [305, 17] | simp only [Set.forall_mem_image] at fb | case intro.intro
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type... | case intro.intro
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : Measure... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | ContinuousOn.intervalIntegral | [283, 1] | [305, 17] | simp only [Set.forall_prod_set, uncurry] at fb | case intro.intro
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type... | case intro.intro
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : Measure... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | ContinuousOn.intervalIntegral | [283, 1] | [305, 17] | have e : ∀ x t, f x t = (uncurry f) (x, t) := by
simp only [Function.uncurry_apply_pair, eq_self_iff_true, forall_const, imp_true_iff] | case intro.intro
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type... | case intro.intro
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : Measure... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | ContinuousOn.intervalIntegral | [283, 1] | [305, 17] | intro x xs | case intro.intro
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type... | case intro.intro
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : Measure... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | ContinuousOn.intervalIntegral | [283, 1] | [305, 17] | apply intervalIntegral.continuousWithinAt_of_dominated_interval (bound := fun _ ↦ c) | case intro.intro
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type... | case intro.intro.hF_meas
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : Measure... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | ContinuousOn.intervalIntegral | [283, 1] | [305, 17] | simp only [Function.uncurry_apply_pair, eq_self_iff_true, forall_const, imp_true_iff] | E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type
inst✝³ : Measure... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | ContinuousOn.intervalIntegral | [283, 1] | [305, 17] | apply eventually_nhdsWithin_of_forall | case intro.intro.hF_meas
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
... | case intro.intro.hF_meas.h
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace ... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.hF_meas
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ :... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | ContinuousOn.intervalIntegral | [283, 1] | [305, 17] | intro y ys | case intro.intro.hF_meas.h
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace ... | case intro.intro.hF_meas.h
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace ... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.hF_meas.h
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | ContinuousOn.intervalIntegral | [283, 1] | [305, 17] | refine ContinuousOn.aestronglyMeasurable ?_ measurableSet_Ioc | case intro.intro.hF_meas.h
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace ... | case intro.intro.hF_meas.h
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace ... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.hF_meas.h
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | ContinuousOn.intervalIntegral | [283, 1] | [305, 17] | rw [Set.uIoc_of_le ab] | case intro.intro.hF_meas.h
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace ... | case intro.intro.hF_meas.h
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace ... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.hF_meas.h
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | ContinuousOn.intervalIntegral | [283, 1] | [305, 17] | simp_rw [e] | case intro.intro.hF_meas.h
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace ... | case intro.intro.hF_meas.h
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace ... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.hF_meas.h
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | ContinuousOn.intervalIntegral | [283, 1] | [305, 17] | apply fc.comp | case intro.intro.hF_meas.h
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace ... | case intro.intro.hF_meas.h.hf
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpa... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.hF_meas.h
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | ContinuousOn.intervalIntegral | [283, 1] | [305, 17] | apply Continuous.continuousOn | case intro.intro.hF_meas.h.hf
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpa... | case intro.intro.hF_meas.h.hf.h
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelS... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.hF_meas.h.hf
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
ins... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | ContinuousOn.intervalIntegral | [283, 1] | [305, 17] | exact Continuous.Prod.mk y | case intro.intro.hF_meas.h.hf.h
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelS... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.hF_meas.h.hf.h
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
i... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | ContinuousOn.intervalIntegral | [283, 1] | [305, 17] | intro t ts | case intro.intro.hF_meas.h.h
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpac... | case intro.intro.hF_meas.h.h
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpac... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.hF_meas.h.h
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | ContinuousOn.intervalIntegral | [283, 1] | [305, 17] | exact Set.mk_mem_prod ys (Set.Ioc_subset_Icc_self ts) | case intro.intro.hF_meas.h.h
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpac... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.hF_meas.h.h
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | ContinuousOn.intervalIntegral | [283, 1] | [305, 17] | apply eventually_nhdsWithin_of_forall | case intro.intro.h_bound
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
... | case intro.intro.h_bound.h
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace ... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.h_bound
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ :... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | ContinuousOn.intervalIntegral | [283, 1] | [305, 17] | intro y ys | case intro.intro.h_bound.h
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace ... | case intro.intro.h_bound.h
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace ... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.h_bound.h
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | ContinuousOn.intervalIntegral | [283, 1] | [305, 17] | rw [Set.uIoc_of_le ab] | case intro.intro.h_bound.h
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace ... | case intro.intro.h_bound.h
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace ... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.h_bound.h
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | ContinuousOn.intervalIntegral | [283, 1] | [305, 17] | apply ae_of_all | case intro.intro.h_bound.h
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace ... | case intro.intro.h_bound.h.a
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpac... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.h_bound.h
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | ContinuousOn.intervalIntegral | [283, 1] | [305, 17] | intro t ts | case intro.intro.h_bound.h.a
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpac... | case intro.intro.h_bound.h.a
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpac... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.h_bound.h.a
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | ContinuousOn.intervalIntegral | [283, 1] | [305, 17] | apply fb _ ys _ (Set.Ioc_subset_Icc_self ts) | case intro.intro.h_bound.h.a
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpac... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.h_bound.h.a
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | ContinuousOn.intervalIntegral | [283, 1] | [305, 17] | exact intervalIntegrable_const | case intro.intro.bound_integrable
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : Bore... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.bound_integrable
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | ContinuousOn.intervalIntegral | [283, 1] | [305, 17] | apply ae_of_all | case intro.intro.h_cont
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y... | case intro.intro.h_cont.a
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.h_cont
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | ContinuousOn.intervalIntegral | [283, 1] | [305, 17] | intro t ts | case intro.intro.h_cont.a
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X... | case intro.intro.h_cont.a
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.h_cont.a
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | ContinuousOn.intervalIntegral | [283, 1] | [305, 17] | simp_rw [e] | case intro.intro.h_cont.a
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X... | case intro.intro.h_cont.a
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.h_cont.a
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | ContinuousOn.intervalIntegral | [283, 1] | [305, 17] | apply fc.comp | case intro.intro.h_cont.a
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X... | case intro.intro.h_cont.a.hf
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpac... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.h_cont.a
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | ContinuousOn.intervalIntegral | [283, 1] | [305, 17] | apply Continuous.continuousOn | case intro.intro.h_cont.a.hf
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpac... | case intro.intro.h_cont.a.hf.h
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSp... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.h_cont.a.hf
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | ContinuousOn.intervalIntegral | [283, 1] | [305, 17] | exact Continuous.Prod.mk_left t | case intro.intro.h_cont.a.hf.h
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSp... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.h_cont.a.hf.h
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
in... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | ContinuousOn.intervalIntegral | [283, 1] | [305, 17] | rw [Set.uIoc_of_le ab] at ts | case intro.intro.h_cont.a.h
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace... | case intro.intro.h_cont.a.h
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.h_cont.a.h
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | ContinuousOn.intervalIntegral | [283, 1] | [305, 17] | intro y ys | case intro.intro.h_cont.a.h
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace... | case intro.intro.h_cont.a.h
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.h_cont.a.h
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | ContinuousOn.intervalIntegral | [283, 1] | [305, 17] | exact Set.mk_mem_prod ys (Set.Ioc_subset_Icc_self ts) | case intro.intro.h_cont.a.h
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.h_cont.a.h
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | ContinuousOn.intervalIntegral | [283, 1] | [305, 17] | assumption | case intro.intro.h_cont.a.a
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.h_cont.a.a
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | aEMeasurable_liminf' | [308, 1] | [313, 64] | simp_rw [uc.toHasBasis.liminf_eq_iSup_iInf] | E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type
inst✝³ : Measure... | E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type
inst✝³ : Measure... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | aEMeasurable_liminf' | [308, 1] | [313, 64] | refine aemeasurable_biSup _ uc.countable ?_ | E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type
inst✝³ : Measure... | E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type
inst✝³ : Measure... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | aEMeasurable_liminf' | [308, 1] | [313, 64] | intro i _ | E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type
inst✝³ : Measure... | E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type
inst✝³ : Measure... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | aEMeasurable_liminf' | [308, 1] | [313, 64] | exact aemeasurable_biInf _ (sc i) (fun n _ ↦ fm n) | E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type
inst✝³ : Measure... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | set_lintegral_mono_aEMeasurable | [320, 1] | [322, 74] | apply lintegral_mono_ae | E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type
inst✝³ : Measure... | case h
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type
inst✝³ : ... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | set_lintegral_mono_aEMeasurable | [320, 1] | [322, 74] | rw [ae_restrict_iff' sm] | case h
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type
inst✝³ : ... | case h
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type
inst✝³ : ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
in... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Misc/Measure.lean | set_lintegral_mono_aEMeasurable | [320, 1] | [322, 74] | exact ae_of_all _ fg | case h
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
inst✝⁵ : MetricSpace X
inst✝⁴ : BorelSpace X
Y : Type
inst✝³ : ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h
E : Type
inst✝¹³ : NormedAddCommGroup E
inst✝¹² : NormedSpace ℝ E
inst✝¹¹ : CompleteSpace E
inst✝¹⁰ : SecondCountableTopology E
F : Type
inst✝⁹ : NormedAddCommGroup F
inst✝⁸ : NormedSpace ℝ F
inst✝⁷ : CompleteSpace F
X : Type
inst✝⁶ : MeasureSpace X
in... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | iterate'_correct | [53, 1] | [91, 16] | induction' n with n h generalizing k z z' | c z : Box
rs : Floating
c' z' : ℂ
rs' : ℝ
cm : c' ∈ approx c
zm : z' ∈ approx z
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
k n : ℕ
⊢ let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Complex.abs w' ^ 2) | case zero
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
z : Box
z' : ℂ
zm : z' ∈ approx z
k : ℕ
⊢ let i := iterate' c z rs k 0;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Complex.abs w' ^ 2)
case succ
c : Box
rs : Floating
... | Please generate a tactic in lean4 to solve the state.
STATE:
c z : Box
rs : Floating
c' z' : ℂ
rs' : ℝ
cm : c' ∈ approx c
zm : z' ∈ approx z
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
k n : ℕ
⊢ let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Complex.ab... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | iterate'_correct | [53, 1] | [91, 16] | simpa only [iterate', le_refl, ge_iff_le, tsub_eq_zero_of_le, Function.iterate_zero, id_eq,
IsEmpty.forall_iff, and_true, true_and] | case zero
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
z : Box
z' : ℂ
zm : z' ∈ approx z
k : ℕ
⊢ let i := iterate' c z rs k 0;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Complex.abs w' ^ 2) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case zero
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
z : Box
z' : ℂ
zm : z' ∈ approx z
k : ℕ
⊢ let i := iterate' c z rs k 0;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | iterate'_correct | [53, 1] | [91, 16] | simp only [iterate', Floating.val_lt_val] | case succ
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Comp... | case succ
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Comp... | Please generate a tactic in lean4 to solve the state.
STATE:
case succ
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | iterate'_correct | [53, 1] | [91, 16] | generalize hzr2 : z.re.sqr = zr2 | case succ
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Comp... | case succ
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Comp... | Please generate a tactic in lean4 to solve the state.
STATE:
case succ
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | iterate'_correct | [53, 1] | [91, 16] | generalize hzi2 : z.im.sqr = zi2 | case succ
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Comp... | case succ
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Comp... | Please generate a tactic in lean4 to solve the state.
STATE:
case succ
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | iterate'_correct | [53, 1] | [91, 16] | generalize hz2 : zr2.lo.add zi2.lo false = z2 | case succ
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Comp... | case succ
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Comp... | Please generate a tactic in lean4 to solve the state.
STATE:
case succ
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | iterate'_correct | [53, 1] | [91, 16] | generalize hw : (⟨zr2 - zi2, (z.re * z.im).scaleB 1⟩ : Box) + c = w | case succ
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Comp... | case succ
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Comp... | Please generate a tactic in lean4 to solve the state.
STATE:
case succ
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | iterate'_correct | [53, 1] | [91, 16] | have we : w = z.sqr + c := by rw [←hw, Box.sqr, hzr2, hzi2] | case succ
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Comp... | case succ
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Comp... | Please generate a tactic in lean4 to solve the state.
STATE:
case succ
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | iterate'_correct | [53, 1] | [91, 16] | have wa : f' 2 c' z' ∈ approx w := by rw [we, f']; mono | case succ
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Comp... | case succ
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Comp... | Please generate a tactic in lean4 to solve the state.
STATE:
case succ
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | iterate'_correct | [53, 1] | [91, 16] | generalize hw' : f' 2 c' z' = w' at wa | case succ
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Comp... | case succ
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Comp... | Please generate a tactic in lean4 to solve the state.
STATE:
case succ
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | iterate'_correct | [53, 1] | [91, 16] | by_cases z2n : z2 = nan | case succ
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Comp... | case pos
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Compl... | Please generate a tactic in lean4 to solve the state.
STATE:
case succ
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | iterate'_correct | [53, 1] | [91, 16] | by_cases rz : rs.val < z2.val | case neg
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Compl... | case pos
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Compl... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | iterate'_correct | [53, 1] | [91, 16] | rw [←hw, Box.sqr, hzr2, hzi2] | c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Complex.abs w'... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | iterate'_correct | [53, 1] | [91, 16] | rw [we, f'] | c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Complex.abs w'... | c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Complex.abs w'... | Please generate a tactic in lean4 to solve the state.
STATE:
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | iterate'_correct | [53, 1] | [91, 16] | mono | c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Complex.abs w'... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ ... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | iterate'_correct | [53, 1] | [91, 16] | simpa only [z2n, ite_true, le_refl, ge_iff_le, tsub_eq_zero_of_le, Function.iterate_zero,
id_eq, IsEmpty.forall_iff, and_true, true_and] | case pos
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Compl... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | iterate'_correct | [53, 1] | [91, 16] | simp only [z2n, rz, ite_true, le_refl, ge_iff_le, tsub_eq_zero_of_le, Function.iterate_zero,
id_eq, zm, forall_true_left, true_and, Complex.abs_def,
Real.sq_sqrt (Complex.normSq_nonneg _), if_false] | case pos
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Compl... | case pos
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Compl... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | iterate'_correct | [53, 1] | [91, 16] | refine lt_of_le_of_lt rsm (lt_of_lt_of_le rz ?_) | case pos
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Compl... | case pos
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Compl... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | iterate'_correct | [53, 1] | [91, 16] | simp only [Complex.normSq_apply, ←sq, ←hz2, ←hzr2, ←hzi2] at z2n ⊢ | case pos
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Compl... | case pos
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Compl... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | iterate'_correct | [53, 1] | [91, 16] | rcases Floating.ne_nan_of_add z2n with ⟨nr, ni⟩ | case pos
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' < Compl... | case pos.intro
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' <... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k... |
https://github.com/girving/ray.git | 0be790285dd0fce78913b0cb9bddaffa94bd25f9 | Ray/Render/Iterate.lean | iterate'_correct | [53, 1] | [91, 16] | simp only [ne_eq, Interval.lo_eq_nan] at nr ni | case pos.intro
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' <... | case pos.intro
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
k ≤ i.n ∧ w' ∈ approx i.z ∧ (i.exit = Exit.large → rs' <... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos.intro
c : Box
rs : Floating
c' : ℂ
rs' : ℝ
cm : c' ∈ approx c
rsn : rs ≠ nan
rsm : rs' ≤ rs.val
n : ℕ
h :
∀ {z : Box} {z' : ℂ},
z' ∈ approx z →
∀ (k : ℕ),
let i := iterate' c z rs k n;
let w' := (f' 2 c')^[i.n - k] z';
... |
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