Theorem: measurableSet_of_differentiableAt_of_isComplete
File: Mathlib/Analysis/Calculus/FDerivMeasurable.lean

tactic: simp only [D, differentiable_set_eq_d K hK]
state_before: 𝕜 : Type u_3
inst✝⁶ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝⁵ : NormedAddCommGroup E
inst✝⁴ : NormedSpace 𝕜 E
F : Type u_1
inst✝³ : NormedAddCommGroup F
inst✝² : NormedSpace 𝕜 F
f : E → F
K✝ : Set (E →L[𝕜] F)
inst✝¹ : MeasurableSpace E
inst✝ : OpensMeasurableSpace E
K : Set (E →L[𝕜] F)
hK : IsComplete K
⊢ MeasurableSet {x | DifferentiableAt 𝕜 f x ∧ fderiv 𝕜 f x ∈ K}

tactic: refine MeasurableSet.iInter fun _ => ?_
state_before: 𝕜 : Type u_3
inst✝⁶ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝⁵ : NormedAddCommGroup E
inst✝⁴ : NormedSpace 𝕜 E
F : Type u_1
inst✝³ : NormedAddCommGroup F
inst✝² : NormedSpace 𝕜 F
f : E → F
K✝ : Set (E →L[𝕜] F)
inst✝¹ : MeasurableSpace E
inst✝ : OpensMeasurableSpace E
K : Set (E →L[𝕜] F)
hK : IsComplete K
⊢ MeasurableSet
    (⋂ (e : ℕ), ⋃ (n : ℕ), ⋂ (p : ℕ) (_ : p ≥ n) (q : ℕ) (_ : q ≥ n), B f K ((1 / 2) ^ p) ((1 / 2) ^ q) ((1 / 2) ^ e))

tactic: refine MeasurableSet.iUnion fun _ => ?_
state_before: 𝕜 : Type u_3
inst✝⁶ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝⁵ : NormedAddCommGroup E
inst✝⁴ : NormedSpace 𝕜 E
F : Type u_1
inst✝³ : NormedAddCommGroup F
inst✝² : NormedSpace 𝕜 F
f : E → F
K✝ : Set (E →L[𝕜] F)
inst✝¹ : MeasurableSpace E
inst✝ : OpensMeasurableSpace E
K : Set (E →L[𝕜] F)
hK : IsComplete K
x✝ : ℕ
⊢ MeasurableSet (⋃ (n : ℕ), ⋂ (p : ℕ) (_ : p ≥ n) (q : ℕ) (_ : q ≥ n), B f K ((1 / 2) ^ p) ((1 / 2) ^ q) ((1 / 2) ^ x✝))

tactic: refine MeasurableSet.iInter fun _ => ?_
state_before: 𝕜 : Type u_3
inst✝⁶ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝⁵ : NormedAddCommGroup E
inst✝⁴ : NormedSpace 𝕜 E
F : Type u_1
inst✝³ : NormedAddCommGroup F
inst✝² : NormedSpace 𝕜 F
f : E → F
K✝ : Set (E →L[𝕜] F)
inst✝¹ : MeasurableSpace E
inst✝ : OpensMeasurableSpace E
K : Set (E →L[𝕜] F)
hK : IsComplete K
x✝¹ x✝ : ℕ
⊢ MeasurableSet (⋂ (p : ℕ) (_ : p ≥ x✝) (q : ℕ) (_ : q ≥ x✝), B f K ((1 / 2) ^ p) ((1 / 2) ^ q) ((1 / 2) ^ x✝¹))

tactic: refine MeasurableSet.iInter fun _ => ?_
state_before: 𝕜 : Type u_3
inst✝⁶ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝⁵ : NormedAddCommGroup E
inst✝⁴ : NormedSpace 𝕜 E
F : Type u_1
inst✝³ : NormedAddCommGroup F
inst✝² : NormedSpace 𝕜 F
f : E → F
K✝ : Set (E →L[𝕜] F)
inst✝¹ : MeasurableSpace E
inst✝ : OpensMeasurableSpace E
K : Set (E →L[𝕜] F)
hK : IsComplete K
x✝² x✝¹ x✝ : ℕ
⊢ MeasurableSet (⋂ (_ : x✝ ≥ x✝¹) (q : ℕ) (_ : q ≥ x✝¹), B f K ((1 / 2) ^ x✝) ((1 / 2) ^ q) ((1 / 2) ^ x✝²))

tactic: refine MeasurableSet.iInter fun _ => ?_
state_before: 𝕜 : Type u_3
inst✝⁶ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝⁵ : NormedAddCommGroup E
inst✝⁴ : NormedSpace 𝕜 E
F : Type u_1
inst✝³ : NormedAddCommGroup F
inst✝² : NormedSpace 𝕜 F
f : E → F
K✝ : Set (E →L[𝕜] F)
inst✝¹ : MeasurableSpace E
inst✝ : OpensMeasurableSpace E
K : Set (E →L[𝕜] F)
hK : IsComplete K
x✝³ x✝² x✝¹ : ℕ
x✝ : x✝¹ ≥ x✝²
⊢ MeasurableSet (⋂ (q : ℕ) (_ : q ≥ x✝²), B f K ((1 / 2) ^ x✝¹) ((1 / 2) ^ q) ((1 / 2) ^ x✝³))

tactic: refine MeasurableSet.iInter fun _ => ?_
state_before: 𝕜 : Type u_3
inst✝⁶ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝⁵ : NormedAddCommGroup E
inst✝⁴ : NormedSpace 𝕜 E
F : Type u_1
inst✝³ : NormedAddCommGroup F
inst✝² : NormedSpace 𝕜 F
f : E → F
K✝ : Set (E →L[𝕜] F)
inst✝¹ : MeasurableSpace E
inst✝ : OpensMeasurableSpace E
K : Set (E →L[𝕜] F)
hK : IsComplete K
x✝⁴ x✝³ x✝² : ℕ
x✝¹ : x✝² ≥ x✝³
x✝ : ℕ
⊢ MeasurableSet (⋂ (_ : x✝ ≥ x✝³), B f K ((1 / 2) ^ x✝²) ((1 / 2) ^ x✝) ((1 / 2) ^ x✝⁴))

tactic: refine isOpen_b.measurableSet
state_before: 𝕜 : Type u_3
inst✝⁶ : NontriviallyNormedField 𝕜
E : Type u_2
inst✝⁵ : NormedAddCommGroup E
inst✝⁴ : NormedSpace 𝕜 E
F : Type u_1
inst✝³ : NormedAddCommGroup F
inst✝² : NormedSpace 𝕜 F
f : E → F
K✝ : Set (E →L[𝕜] F)
inst✝¹ : MeasurableSpace E
inst✝ : OpensMeasurableSpace E
K : Set (E →L[𝕜] F)
hK : IsComplete K
x✝⁵ x✝⁴ x✝³ : ℕ
x✝² : x✝³ ≥ x✝⁴
x✝¹ : ℕ
x✝ : x✝¹ ≥ x✝⁴
⊢ MeasurableSet (B f K ((1 / 2) ^ x✝³) ((1 / 2) ^ x✝¹) ((1 / 2) ^ x✝⁵))