l3lab/ntp-mathlib huggingface dataset:
theorem snorm_one_le_of_le {r : ℝ≥0} {f : α → ℝ} (hfint : Integrable f μ) (hfint' : 0 ≤ ∫ x, f x ∂μ)
    (hf : ∀ᵐ ω ∂μ, f ω ≤ r) : snorm f 1 μ ≤ 2 * μ Set.univ * r := by
  by_cases hr : r = 0
  · suffices f =ᵐ[μ] 0 by
      rw [snorm_congr_ae this, snorm_zero, hr, ENNReal.coe_zero, mul_zero]
    rw [hr] at hf
    

Proof state:
case pos
α : Type u_1
E : Type u_2
F : Type u_3
𝕜 : Type u_4
inst✝⁹ : NormedAddCommGroup E
inst✝⁸ : NormedSpace ℝ E
hE : CompleteSpace E
inst✝⁷ : NontriviallyNormedField 𝕜
inst✝⁶ : NormedSpace 𝕜 E
inst✝⁵ : SMulCommClass ℝ 𝕜 E
inst✝⁴ : NormedAddCommGroup F
inst✝³ : NormedSpace ℝ F
inst✝² : CompleteSpace F
G : Type u_5
inst✝¹ : NormedAddCommGroup G
inst✝ : NormedSpace ℝ G
m0 : MeasurableSpace α
μ : Measure α
r : ℝ≥0
f : α → ℝ
hfint : Integrable f
hfint' : 0 ≤ ∫ (x : α), f x ∂μ
hf : ∀ᵐ (ω : α) ∂μ, f ω ≤ ↑0
hr : r = 0
⊢ f =ᵐ[μ] 0

Next tactic:
norm_cast at hf
theorem snorm_one_le_of_le {r : ℝ≥0} {f : α → ℝ} (hfint : Integrable f μ) (hfint' : 0 ≤ ∫ x, f x ∂μ)
    (hf : ∀ᵐ ω ∂μ, f ω ≤ r) : snorm f 1 μ ≤ 2 * μ Set.univ * r := by
  by_cases hr : r = 0
  · suffices f =ᵐ[μ] 0 by
      rw [snorm_congr_ae this, snorm_zero, hr, ENNReal.coe_zero, mul_zero]
    rw [hr] at hf
    norm_cast at hf
    -- Porting note: two lines above were
    --rw [hr, Nonneg.coe_zero] at hf
    

Proof state:
case pos
α : Type u_1
E : Type u_2
F : Type u_3
𝕜 : Type u_4
inst✝⁹ : NormedAddCommGroup E
inst✝⁸ : NormedSpace ℝ E
hE : CompleteSpace E
inst✝⁷ : NontriviallyNormedField 𝕜
inst✝⁶ : NormedSpace 𝕜 E
inst✝⁵ : SMulCommClass ℝ 𝕜 E
inst✝⁴ : NormedAddCommGroup F
inst✝³ : NormedSpace ℝ F
inst✝² : CompleteSpace F
G : Type u_5
inst✝¹ : NormedAddCommGroup G
inst✝ : NormedSpace ℝ G
m0 : MeasurableSpace α
μ : Measure α
r : ℝ≥0
f : α → ℝ
hfint : Integrable f
hfint' : 0 ≤ ∫ (x : α), f x ∂μ
hr : r = 0
hf : ∀ᵐ (ω : α) ∂μ, f ω ≤ 0
⊢ f =ᵐ[μ] 0

Next tactic:
have hnegf : ∫ x, -f x ∂μ = 0 := by
      rw [integral_neg, neg_eq_zero]
      exact le_antisymm (integral_nonpos_of_ae hf) hfint'
theorem snorm_one_le_of_le {r : ℝ≥0} {f : α → ℝ} (hfint : Integrable f μ) (hfint' : 0 ≤ ∫ x, f x ∂μ)
    (hf : ∀ᵐ ω ∂μ, f ω ≤ r) : snorm f 1 μ ≤ 2 * μ Set.univ * r := by
  by_cases hr : r = 0
  · suffices f =ᵐ[μ] 0 by
      rw [snorm_congr_ae this, snorm_zero, hr, ENNReal.coe_zero, mul_zero]
    rw [hr] at hf
    norm_cast at hf
    -- Porting note: two lines above were
    --rw [hr, Nonneg.coe_zero] at hf
    have hnegf : ∫ x, -f x ∂μ = 0 := by
      

Proof state:
α : Type u_1
E : Type u_2
F : Type u_3
𝕜 : Type u_4
inst✝⁹ : NormedAddCommGroup E
inst✝⁸ : NormedSpace ℝ E
hE : CompleteSpace E
inst✝⁷ : NontriviallyNormedField 𝕜
inst✝⁶ : NormedSpace 𝕜 E
inst✝⁵ : SMulCommClass ℝ 𝕜 E
inst✝⁴ : NormedAddCommGroup F
inst✝³ : NormedSpace ℝ F
inst✝² : CompleteSpace F
G : Type u_5
inst✝¹ : NormedAddCommGroup G
inst✝ : NormedSpace ℝ G
m0 : MeasurableSpace α
μ : Measure α
r : ℝ≥0
f : α → ℝ
hfint : Integrable f
hfint' : 0 ≤ ∫ (x : α), f x ∂μ
hr : r = 0
hf : ∀ᵐ (ω : α) ∂μ, f ω ≤ 0
⊢ ∫ (x : α), -f x ∂μ = 0

Next tactic:
rw [integral_neg, neg_eq_zero]
theorem snorm_one_le_of_le {r : ℝ≥0} {f : α → ℝ} (hfint : Integrable f μ) (hfint' : 0 ≤ ∫ x, f x ∂μ)
    (hf : ∀ᵐ ω ∂μ, f ω ≤ r) : snorm f 1 μ ≤ 2 * μ Set.univ * r := by
  by_cases hr : r = 0
  · suffices f =ᵐ[μ] 0 by
      rw [snorm_congr_ae this, snorm_zero, hr, ENNReal.coe_zero, mul_zero]
    rw [hr] at hf
    norm_cast at hf
    -- Porting note: two lines above were
    --rw [hr, Nonneg.coe_zero] at hf
    have hnegf : ∫ x, -f x ∂μ = 0 := by
      rw [integral_neg, neg_eq_zero]
      

Proof state:
α : Type u_1
E : Type u_2
F : Type u_3
𝕜 : Type u_4
inst✝⁹ : NormedAddCommGroup E
inst✝⁸ : NormedSpace ℝ E
hE : CompleteSpace E
inst✝⁷ : NontriviallyNormedField 𝕜
inst✝⁶ : NormedSpace 𝕜 E
inst✝⁵ : SMulCommClass ℝ 𝕜 E
inst✝⁴ : NormedAddCommGroup F
inst✝³ : NormedSpace ℝ F
inst✝² : CompleteSpace F
G : Type u_5
inst✝¹ : NormedAddCommGroup G
inst✝ : NormedSpace ℝ G
m0 : MeasurableSpace α
μ : Measure α
r : ℝ≥0
f : α → ℝ
hfint : Integrable f
hfint' : 0 ≤ ∫ (x : α), f x ∂μ
hr : r = 0
hf : ∀ᵐ (ω : α) ∂μ, f ω ≤ 0
⊢ ∫ (a : α), f a ∂μ = 0

Next tactic:
exact le_antisymm (integral_nonpos_of_ae hf) hfint'
theorem snorm_one_le_of_le {r : ℝ≥0} {f : α → ℝ} (hfint : Integrable f μ) (hfint' : 0 ≤ ∫ x, f x ∂μ)
    (hf : ∀ᵐ ω ∂μ, f ω ≤ r) : snorm f 1 μ ≤ 2 * μ Set.univ * r := by
  by_cases hr : r = 0
  · suffices f =ᵐ[μ] 0 by
      rw [snorm_congr_ae this, snorm_zero, hr, ENNReal.coe_zero, mul_zero]
    rw [hr] at hf
    norm_cast at hf
    -- Porting note: two lines above were
    --rw [hr, Nonneg.coe_zero] at hf
    have hnegf : ∫ x, -f x ∂μ = 0 := by
      rw [integral_neg, neg_eq_zero]
      exact le_antisymm (integral_nonpos_of_ae hf) hfint'
    

Proof state:
case pos
α : Type u_1
E : Type u_2
F : Type u_3
𝕜 : Type u_4
inst✝⁹ : NormedAddCommGroup E
inst✝⁸ : NormedSpace ℝ E
hE : CompleteSpace E
inst✝⁷ : NontriviallyNormedField 𝕜
inst✝⁶ : NormedSpace 𝕜 E
inst✝⁵ : SMulCommClass ℝ 𝕜 E
inst✝⁴ : NormedAddCommGroup F
inst✝³ : NormedSpace ℝ F
inst✝² : CompleteSpace F
G : Type u_5
inst✝¹ : NormedAddCommGroup G
inst✝ : NormedSpace ℝ G
m0 : MeasurableSpace α
μ : Measure α
r : ℝ≥0
f : α → ℝ
hfint : Integrable f
hfint' : 0 ≤ ∫ (x : α), f x ∂μ
hr : r = 0
hf : ∀ᵐ (ω : α) ∂μ, f ω ≤ 0
hnegf : ∫ (x : α), -f x ∂μ = 0
⊢ f =ᵐ[μ] 0

Next tactic:
have := (integral_eq_zero_iff_of_nonneg_ae ?_ hfint.neg).1 hnegf
theorem snorm_one_le_of_le {r : ℝ≥0} {f : α → ℝ} (hfint : Integrable f μ) (hfint' : 0 ≤ ∫ x, f x ∂μ)
    (hf : ∀ᵐ ω ∂μ, f ω ≤ r) : snorm f 1 μ ≤ 2 * μ Set.univ * r := by
  by_cases hr : r = 0
  · suffices f =ᵐ[μ] 0 by
      rw [snorm_congr_ae this, snorm_zero, hr, ENNReal.coe_zero, mul_zero]
    rw [hr] at hf
    norm_cast at hf
    -- Porting note: two lines above were
    --rw [hr, Nonneg.coe_zero] at hf
    have hnegf : ∫ x, -f x ∂μ = 0 := by
      rw [integral_neg, neg_eq_zero]
      exact le_antisymm (integral_nonpos_of_ae hf) hfint'
    have := (integral_eq_zero_iff_of_nonneg_ae ?_ hfint.neg).1 hnegf
    · 

Proof state:
case pos.refine_2
α : Type u_1
E : Type u_2
F : Type u_3
𝕜 : Type u_4
inst✝⁹ : NormedAddCommGroup E
inst✝⁸ : NormedSpace ℝ E
hE : CompleteSpace E
inst✝⁷ : NontriviallyNormedField 𝕜
inst✝⁶ : NormedSpace 𝕜 E
inst✝⁵ : SMulCommClass ℝ 𝕜 E
inst✝⁴ : NormedAddCommGroup F
inst✝³ : NormedSpace ℝ F
inst✝² : CompleteSpace F
G : Type u_5
inst✝¹ : NormedAddCommGroup G
inst✝ : NormedSpace ℝ G
m0 : MeasurableSpace α
μ : Measure α
r : ℝ≥0
f : α → ℝ
hfint : Integrable f
hfint' : 0 ≤ ∫ (x : α), f x ∂μ
hr : r = 0
hf : ∀ᵐ (ω : α) ∂μ, f ω ≤ 0
hnegf : ∫ (x : α), -f x ∂μ = 0
this : -f =ᵐ[μ] 0
⊢ f =ᵐ[μ] 0

Next tactic:
filter_upwards [this] with ω hω
theorem snorm_one_le_of_le {r : ℝ≥0} {f : α → ℝ} (hfint : Integrable f μ) (hfint' : 0 ≤ ∫ x, f x ∂μ)
    (hf : ∀ᵐ ω ∂μ, f ω ≤ r) : snorm f 1 μ ≤ 2 * μ Set.univ * r := by
  by_cases hr : r = 0
  · suffices f =ᵐ[μ] 0 by
      rw [snorm_congr_ae this, snorm_zero, hr, ENNReal.coe_zero, mul_zero]
    rw [hr] at hf
    norm_cast at hf
    -- Porting note: two lines above were
    --rw [hr, Nonneg.coe_zero] at hf
    have hnegf : ∫ x, -f x ∂μ = 0 := by
      rw [integral_neg, neg_eq_zero]
      exact le_antisymm (integral_nonpos_of_ae hf) hfint'
    have := (integral_eq_zero_iff_of_nonneg_ae ?_ hfint.neg).1 hnegf
    · filter_upwards [this] with ω hω
      

Proof state:
case h
α : Type u_1
E : Type u_2
F : Type u_3
𝕜 : Type u_4
inst✝⁹ : NormedAddCommGroup E
inst✝⁸ : NormedSpace ℝ E
hE : CompleteSpace E
inst✝⁷ : NontriviallyNormedField 𝕜
inst✝⁶ : NormedSpace 𝕜 E
inst✝⁵ : SMulCommClass ℝ 𝕜 E
inst✝⁴ : NormedAddCommGroup F
inst✝³ : NormedSpace ℝ F
inst✝² : CompleteSpace F
G : Type u_5
inst✝¹ : NormedAddCommGroup G
inst✝ : NormedSpace ℝ G
m0 : MeasurableSpace α
μ : Measure α
r : ℝ≥0
f : α → ℝ
hfint : Integrable f
hfint' : 0 ≤ ∫ (x : α), f x ∂μ
hr : r = 0
hf : ∀ᵐ (ω : α) ∂μ, f ω ≤ 0
hnegf : ∫ (x : α), -f x ∂μ = 0
this : -f =ᵐ[μ] 0
ω : α
hω : (-f) ω = OfNat.ofNat 0 ω
⊢ f ω = OfNat.ofNat 0 ω

Next tactic:
rwa [Pi.neg_apply, Pi.zero_apply, neg_eq_zero] at hω
theorem snorm_one_le_of_le {r : ℝ≥0} {f : α → ℝ} (hfint : Integrable f μ) (hfint' : 0 ≤ ∫ x, f x ∂μ)
    (hf : ∀ᵐ ω ∂μ, f ω ≤ r) : snorm f 1 μ ≤ 2 * μ Set.univ * r := by
  by_cases hr : r = 0
  · suffices f =ᵐ[μ] 0 by
      rw [snorm_congr_ae this, snorm_zero, hr, ENNReal.coe_zero, mul_zero]
    rw [hr] at hf
    norm_cast at hf
    -- Porting note: two lines above were
    --rw [hr, Nonneg.coe_zero] at hf
    have hnegf : ∫ x, -f x ∂μ = 0 := by
      rw [integral_neg, neg_eq_zero]
      exact le_antisymm (integral_nonpos_of_ae hf) hfint'
    have := (integral_eq_zero_iff_of_nonneg_ae ?_ hfint.neg).1 hnegf
    · filter_upwards [this] with ω hω
      rwa [Pi.neg_apply, Pi.zero_apply, neg_eq_zero] at hω
    · 

Proof state:
case pos.refine_1
α : Type u_1
E : Type u_2
F : Type u_3
𝕜 : Type u_4
inst✝⁹ : NormedAddCommGroup E
inst✝⁸ : NormedSpace ℝ E
hE : CompleteSpace E
inst✝⁷ : NontriviallyNormedField 𝕜
inst✝⁶ : NormedSpace 𝕜 E
inst✝⁵ : SMulCommClass ℝ 𝕜 E
inst✝⁴ : NormedAddCommGroup F
inst✝³ : NormedSpace ℝ F
inst✝² : CompleteSpace F
G : Type u_5
inst✝¹ : NormedAddCommGroup G
inst✝ : NormedSpace ℝ G
m0 : MeasurableSpace α
μ : Measure α
r : ℝ≥0
f : α → ℝ
hfint : Integrable f
hfint' : 0 ≤ ∫ (x : α), f x ∂μ
hr : r = 0
hf : ∀ᵐ (ω : α) ∂μ, f ω ≤ 0
hnegf : ∫ (x : α), -f x ∂μ = 0
⊢ 0 ≤ᵐ[μ] -f

Next tactic:
filter_upwards [hf] with ω hω
theorem snorm_one_le_of_le {r : ℝ≥0} {f : α → ℝ} (hfint : Integrable f μ) (hfint' : 0 ≤ ∫ x, f x ∂μ)
    (hf : ∀ᵐ ω ∂μ, f ω ≤ r) : snorm f 1 μ ≤ 2 * μ Set.univ * r := by
  by_cases hr : r = 0
  · suffices f =ᵐ[μ] 0 by
      rw [snorm_congr_ae this, snorm_zero, hr, ENNReal.coe_zero, mul_zero]
    rw [hr] at hf
    norm_cast at hf
    -- Porting note: two lines above were
    --rw [hr, Nonneg.coe_zero] at hf
    have hnegf : ∫ x, -f x ∂μ = 0 := by
      rw [integral_neg, neg_eq_zero]
      exact le_antisymm (integral_nonpos_of_ae hf) hfint'
    have := (integral_eq_zero_iff_of_nonneg_ae ?_ hfint.neg).1 hnegf
    · filter_upwards [this] with ω hω
      rwa [Pi.neg_apply, Pi.zero_apply, neg_eq_zero] at hω
    · filter_upwards [hf] with ω hω
      

Proof state:
case h
α : Type u_1
E : Type u_2
F : Type u_3
𝕜 : Type u_4
inst✝⁹ : NormedAddCommGroup E
inst✝⁸ : NormedSpace ℝ E
hE : CompleteSpace E
inst✝⁷ : NontriviallyNormedField 𝕜
inst✝⁶ : NormedSpace 𝕜 E
inst✝⁵ : SMulCommClass ℝ 𝕜 E
inst✝⁴ : NormedAddCommGroup F
inst✝³ : NormedSpace ℝ F
inst✝² : CompleteSpace F
G : Type u_5
inst✝¹ : NormedAddCommGroup G
inst✝ : NormedSpace ℝ G
m0 : MeasurableSpace α
μ : Measure α
r : ℝ≥0
f : α → ℝ
hfint : Integrable f
hfint' : 0 ≤ ∫ (x : α), f x ∂μ
hr : r = 0
hf : ∀ᵐ (ω : α) ∂μ, f ω ≤ 0
hnegf : ∫ (x : α), -f x ∂μ = 0
ω : α
hω : f ω ≤ 0
⊢ OfNat.ofNat 0 ω ≤ (-f) ω

Next tactic:
rwa [Pi.zero_apply, Pi.neg_apply, Right.nonneg_neg_iff]
theorem snorm_one_le_of_le {r : ℝ≥0} {f : α → ℝ} (hfint : Integrable f μ) (hfint' : 0 ≤ ∫ x, f x ∂μ)
    (hf : ∀ᵐ ω ∂μ, f ω ≤ r) : snorm f 1 μ ≤ 2 * μ Set.univ * r := by
  by_cases hr : r = 0
  · suffices f =ᵐ[μ] 0 by
      rw [snorm_congr_ae this, snorm_zero, hr, ENNReal.coe_zero, mul_zero]
    rw [hr] at hf
    norm_cast at hf
    -- Porting note: two lines above were
    --rw [hr, Nonneg.coe_zero] at hf
    have hnegf : ∫ x, -f x ∂μ = 0 := by
      rw [integral_neg, neg_eq_zero]
      exact le_antisymm (integral_nonpos_of_ae hf) hfint'
    have := (integral_eq_zero_iff_of_nonneg_ae ?_ hfint.neg).1 hnegf
    · filter_upwards [this] with ω hω
      rwa [Pi.neg_apply, Pi.zero_apply, neg_eq_zero] at hω
    · filter_upwards [hf] with ω hω
      rwa [Pi.zero_apply, Pi.neg_apply, Right.nonneg_neg_iff]
  

Proof state:
case neg
α : Type u_1
E : Type u_2
F : Type u_3
𝕜 : Type u_4
inst✝⁹ : NormedAddCommGroup E
inst✝⁸ : NormedSpace ℝ E
hE : CompleteSpace E
inst✝⁷ : NontriviallyNormedField 𝕜
inst✝⁶ : NormedSpace 𝕜 E
inst✝⁵ : SMulCommClass ℝ 𝕜 E
inst✝⁴ : NormedAddCommGroup F
inst✝³ : NormedSpace ℝ F
inst✝² : CompleteSpace F
G : Type u_5
inst✝¹ : NormedAddCommGroup G
inst✝ : NormedSpace ℝ G
m0 : MeasurableSpace α
μ : Measure α
r : ℝ≥0
f : α → ℝ
hfint : Integrable f
hfint' : 0 ≤ ∫ (x : α), f x ∂μ
hf : ∀ᵐ (ω : α) ∂μ, f ω ≤ ↑r
hr : ¬r = 0
⊢ snorm f 1 μ ≤ 2 * ↑↑μ univ * ↑r

Next tactic:
by_cases hμ : IsFiniteMeasure μ
theorem snorm_one_le_of_le {r : ℝ≥0} {f : α → ℝ} (hfint : Integrable f μ) (hfint' : 0 ≤ ∫ x, f x ∂μ)
    (hf : ∀ᵐ ω ∂μ, f ω ≤ r) : snorm f 1 μ ≤ 2 * μ Set.univ * r := by
  by_cases hr : r = 0
  · suffices f =ᵐ[μ] 0 by
      rw [snorm_congr_ae this, snorm_zero, hr, ENNReal.coe_zero, mul_zero]
    rw [hr] at hf
    norm_cast at hf
    -- Porting note: two lines above were
    --rw [hr, Nonneg.coe_zero] at hf
    have hnegf : ∫ x, -f x ∂μ = 0 := by
      rw [integral_neg, neg_eq_zero]
      exact le_antisymm (integral_nonpos_of_ae hf) hfint'
    have := (integral_eq_zero_iff_of_nonneg_ae ?_ hfint.neg).1 hnegf
    · filter_upwards [this] with ω hω
      rwa [Pi.neg_apply, Pi.zero_apply, neg_eq_zero] at hω
    · filter_upwards [hf] with ω hω
      rwa [Pi.zero_apply, Pi.neg_apply, Right.nonneg_neg_iff]
  by_cases hμ : IsFiniteMeasure μ
  

Proof state:
case pos
α : Type u_1
E : Type u_2
F : Type u_3
𝕜 : Type u_4
inst✝⁹ : NormedAddCommGroup E
inst✝⁸ : NormedSpace ℝ E
hE : CompleteSpace E
inst✝⁷ : NontriviallyNormedField 𝕜
inst✝⁶ : NormedSpace 𝕜 E
inst✝⁵ : SMulCommClass ℝ 𝕜 E
inst✝⁴ : NormedAddCommGroup F
inst✝³ : NormedSpace ℝ F
inst✝² : CompleteSpace F
G : Type u_5
inst✝¹ : NormedAddCommGroup G
inst✝ : NormedSpace ℝ G
m0 : MeasurableSpace α
μ : Measure α
r : ℝ≥0
f : α → ℝ
hfint : Integrable f
hfint' : 0 ≤ ∫ (x : α), f x ∂μ
hf : ∀ᵐ (ω : α) ∂μ, f ω ≤ ↑r
hr : ¬r = 0
hμ : IsFiniteMeasure μ
⊢ snorm f 1 μ ≤ 2 * ↑↑μ univ * ↑r
case neg
α : Type u_1
E : Type u_2
F : Type u_3
𝕜 : Type u_4
inst✝⁹ : NormedAddCommGroup E
inst✝⁸ : NormedSpace ℝ E
hE : CompleteSpace E
inst✝⁷ : NontriviallyNormedField 𝕜
inst✝⁶ : NormedSpace 𝕜 E
inst✝⁵ : SMulCommClass ℝ 𝕜 E
inst✝⁴ : NormedAddCommGroup F
inst✝³ : NormedSpace ℝ F
inst✝² : CompleteSpace F
G : Type u_5
inst✝¹ : NormedAddCommGroup G
inst✝ : NormedSpace ℝ G
m0 : MeasurableSpace α
μ : Measure α
r : ℝ≥0
f : α → ℝ
hfint : Integrable f
hfint' : 0 ≤ ∫ (x : α), f x ∂μ
hf : ∀ᵐ (ω : α) ∂μ, f ω ≤ ↑r
hr : ¬r = 0
hμ : ¬IsFiniteMeasure μ
⊢ snorm f 1 μ ≤ 2 * ↑↑μ univ * ↑r

Next tactic:
swap
theorem snorm_one_le_of_le {r : ℝ≥0} {f : α → ℝ} (hfint : Integrable f μ) (hfint' : 0 ≤ ∫ x, f x ∂μ)
    (hf : ∀ᵐ ω ∂μ, f ω ≤ r) : snorm f 1 μ ≤ 2 * μ Set.univ * r := by
  by_cases hr : r = 0
  · suffices f =ᵐ[μ] 0 by
      rw [snorm_congr_ae this, snorm_zero, hr, ENNReal.coe_zero, mul_zero]
    rw [hr] at hf
    norm_cast at hf
    -- Porting note: two lines above were
    --rw [hr, Nonneg.coe_zero] at hf
    have hnegf : ∫ x, -f x ∂μ = 0 := by
      rw [integral_neg, neg_eq_zero]
      exact le_antisymm (integral_nonpos_of_ae hf) hfint'
    have := (integral_eq_zero_iff_of_nonneg_ae ?_ hfint.neg).1 hnegf
    · filter_upwards [this] with ω hω
      rwa [Pi.neg_apply, Pi.zero_apply, neg_eq_zero] at hω
    · filter_upwards [hf] with ω hω
      rwa [Pi.zero_apply, Pi.neg_apply, Right.nonneg_neg_iff]
  by_cases hμ : IsFiniteMeasure μ
  swap
  · 

Proof state:
case neg
α : Type u_1
E : Type u_2
F : Type u_3
𝕜 : Type u_4
inst✝⁹ : NormedAddCommGroup E
inst✝⁸ : NormedSpace ℝ E
hE : CompleteSpace E
inst✝⁷ : NontriviallyNormedField 𝕜
inst✝⁶ : NormedSpace 𝕜 E
inst✝⁵ : SMulCommClass ℝ 𝕜 E
inst✝⁴ : NormedAddCommGroup F
inst✝³ : NormedSpace ℝ F
inst✝² : CompleteSpace F
G : Type u_5
inst✝¹ : NormedAddCommGroup G
inst✝ : NormedSpace ℝ G
m0 : MeasurableSpace α
μ : Measure α
r : ℝ≥0
f : α → ℝ
hfint : Integrable f
hfint' : 0 ≤ ∫ (x : α), f x ∂μ
hf : ∀ᵐ (ω : α) ∂μ, f ω ≤ ↑r
hr : ¬r = 0
hμ : ¬IsFiniteMeasure μ
⊢ snorm f 1 μ ≤ 2 * ↑↑μ univ * ↑r

Next tactic:
have : μ Set.univ = ∞ := by
      by_contra hμ'
      exact hμ (IsFiniteMeasure.mk <| lt_top_iff_ne_top.2 hμ')
theorem snorm_one_le_of_le {r : ℝ≥0} {f : α → ℝ} (hfint : Integrable f μ) (hfint' : 0 ≤ ∫ x, f x ∂μ)
    (hf : ∀ᵐ ω ∂μ, f ω ≤ r) : snorm f 1 μ ≤ 2 * μ Set.univ * r := by
  by_cases hr : r = 0
  · suffices f =ᵐ[μ] 0 by
      rw [snorm_congr_ae this, snorm_zero, hr, ENNReal.coe_zero, mul_zero]
    rw [hr] at hf
    norm_cast at hf
    -- Porting note: two lines above were
    --rw [hr, Nonneg.coe_zero] at hf
    have hnegf : ∫ x, -f x ∂μ = 0 := by
      rw [integral_neg, neg_eq_zero]
      exact le_antisymm (integral_nonpos_of_ae hf) hfint'
    have := (integral_eq_zero_iff_of_nonneg_ae ?_ hfint.neg).1 hnegf
    · filter_upwards [this] with ω hω
      rwa [Pi.neg_apply, Pi.zero_apply, neg_eq_zero] at hω
    · filter_upwards [hf] with ω hω
      rwa [Pi.zero_apply, Pi.neg_apply, Right.nonneg_neg_iff]
  by_cases hμ : IsFiniteMeasure μ
  swap
  · have : μ Set.univ = ∞ := by
      

Proof state:
α : Type u_1
E : Type u_2
F : Type u_3
𝕜 : Type u_4
inst✝⁹ : NormedAddCommGroup E
inst✝⁸ : NormedSpace ℝ E
hE : CompleteSpace E
inst✝⁷ : NontriviallyNormedField 𝕜
inst✝⁶ : NormedSpace 𝕜 E
inst✝⁵ : SMulCommClass ℝ 𝕜 E
inst✝⁴ : NormedAddCommGroup F
inst✝³ : NormedSpace ℝ F
inst✝² : CompleteSpace F
G : Type u_5
inst✝¹ : NormedAddCommGroup G
inst✝ : NormedSpace ℝ G
m0 : MeasurableSpace α
μ : Measure α
r : ℝ≥0
f : α → ℝ
hfint : Integrable f
hfint' : 0 ≤ ∫ (x : α), f x ∂μ
hf : ∀ᵐ (ω : α) ∂μ, f ω ≤ ↑r
hr : ¬r = 0
hμ : ¬IsFiniteMeasure μ
⊢ ↑↑μ univ = ⊤

Next tactic:
by_contra hμ'
theorem snorm_one_le_of_le {r : ℝ≥0} {f : α → ℝ} (hfint : Integrable f μ) (hfint' : 0 ≤ ∫ x, f x ∂μ)
    (hf : ∀ᵐ ω ∂μ, f ω ≤ r) : snorm f 1 μ ≤ 2 * μ Set.univ * r := by
  by_cases hr : r = 0
  · suffices f =ᵐ[μ] 0 by
      rw [snorm_congr_ae this, snorm_zero, hr, ENNReal.coe_zero, mul_zero]
    rw [hr] at hf
    norm_cast at hf
    -- Porting note: two lines above were
    --rw [hr, Nonneg.coe_zero] at hf
    have hnegf : ∫ x, -f x ∂μ = 0 := by
      rw [integral_neg, neg_eq_zero]
      exact le_antisymm (integral_nonpos_of_ae hf) hfint'
    have := (integral_eq_zero_iff_of_nonneg_ae ?_ hfint.neg).1 hnegf
    · filter_upwards [this] with ω hω
      rwa [Pi.neg_apply, Pi.zero_apply, neg_eq_zero] at hω
    · filter_upwards [hf] with ω hω
      rwa [Pi.zero_apply, Pi.neg_apply, Right.nonneg_neg_iff]
  by_cases hμ : IsFiniteMeasure μ
  swap
  · have : μ Set.univ = ∞ := by
      by_contra hμ'
      

Proof state:
α : Type u_1
E : Type u_2
F : Type u_3
𝕜 : Type u_4
inst✝⁹ : NormedAddCommGroup E
inst✝⁸ : NormedSpace ℝ E
hE : CompleteSpace E
inst✝⁷ : NontriviallyNormedField 𝕜
inst✝⁶ : NormedSpace 𝕜 E
inst✝⁵ : SMulCommClass ℝ 𝕜 E
inst✝⁴ : NormedAddCommGroup F
inst✝³ : NormedSpace ℝ F
inst✝² : CompleteSpace F
G : Type u_5
inst✝¹ : NormedAddCommGroup G
inst✝ : NormedSpace ℝ G
m0 : MeasurableSpace α
μ : Measure α
r : ℝ≥0
f : α → ℝ
hfint : Integrable f
hfint' : 0 ≤ ∫ (x : α), f x ∂μ
hf : ∀ᵐ (ω : α) ∂μ, f ω ≤ ↑r
hr : ¬r = 0
hμ : ¬IsFiniteMeasure μ
hμ' : ¬↑↑μ univ = ⊤
⊢ False

Next tactic:
exact hμ (IsFiniteMeasure.mk <| lt_top_iff_ne_top.2 hμ')
theorem snorm_one_le_of_le {r : ℝ≥0} {f : α → ℝ} (hfint : Integrable f μ) (hfint' : 0 ≤ ∫ x, f x ∂μ)
    (hf : ∀ᵐ ω ∂μ, f ω ≤ r) : snorm f 1 μ ≤ 2 * μ Set.univ * r := by
  by_cases hr : r = 0
  · suffices f =ᵐ[μ] 0 by
      rw [snorm_congr_ae this, snorm_zero, hr, ENNReal.coe_zero, mul_zero]
    rw [hr] at hf
    norm_cast at hf
    -- Porting note: two lines above were
    --rw [hr, Nonneg.coe_zero] at hf
    have hnegf : ∫ x, -f x ∂μ = 0 := by
      rw [integral_neg, neg_eq_zero]
      exact le_antisymm (integral_nonpos_of_ae hf) hfint'
    have := (integral_eq_zero_iff_of_nonneg_ae ?_ hfint.neg).1 hnegf
    · filter_upwards [this] with ω hω
      rwa [Pi.neg_apply, Pi.zero_apply, neg_eq_zero] at hω
    · filter_upwards [hf] with ω hω
      rwa [Pi.zero_apply, Pi.neg_apply, Right.nonneg_neg_iff]
  by_cases hμ : IsFiniteMeasure μ
  swap
  · have : μ Set.univ = ∞ := by
      by_contra hμ'
      exact hμ (IsFiniteMeasure.mk <| lt_top_iff_ne_top.2 hμ')
    

Proof state:
case neg
α : Type u_1
E : Type u_2
F : Type u_3
𝕜 : Type u_4
inst✝⁹ : NormedAddCommGroup E
inst✝⁸ : NormedSpace ℝ E
hE : CompleteSpace E
inst✝⁷ : NontriviallyNormedField 𝕜
inst✝⁶ : NormedSpace 𝕜 E
inst✝⁵ : SMulCommClass ℝ 𝕜 E
inst✝⁴ : NormedAddCommGroup F
inst✝³ : NormedSpace ℝ F
inst✝² : CompleteSpace F
G : Type u_5
inst✝¹ : NormedAddCommGroup G
inst✝ : NormedSpace ℝ G
m0 : MeasurableSpace α
μ : Measure α
r : ℝ≥0
f : α → ℝ
hfint : Integrable f
hfint' : 0 ≤ ∫ (x : α), f x ∂μ
hf : ∀ᵐ (ω : α) ∂μ, f ω ≤ ↑r
hr : ¬r = 0
hμ : ¬IsFiniteMeasure μ
this : ↑↑μ univ = ⊤
⊢ snorm f 1 μ ≤ 2 * ↑↑μ univ * ↑r

Next tactic:
rw [this, ENNReal.mul_top', if_neg, ENNReal.top_mul', if_neg]
theorem snorm_one_le_of_le {r : ℝ≥0} {f : α → ℝ} (hfint : Integrable f μ) (hfint' : 0 ≤ ∫ x, f x ∂μ)
    (hf : ∀ᵐ ω ∂μ, f ω ≤ r) : snorm f 1 μ ≤ 2 * μ Set.univ * r := by
  by_cases hr : r = 0
  · suffices f =ᵐ[μ] 0 by
      rw [snorm_congr_ae this, snorm_zero, hr, ENNReal.coe_zero, mul_zero]
    rw [hr] at hf
    norm_cast at hf
    -- Porting note: two lines above were
    --rw [hr, Nonneg.coe_zero] at hf
    have hnegf : ∫ x, -f x ∂μ = 0 := by
      rw [integral_neg, neg_eq_zero]
      exact le_antisymm (integral_nonpos_of_ae hf) hfint'
    have := (integral_eq_zero_iff_of_nonneg_ae ?_ hfint.neg).1 hnegf
    · filter_upwards [this] with ω hω
      rwa [Pi.neg_apply, Pi.zero_apply, neg_eq_zero] at hω
    · filter_upwards [hf] with ω hω
      rwa [Pi.zero_apply, Pi.neg_apply, Right.nonneg_neg_iff]
  by_cases hμ : IsFiniteMeasure μ
  swap
  · have : μ Set.univ = ∞ := by
      by_contra hμ'
      exact hμ (IsFiniteMeasure.mk <| lt_top_iff_ne_top.2 hμ')
    rw [this, ENNReal.mul_top', if_neg, ENNReal.top_mul', if_neg]
    · 

Proof state:
case neg
α : Type u_1
E : Type u_2
F : Type u_3
𝕜 : Type u_4
inst✝⁹ : NormedAddCommGroup E
inst✝⁸ : NormedSpace ℝ E
hE : CompleteSpace E
inst✝⁷ : NontriviallyNormedField 𝕜
inst✝⁶ : NormedSpace 𝕜 E
inst✝⁵ : SMulCommClass ℝ 𝕜 E
inst✝⁴ : NormedAddCommGroup F
inst✝³ : NormedSpace ℝ F
inst✝² : CompleteSpace F
G : Type u_5
inst✝¹ : NormedAddCommGroup G
inst✝ : NormedSpace ℝ G
m0 : MeasurableSpace α
μ : Measure α
r : ℝ≥0
f : α → ℝ
hfint : Integrable f
hfint' : 0 ≤ ∫ (x : α), f x ∂μ
hf : ∀ᵐ (ω : α) ∂μ, f ω ≤ ↑r
hr : ¬r = 0
hμ : ¬IsFiniteMeasure μ
this : ↑↑μ univ = ⊤
⊢ snorm f 1 μ ≤ ⊤

Next tactic:
exact le_top
theorem snorm_one_le_of_le {r : ℝ≥0} {f : α → ℝ} (hfint : Integrable f μ) (hfint' : 0 ≤ ∫ x, f x ∂μ)
    (hf : ∀ᵐ ω ∂μ, f ω ≤ r) : snorm f 1 μ ≤ 2 * μ Set.univ * r := by
  by_cases hr : r = 0
  · suffices f =ᵐ[μ] 0 by
      rw [snorm_congr_ae this, snorm_zero, hr, ENNReal.coe_zero, mul_zero]
    rw [hr] at hf
    norm_cast at hf
    -- Porting note: two lines above were
    --rw [hr, Nonneg.coe_zero] at hf
    have hnegf : ∫ x, -f x ∂μ = 0 := by
      rw [integral_neg, neg_eq_zero]
      exact le_antisymm (integral_nonpos_of_ae hf) hfint'
    have := (integral_eq_zero_iff_of_nonneg_ae ?_ hfint.neg).1 hnegf
    · filter_upwards [this] with ω hω
      rwa [Pi.neg_apply, Pi.zero_apply, neg_eq_zero] at hω
    · filter_upwards [hf] with ω hω
      rwa [Pi.zero_apply, Pi.neg_apply, Right.nonneg_neg_iff]
  by_cases hμ : IsFiniteMeasure μ
  swap
  · have : μ Set.univ = ∞ := by
      by_contra hμ'
      exact hμ (IsFiniteMeasure.mk <| lt_top_iff_ne_top.2 hμ')
    rw [this, ENNReal.mul_top', if_neg, ENNReal.top_mul', if_neg]
    · exact le_top
    · 

Proof state:
case neg.hnc
α : Type u_1
E : Type u_2
F : Type u_3
𝕜 : Type u_4
inst✝⁹ : NormedAddCommGroup E
inst✝⁸ : NormedSpace ℝ E
hE : CompleteSpace E
inst✝⁷ : NontriviallyNormedField 𝕜
inst✝⁶ : NormedSpace 𝕜 E
inst✝⁵ : SMulCommClass ℝ 𝕜 E
inst✝⁴ : NormedAddCommGroup F
inst✝³ : NormedSpace ℝ F
inst✝² : CompleteSpace F
G : Type u_5
inst✝¹ : NormedAddCommGroup G
inst✝ : NormedSpace ℝ G
m0 : MeasurableSpace α
μ : Measure α
r : ℝ≥0
f : α → ℝ
hfint : Integrable f
hfint' : 0 ≤ ∫ (x : α), f x ∂μ
hf : ∀ᵐ (ω : α) ∂μ, f ω ≤ ↑r
hr : ¬r = 0
hμ : ¬IsFiniteMeasure μ
this : ↑↑μ univ = ⊤
⊢ ¬↑r = 0

Next tactic:
simp [hr]