-- File: FoML/FoML/McDiarmid.lean
Theorem statement:
theorem extracted_formal_statement_24.{u_5, u_4, u_3, u_2} {Ω : Type u_2} {ι : Type u_3} {ι' : Type u_4}
  {_mΩ : MeasurableSpace Ω} {μ : Measure Ω} {β : ι → Type u_5} {mβ : (i : ι) → MeasurableSpace (β i)}
  {f : (i : ι) → Ω → β i} {g : ι' → ι} (hg : Function.Injective g)
  (h : ∀ (s : Finset ι) {f_1 : ι → Set Ω}, (∀ i ∈ s, MeasurableSet (f_1 i)) → μ (⋂ i ∈ s, f_1 i) = ∏ x ∈ s, μ (f_1 x))
  (s' : Finset ι') {f₁' : ι' → Set Ω} (h₁' : ∀ i ∈ s', MeasurableSet (f₁' i)) (i : ι) (y₁ y₂ : ι') (left : y₁ ∈ s')
  (hy₁ : g y₁ = i) (left_1 : y₂ ∈ s') (hy₂ : g y₂ = i) : y₁ = y₂ := sorry

Tactic state before:
Ω : Type u_2
ι : Type u_3
ι' : Type u_4
inst✝ : DecidableEq ι
_mΩ : MeasurableSpace Ω
μ : Measure Ω
β : ι → Type u_5
mβ : (i : ι) → MeasurableSpace (β i)
f : (i : ι) → Ω → β i
g : ι' → ι
hg : Function.Injective g
h : ∀ (s : Finset ι) {f_1 : ι → Set Ω}, (∀ i ∈ s, MeasurableSet (f_1 i)) → μ (⋂ i ∈ s, f_1 i) = ∏ x ∈ s, μ (f_1 x)
s' : Finset ι'
f₁' : ι' → Set Ω
h₁' : ∀ i ∈ s', MeasurableSet (f₁' i)
s : Finset ι := Finset.image g s'
i : ι
y₁ y₂ : ι'
left✝¹ : y₁ ∈ s'
hy₁ : g y₁ = i
left✝ : y₂ ∈ s'
hy₂ : g y₂ = i
⊢ y₁ = y₂

Tactic: exact hg <| hy₁.trans hy₂.symm

Tactic state after:

Premises used: