have q : ∀ Q ∈ 𝒜.filter fun A ↦ compress U V A ∉ 𝒜, compress U V Q ≠ Q := by
  simp_rw [mem_filter]
  intro Q hQ h
  rw [h] at hQ
  exact hQ.2 hQ.1
α : Type u_1
inst✝ : LinearOrder α
s U✝ V✝ : Finset α
n : ℕ
U V : Finset (Fin n)
hU : U.Nonempty
hV : V.Nonempty
h : U.max' hU < V.max' hV
𝒜 : Finset (Finset (Fin n))
a : filter (fun x => compress U V x ∈ 𝒜) 𝒜 ∪ filter (fun x => x ∉ 𝒜) (image (compress U V) 𝒜) ≠ 𝒜
⊢ Finset.UV.familyMeasure (filter (fun x => compress U V x ∈ 𝒜) 𝒜 ∪ filter (fun x => x ∉ 𝒜) (image (compress U V) 𝒜)) <
    Finset.UV.familyMeasure 𝒜
α : Type u_1
inst✝ : LinearOrder α
s U✝ V✝ : Finset α
n : ℕ
U V : Finset (Fin n)
hU : U.Nonempty
hV : V.Nonempty
h : U.max' hU < V.max' hV
𝒜 : Finset (Finset (Fin n))
a : filter (fun x => compress U V x ∈ 𝒜) 𝒜 ∪ filter (fun x => x ∉ 𝒜) (image (compress U V) 𝒜) ≠ 𝒜
q : ∀ Q ∈ filter (fun A => compress U V A ∉ 𝒜) 𝒜, compress U V Q ≠ Q
⊢ Finset.UV.familyMeasure (filter (fun x => compress U V x ∈ 𝒜) 𝒜 ∪ filter (fun x => x ∉ 𝒜) (image (compress U V) 𝒜)) <
    Finset.UV.familyMeasure 𝒜