no goals
α : Type u_1
ι : Sort u_2
ι' : Sort u_3
inst✝ : LinearOrder α
Ixx : α → α → Set α
p : α → α → Prop
Hne : ∀ {a b : α}, Set.Nonempty (Ixx a b) → p a b
Hi : ∀ {a₁ b₁ a₂ b₂ : α}, Ixx a₁ b₁ ∩ Ixx a₂ b₂ = Ixx (max a₁ a₂) (min b₁ b₂)
f : ι → α
g : ι' → α
⊢ IsPiSystem {S | ∃ i j, p (f i) (g j) ∧ Ixx (f i) (g j) = S}
simpa only [exists_range_iff] using isPiSystem_Ixx_mem (@Hne) (@Hi) (range f) (range g)