α : Type u_1
β : Type u_2
γ : Type ?u.239402
ι : Sort ?u.239405
ι' : Sort ?u.239408
ι₂ : Sort ?u.239411
κ : ι → Sort ?u.239416
κ₁ : ι → Sort ?u.239421
κ₂ : ι → Sort ?u.239426
κ' : ι' → Sort ?u.239431
S : Set (Set α)
hS : Set.Nonempty S
t : Set β
⊢ (⋂ (r : Set α × Set β) (_ : r ∈ S ×ˢ {t}), r.fst ×ˢ r.snd) = ⋂ (s : Set α) (_ : s ∈ S), s ×ˢ t
α : Type u_1
β : Type u_2
γ : Type ?u.239402
ι : Sort ?u.239405
ι' : Sort ?u.239408
ι₂ : Sort ?u.239411
κ : ι → Sort ?u.239416
κ₁ : ι → Sort ?u.239421
κ₂ : ι → Sort ?u.239426
κ' : ι' → Sort ?u.239431
S : Set (Set α)
hS : Set.Nonempty S
t : Set β
⊢ ⋂₀ S ×ˢ t = ⋂ (s : Set α) (_ : s ∈ S), s ×ˢ t
rw [← sInter_singleton t, sInter_prod_sInter hS (singleton_nonempty t), sInter_singleton]
no goals
α : Type u_1
β : Type u_2
γ : Type ?u.239402
ι : Sort ?u.239405
ι' : Sort ?u.239408
ι₂ : Sort ?u.239411
κ : ι → Sort ?u.239416
κ₁ : ι → Sort ?u.239421
κ₂ : ι → Sort ?u.239426
κ' : ι' → Sort ?u.239431
S : Set (Set α)
hS : Set.Nonempty S
t : Set β
⊢ (⋂ (r : Set α × Set β) (_ : r ∈ S ×ˢ {t}), r.fst ×ˢ r.snd) = ⋂ (s : Set α) (_ : s ∈ S), s ×ˢ t
simp_rw [prod_singleton, mem_image, iInter_exists, biInter_and', iInter_iInter_eq_right]