α : Type u_1
β : Type u_2
γ : Type ?u.517176
inst✝ : DecidableEq β
s s₁ s₂ : Finset α
t t₁ t₂ : α → Finset β
h : ∀ (a : α), a ∈ s → t₁ a ⊆ t₂ a
this : ∀ (b : β) (a : α), a ∈ s → b ∈ t₁ a → ∃ a, a ∈ s ∧ b ∈ t₂ a
⊢ Finset.biUnion s t₁ ⊆ Finset.biUnion s t₂
α : Type u_1
β : Type u_2
γ : Type ?u.517176
inst✝ : DecidableEq β
s s₁ s₂ : Finset α
t t₁ t₂ : α → Finset β
h : ∀ (a : α), a ∈ s → t₁ a ⊆ t₂ a
⊢ Finset.biUnion s t₁ ⊆ Finset.biUnion s t₂
have : ∀ b a, a ∈ s → b ∈ t₁ a → ∃ a : α, a ∈ s ∧ b ∈ t₂ a := fun b a ha hb =>
  ⟨a, ha, Finset.mem_of_subset (h a ha) hb⟩
no goals
α : Type u_1
β : Type u_2
γ : Type ?u.517176
inst✝ : DecidableEq β
s s₁ s₂ : Finset α
t t₁ t₂ : α → Finset β
h : ∀ (a : α), a ∈ s → t₁ a ⊆ t₂ a
this : ∀ (b : β) (a : α), a ∈ s → b ∈ t₁ a → ∃ a, a ∈ s ∧ b ∈ t₂ a
⊢ Finset.biUnion s t₁ ⊆ Finset.biUnion s t₂
simpa only [subset_iff, mem_biUnion, exists_imp, and_imp, exists_prop]