no goals
α : Type u
β : Type v
γ : Type w
ι : Sort x
inst✝¹ : Preorder α
inst✝ : Preorder β
s✝ t : Set α
a✝ b a : α
s : Set α
⊢ lowerBounds (insert a s) = Iic a ∩ lowerBounds s
rw [insert_eq, lowerBounds_union, lowerBounds_singleton]