intros b c hbc s hs
case h
α : Type u_1
b c : Basis α
⊢ ∀ (b c : Basis α), as_filter b = as_filter c → b ≤' c
case h
α : Type u_1
b✝ c✝ b c : Basis α
hbc : as_filter b = as_filter c
s : Set α
hs : s ∈ c
⊢ ∃ t, t ∈ b ∧ t ⊆ s