. intros h
  apply le_antisymm
  . exact Basis.as_filter_le h.1
  . exact Basis.as_filter_le h.2
case mp
α : Type u_1
b c : Basis α
⊢ b ≤' c ∧ c ≤' b → as_filter b = as_filter c

case mpr
α : Type u_1
b c : Basis α
⊢ as_filter b = as_filter c → b ≤' c ∧ c ≤' b
case mpr
α : Type u_1
b c : Basis α
⊢ as_filter b = as_filter c → b ≤' c ∧ c ≤' b