. intros heq
  exact ⟨h _ _ heq, h _ _ heq.symm⟩
case mpr
α : Type u_1
b c : Basis α
h : ∀ (b c : Basis ?m.10532), as_filter b = as_filter c → b ≤' c
⊢ as_filter b = as_filter c → b ≤' c ∧ c ≤' b

case h
α : Type u_1
b c : Basis α
⊢ ∀ (b c : Basis ?m.10532), as_filter b = as_filter c → b ≤' c
case h
α : Type u_1
b c : Basis α
⊢ ∀ (b c : Basis α), as_filter b = as_filter c → b ≤' c