refine BishopFin.card_eq_card_of_bij ?_ ?_ ?_
n : Nat
x : Permutation n
⊢ BishopFin.card (Inversion x) = BishopFin.card { a // ↑a.fst < ↑a.snd ∧ ↑x[↑a.fst] > ↑x[↑a.snd] }
case refine_1
n : Nat
x : Permutation n
⊢ Inversion x → { a // ↑a.fst < ↑a.snd ∧ ↑x[↑a.fst] > ↑x[↑a.snd] }

case refine_2
n : Nat
x : Permutation n
⊢ ∀ (b : { a // ↑a.fst < ↑a.snd ∧ ↑x[↑a.fst] > ↑x[↑a.snd] }), ∃ a, ?refine_1 a = b

case refine_3
n : Nat
x : Permutation n
⊢ ∀ (a₁ a₂ : Inversion x), ?refine_1 a₁ = ?refine_1 a₂ → a₁ = a₂