apply BishopFin.count_congr
case refine_4
n : Nat
x y : Permutation n
this : ∀ (a b c d : Nat), a + b + (c + d) = a + c + (b + d)
⊢ (BishopFin.count fun a => (↑a.fst < ↑a.snd ∧ ↑y[↑a.fst] > ↑y[↑a.snd]) ∧ ¬↑(x * y)[↑a.fst] > ↑(x * y)[↑a.snd]) =
    BishopFin.count fun t => ↑t.fst < ↑t.snd ∧ ↑y[↑t.fst] > ↑y[↑t.snd] ∧ ↑(x * y)[↑t.fst] < ↑(x * y)[↑t.snd]
case refine_4.h
n : Nat
x y : Permutation n
this : ∀ (a b c d : Nat), a + b + (c + d) = a + c + (b + d)
⊢ ∀ (a : Fin n × Fin n),
    (↑a.fst < ↑a.snd ∧ ↑y[↑a.fst] > ↑y[↑a.snd]) ∧ ¬↑(x * y)[↑a.fst] > ↑(x * y)[↑a.snd] ↔
      ↑a.fst < ↑a.snd ∧ ↑y[↑a.fst] > ↑y[↑a.snd] ∧ ↑(x * y)[↑a.fst] < ↑(x * y)[↑a.snd]