intro k hk
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
i : ℕ
v : α
j : ℕ
M : MultiPart α
hvi : i ∈ range (M.t + 1) ∧ v ∈ MultiPart.P M i
hj : j ∈ range (M.t + 1) ∧ j ≠ i
⊢ ∀ (x : ℕ),
    x ∈ erase (erase (range (M.t + 1)) j) i →
      card (MultiPart.P (move M hvi hj) x) * card ((move M hvi hj).A \ MultiPart.P (move M hvi hj) x) =
        card (MultiPart.P M x) * card (M.A \ MultiPart.P M x)
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
i : ℕ
v : α
j : ℕ
M : MultiPart α
hvi : i ∈ range (M.t + 1) ∧ v ∈ MultiPart.P M i
hj : j ∈ range (M.t + 1) ∧ j ≠ i
k : ℕ
hk : k ∈ erase (erase (range (M.t + 1)) j) i
⊢ card (MultiPart.P (move M hvi hj) k) * card ((move M hvi hj).A \ MultiPart.P (move M hvi hj) k) =
    card (MultiPart.P M k) * card (M.A \ MultiPart.P M k)