rw [card_biUnion]
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
M : MultiPart α
⊢ card (Finset.biUnion (range (M.t + 1)) fun i => MultiPart.P M i) = ∑ i in range (M.t + 1), card (MultiPart.P M i)
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
M : MultiPart α
⊢ ∀ (x : ℕ), x ∈ range (M.t + 1) → ∀ (y : ℕ), y ∈ range (M.t + 1) → x ≠ y → Disjoint (MultiPart.P M x) (MultiPart.P M y)