apply Nat.add_le_add_right
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
i j : ℕ
M : MultiPart α
hi : i ∈ range (M.t + 1)
hj : j ∈ range (M.t + 1)
hne : i ≠ j
⊢ card (MultiPart.P M i) + card (MultiPart.P M j) ≤
    ∑ x in erase (range (M.t + 1)) j, card (MultiPart.P M x) + card (MultiPart.P M j)
case h
α : Type u_1
inst✝¹ : Fintype α
inst✝ : DecidableEq α
i j : ℕ
M : MultiPart α
hi : i ∈ range (M.t + 1)
hj : j ∈ range (M.t + 1)
hne : i ≠ j
⊢ card (MultiPart.P M i) ≤ ∑ x in erase (range (M.t + 1)) j, card (MultiPart.P M x)