simp only [Finset.Nat.mem_antidiagonalTuple, Finset.mem_coe, Finset.mem_mk, Weight.sum]
case h
n d : ℕ
inst✝ : NeZero d
a : Fin (Nat.succ n) → ℕ
⊢ a ∈ ↑(Finset.Nat.antidiagonalTuple (Nat.succ n) d) ↔ a ∈ {w | Weight.sum w = d}
case h
n d : ℕ
inst✝ : NeZero d
a : Fin (Nat.succ n) → ℕ
⊢ ∑ i : Fin (Nat.succ n), a i = d ↔ a ∈ {w | ∑ j : Fin (Nat.succ n), w j = d}