rw [Nat.add_comm s, Nat.sub_add_cancel (Nat.le_of_lt_succ hs)]
n t s : Nat
hs : s < t + 1
h : n.split = ⟨t, ⟨s, hs⟩⟩
⊢ (↑⟨t, ⟨s, hs⟩⟩.snd + (⟨t, ⟨s, hs⟩⟩.fst - ↑⟨t, ⟨s, hs⟩⟩.snd)).tri + ↑⟨t, ⟨s, hs⟩⟩.snd = n
n t s : Nat
hs : s < t + 1
h : n.split = ⟨t, ⟨s, hs⟩⟩
⊢ t.tri + ↑⟨t, ⟨s, hs⟩⟩.snd = n