apply Nat.tri_add_self_lt_tri_of_lt
case h.right.left
m₁ n₁ m₂ n₂ : Nat
h₁ : m₁ ≤ n₁
h₂ : m₂ ≤ n₂
h : n₁.tri + m₁ = n₂.tri + m₂
x✝ : Decidable (n₁ ≤ n₂)
hlt : ¬n₁ ≥ n₂
⊢ n₁.tri + n₁ < n₂.tri
case h.right.left.a
m₁ n₁ m₂ n₂ : Nat
h₁ : m₁ ≤ n₁
h₂ : m₂ ≤ n₂
h : n₁.tri + m₁ = n₂.tri + m₂
x✝ : Decidable (n₁ ≤ n₂)
hlt : ¬n₁ ≥ n₂
⊢ n₁ < n₂