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