apply Nat.ne_of_lt
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 + m₁ = n₂.tri + m₂
case h
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 + m₁ < n₂.tri + m₂