antisymmetry using LE.le
m₁ n₁ m₂ n₂ : Nat
h₁ : m₁ ≤ n₁
h₂ : m₂ ≤ n₂
h : n₁.tri + m₁ = n₂.tri + m₂
hle : n₁ ≤ n₂
hge : n₁ ≥ n₂
⊢ n₁ = n₂
case a
m₁ n₁ m₂ n₂ : Nat
h₁ : m₁ ≤ n₁
h₂ : m₂ ≤ n₂
h : n₁.tri + m₁ = n₂.tri + m₂
hle : n₁ ≤ n₂
hge : n₁ ≥ n₂
⊢ n₁ ≤ n₂

case a
m₁ n₁ m₂ n₂ : Nat
h₁ : m₁ ≤ n₁
h₂ : m₂ ≤ n₂
h : n₁.tri + m₁ = n₂.tri + m₂
hle : n₁ ≤ n₂
hge : n₁ ≥ n₂
⊢ n₂ ≤ n₁