have : ¬(n < m) := by assumption
n m : Nat
x✝ : lt n m
h✝ : ¬n < m
⊢ (if n = m then Ordering.eq else Ordering.gt) = Ordering.lt
n m : Nat
x✝ : lt n m
h✝ this : ¬n < m
⊢ (if n = m then Ordering.eq else Ordering.gt) = Ordering.lt