have : n < m := prelude_lt_iff_impl_lt.mpr ‹lt n m›
n m : Nat
x✝ : lt n m
h✝ this : ¬n < m
⊢ (if n = m then Ordering.eq else Ordering.gt) = Ordering.lt
n m : Nat
x✝ : lt n m
h✝ this✝ : ¬n < m
this : n < m
⊢ (if n = m then Ordering.eq else Ordering.gt) = Ordering.lt