have : n + k < m + j := calc
  n + k < m + k := lt_substL_add ‹n < m›
  m + k < m + j := lt_substR_add ‹k < j›
ℕ : Type
inst✝⁴ : Core ℕ
inst✝³ : Induction ℕ
inst✝² : Addition ℕ
inst✝¹ : Sign ℕ
order_inst : Order ℕ
inst✝ : Compare ℕ
ord : Ordering
n m k j : ℕ
x✝¹ : compare n m = Ordering.lt
x✝ : compare k j = Ordering.lt
this✝ : n < m
this : k < j
⊢ compare (n + k) (m + j) = Ordering.lt
ℕ : Type
inst✝⁴ : Core ℕ
inst✝³ : Induction ℕ
inst✝² : Addition ℕ
inst✝¹ : Sign ℕ
order_inst : Order ℕ
inst✝ : Compare ℕ
ord : Ordering
n m k j : ℕ
x✝¹ : compare n m = Ordering.lt
x✝ : compare k j = Ordering.lt
this✝¹ : n < m
this✝ : k < j
this : n + k < m + j
⊢ compare (n + k) (m + j) = Ordering.lt