case zero =>
  intro (_ : m ≤ 0)
  have ⟨e, (_ : m + e ≃ 0)⟩ := le_defn.mp ‹m ≤ 0›
  show n ≤ 0
  apply le_defn.mpr
  exists d + e
  show n + (d + e) ≃ 0
  calc
    n + (d + e) ≃ _ := Rel.symm AA.assoc
    (n + d) + e ≃ _ := AA.substL ‹n + d ≃ m›
    m + e       ≃ _ := ‹m + e ≃ 0›
    0           ≃ _ := Rel.refl
ℕ : Type
inst✝³ : Core ℕ
inst✝² : Induction ℕ
inst✝¹ : Addition ℕ
inst✝ : Sign ℕ
order_inst : Order ℕ
n m k : ℕ
x✝ : n ≤ m
d : ℕ
h✝ : n + d ≃ m
⊢ m ≤ 0 → n ≤ 0
no goals