have : 1 < n * m := calc
  1     ≤ _ := positive_ge.mp ‹Positive m›
  m     ≃ _ := Rel.symm AA.identL
  1 * m < _ := subst_mul_lt ‹Positive m› ‹1 < n›
  n * m ≃ _ := Rel.refl
ℕ : Type
inst✝⁵ : Core ℕ
inst✝⁴ : Induction ℕ
inst✝³ : Addition ℕ
inst✝² : Sign ℕ
inst✝¹ : Order ℕ
inst✝ : Multiplication ℕ
n m : ℕ
x✝ : n * m ≃ 1
this✝¹ : Positive (n * m)
left✝ : Positive n
right✝ : Positive m
this✝ : n ≥ 1
this : n > 1 ∨ n ≃ 1
h✝ : n > 1
⊢ n ≃ 1 ∧ m ≃ 1
ℕ : Type
inst✝⁵ : Core ℕ
inst✝⁴ : Induction ℕ
inst✝³ : Addition ℕ
inst✝² : Sign ℕ
inst✝¹ : Order ℕ
inst✝ : Multiplication ℕ
n m : ℕ
x✝ : n * m ≃ 1
this✝² : Positive (n * m)
left✝ : Positive n
right✝ : Positive m
this✝¹ : n ≥ 1
this✝ : n > 1 ∨ n ≃ 1
h✝ : n > 1
this : 1 < n * m
⊢ n ≃ 1 ∧ m ≃ 1