have (Integer.NonzeroWithSign.intro
      (n : ℕ) (_ : Positive n) (_ : x ≃ -1 * coe n)) :=
  Impl.sign_props.negative_iff_sign_neg1.mp ‹Negative x›
x : ℤ
x✝ : Negative x
⊢ ∃ n, Positive n ∧ x ≃ -coe n
x : ℤ
x✝ : Negative x
n : ℕ
pos✝ : Positive n
eqv✝ : x ≃ -1 * coe n
⊢ ∃ n, Positive n ∧ x ≃ -coe n