no goals
a : ℤ
⊢ (↑a)⁻¹.num = Int.sign a
induction a using Int.induction_on <;>
  simp [← Int.negSucc_coe', Int.negSucc_coe, -neg_add_rev, Rat.inv_neg, Int.ofNat_add_one_out,
    -Nat.cast_succ, inv_coe_nat_num_of_pos, -Int.cast_negSucc, @eq_comm ℤ 1,
    Int.sign_eq_one_of_pos, ofInt_eq_cast]