calc
  (pn//pd)⁻¹ * pn//pd
    ≃ _ := eqv_refl
  (pd * sgn pn)//(pn * sgn pn) * pn//pd
    ≃ _ := eqv_refl
  ((pd * sgn pn) * pn)//((pn * sgn pn) * pd)
    ≃ _ := substN AA.assoc
  (pd * (sgn pn * pn))//((pn * sgn pn) * pd)
    ≃ _ := substN (AA.substR AA.comm)
  (pd * (pn * sgn pn))//((pn * sgn pn) * pd)
    ≃ _ := substN AA.comm
  ((pn * sgn pn) * pd)//((pn * sgn pn) * pd)
    ≃ _ := eqv_one_iff_numer_eqv_denom.mpr Rel.refl
  1
    ≃ _ := eqv_refl
ℕ : Type
inst✝¹ : Natural ℕ
ℤ : Type
inst✝ : Integer ℤ
pn pd : ℤ
denominator_positive✝ : AP (Positive pd)
x✝ : AP (pn//pd ≄ 0)
this : Integer.Nonzero pn
⊢ (pn//pd)⁻¹ * pn//pd ≃ 1
no goals