no goals
M : Type u_2
inst✝² : CommMonoid M
S : Submonoid M
N : Type u_1
inst✝¹ : CommMonoid N
P : Type ?u.739560
inst✝ : CommMonoid P
f : LocalizationMap S N
z : N
⊢ ↑(toMap f) (sec f z).fst *
      ↑(↑(IsUnit.liftRight (MonoidHom.restrict (toMap f) S) (_ : ∀ (y : { x // x ∈ S }), IsUnit (↑(toMap f) ↑y)))
            (sec f z).snd)⁻¹ =
    z
rw [← sec_spec, mul_inv_left, mul_comm]