rwa [map_comap_of_surjective _ Quotient.mk_surjective] at this
R : Type u_1
S : Type u_2
inst✝¹ : CommRing R
ι : Type ?u.16994
inst✝ : CommRing S
I : Ideal R
f : R →+* S
H : ∀ a ∈ I, f a = 0
this : map (Quotient.mk I) (comap (Quotient.mk I) (comap (Quotient.lift I f H) ⊥)) = map (Quotient.mk I) (ker f)
⊢ ker (Quotient.lift I f H) = map (Quotient.mk I) (ker f)
no goals