simp only [RingHom.toIntAlgHom, RingHom.toMonoidHom_eq_coe, AlgHom.coe_mk, RingHom.coe_mk,
  MonoidHom.coe_coe, RingHom.coe_comp, RingHom.coe_coe, Function.comp_apply]
case a.h
K : Type u_1
p : ℕ+
hpri : Fact p.Prime
inst✝² : Field K
inst✝¹ : CharZero K
inst✝ : IsCyclotomicExtension {p} ℚ K
ζ : K
hζ : IsPrimitiveRoot ζ ↑p
hp : p ≠ 2
σ : 𝓞 K →+* 𝓞 K
this✝¹ : Fact (↑p).Prime
this✝ : NumberField K := IsCyclotomicExtension.numberField {p} ℚ K
this : AddGroup (𝓞 K ⧸ Ideal.span {↑hζ.unit' - 1}) := inferInstance
⊢ ((Ideal.Quotient.mk (Ideal.span {↑hζ.unit' - 1})).comp σ).toIntAlgHom ↑hζ.unit' =
    (Ideal.Quotient.mk (Ideal.span {↑hζ.unit' - 1})).toIntAlgHom ↑hζ.unit'
case a.h
K : Type u_1
p : ℕ+
hpri : Fact p.Prime
inst✝² : Field K
inst✝¹ : CharZero K
inst✝ : IsCyclotomicExtension {p} ℚ K
ζ : K
hζ : IsPrimitiveRoot ζ ↑p
hp : p ≠ 2
σ : 𝓞 K →+* 𝓞 K
this✝¹ : Fact (↑p).Prime
this✝ : NumberField K := IsCyclotomicExtension.numberField {p} ℚ K
this : AddGroup (𝓞 K ⧸ Ideal.span {↑hζ.unit' - 1}) := inferInstance
⊢ (Ideal.Quotient.mk (Ideal.span {↑hζ.unit' - 1})) (σ ↑hζ.unit') =
    (Ideal.Quotient.mk (Ideal.span {↑hζ.unit' - 1})) ↑hζ.unit'