rwa [Ne, Ideal.map_eq_bot_iff_of_injective (NoZeroSMulDivisors.algebraMap_injective R S)]
R : Type u_1
S : Type u_2
inst✝⁵ : CommRing R
inst✝⁴ : CommRing S
inst✝³ : Algebra R S
inst✝² : Ring.DimensionLEOne R
inst✝¹ : IsDedekindDomain S
inst✝ : NoZeroSMulDivisors R S
p : Ideal R
hp : p ≠ ⊥
hp' : p.IsPrime
P : Ideal S
⊢ Ideal.map (algebraMap R S) p ≠ ⊥
no goals