∀ {R : Type u_1} [inst : CommSemiring R] (I : Ideal R) [hI : I.IsPrime] (x : { p // p.IsPrime ∧ p ≤ I }),
  ⟨(↑⟨{ asIdeal := ↑x, isPrime := ⋯ }, ⋯⟩).asIdeal, ⋯⟩ = ⟨(↑⟨{ asIdeal := ↑x, isPrime := ⋯ }, ⋯⟩).asIdeal, ⋯⟩