Theorems · Theorem · number theory

PadicInt.pow_dvd_nthHom_sub

∀ {R : Type u_1} [inst : NonAssocSemiring R] {p : ℕ} {f : (k : ℕ) → R →+* ZMod (p ^ k)} [hp_prime : Fact (Nat.Prime p)],
  (∀ (k1 k2 : ℕ) (hk : k1 ≤ k2), (ZMod.castHom ⋯ (ZMod (p ^ k1))).comp (f k2) = f k1) →
    ∀ (r : R) (i j : ℕ), i ≤ j → ↑p ^ i ∣ PadicInt.nthHom f r j - PadicInt.nthHom f r i

Defined in

Mathlib.NumberTheory.Padics.RingHoms

Cited by

2 results in Mathlib

Foundations

Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NonAssocSemiringFact