Theorems · Theorem · number theory

PadicInt.isCauSeq_nthHom

∀ {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), IsCauSeq (padicNorm p) fun n => ↑(PadicInt.nthHom f r n)

Defined in

Mathlib.NumberTheory.Padics.RingHoms

Cited by

3 results in Mathlib

Foundations

Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NonAssocSemiringFact