Theorems · Theorem · commutative algebra
RingSeminorm.exists_index_pow_le
∀ {R : Type u_1} [inst : CommRing R] (p : RingSeminorm R),
IsNonarchimedean ⇑p →
∀ (x y : R) (n : ℕ), ∃ m < n + 1, p ((x + y) ^ n) ^ (1 / ↑n) ≤ (p (x ^ m) * p (y ^ (n - m))) ^ (1 / ↑n)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- CommRingstatement and proof · cited by 17,173
- Nat.cast_oneproof · cited by 2,501
- Nat.cast_nonneg'proof · cited by 245
- NonnegHomClass.apply_nonnegproof · cited by 79
- IsNonarchimedeanstatement and proof · cited by 77
- RingSeminormstatement and proof · cited by 58
- Real.rpow_le_rpowproof · cited by 38
- Mathlib.Meta.Positivity.div_nonneg_of_pos_of_nonnegproof · cited by 29
- IsNonarchimedean.add_pow_leproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- isNonarchimedean_smoothingFunproof · cited by 1