Theorems · Theorem · commutative algebra
smoothingFun_le
∀ {R : Type u_1} [inst : CommRing R] (μ : RingSeminorm R) (x : R) (n : ℕ+), smoothingFun μ x ≤ μ (x ^ ↑n) ^ (1 / ↑↑n)For any x and any positive n, smoothingFun μ x ≤ μ (x ^ (n : ℕ))^(1 / n : ℝ).
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 197 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Realstatement · cited by 25,697
- CommRingstatement and proof · cited by 17,173
- PNatstatement and proof · cited by 392
- PNat.valstatement · cited by 226
- RingSeminormstatement and proof · cited by 58
- ciInf_leproof · cited by 25
- smoothingFunstatement · cited by 13
- smoothingSeminormSeq_bddBelowproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- smoothingFun_le_selfproof · cited by 0