Theorems · Theorem · commutative algebra
smoothingSeminormSeq_bddBelow
∀ {R : Type u_1} [inst : CommRing R] (μ : RingSeminorm R) (x : R), BddBelow (Set.range fun n => μ (x ^ ↑n) ^ (1 / ↑↑n))smoothingSeminormSeq is bounded below (by zero).
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 196 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
- Set.rangestatement · cited by 4,705
- BddBelowstatement · cited by 401
- PNatstatement · cited by 392
- PNat.valstatement · cited by 226
- RingSeminormstatement and proof · cited by 58
- zero_mem_lowerBounds_smoothingSeminormSeq_rangeproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- isNonarchimedean_smoothingFunproof · cited by 1
- tendsto_smoothingFun_of_eq_zeroproof · cited by 1
- tendsto_smoothingFun_of_ne_zeroproof · cited by 1
- smoothingFun_leproof · cited by 1