Theorems · Theorem · commutative algebra
isNonarchimedean_smoothingFun
∀ {R : Type u_1} [inst : CommRing R] (μ : RingSeminorm R),
μ 1 ≤ 1 → IsNonarchimedean ⇑μ → IsNonarchimedean (smoothingFun μ)If μ 1 ≤ 1 and μ is nonarchimedean, then smoothingFun μ is nonarchimedean.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 209 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.
Cites68
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
- Setproof · cited by 53,352
- Realstatement and proof · cited by 25,697
- CommRingstatement and proof · cited by 17,173
- nhdsproof · cited by 5,554
- Filter.Tendstoproof · cited by 3,814
- LE.le.transproof · cited by 3,151
- Filter.atTopproof · cited by 2,405
- LT.lt.leproof · cited by 2,189
- le_reflproof · cited by 2,061
- Set.Iccproof · cited by 1,702
- closureproof · cited by 1,254
Cited by1
Results whose statement or proof uses this declaration.
- exists_nonarchimedean_pow_mul_seminorm_of_finiteDimensionalproof · cited by 5