Theorems · Theorem · commutative algebra
isPowMul_smoothingFun
∀ {R : Type u_1} [inst : CommRing R] (μ : RingSeminorm R), μ 1 ≤ 1 → IsPowMul (smoothingFun μ)If μ 1 ≤ 1 and μ is nonarchimedean, then smoothingFun μ is
power-multiplicative.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 208 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.
Cites31
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
- nhdsproof · cited by 5,554
- mul_oneproof · cited by 3,885
- Filter.Tendstoproof · cited by 3,814
- Filter.atTopproof · cited by 2,405
- mul_commproof · cited by 2,262
- mul_assocproof · cited by 1,667
- ne_of_gtproof · cited by 637
- zero_lt_oneproof · cited by 598
- Filter.Tendsto.compproof · cited by 560
Cited by1
Results whose statement or proof uses this declaration.
- exists_nonarchimedean_pow_mul_seminorm_of_finiteDimensionalproof · cited by 5