Theorems · Theorem · commutative algebra
seminormFromConst_const_mul
∀ {R : Type u_1} [inst : CommRing R] {c : R} {f : RingSeminorm R},
f 1 ≤ 1 →
f c ≠ 0 →
IsPowMul ⇑f → ∀ (x : R), seminormFromConst' c f (c * x) = seminormFromConst' c f c * seminormFromConst' c f x- Cited by
- 1 results in Mathlib
- Foundations
- Depth 160 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.
Cites23
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
- add_zeroproof · cited by 2,707
- Filter.atTopproof · cited by 2,405
- mul_assocproof · cited by 1,667
- pow_oneproof · cited by 894
- Filter.Tendsto.compproof · cited by 560
- tendsto_const_nhdsproof · cited by 330
Cited by1
Results whose statement or proof uses this declaration.
- spectralAlgNorm_mulproof · cited by 0