Theorems · Theorem · functional analysis
SeminormedRing.norm_mul_le
∀ {α : Type u_5} [self : SeminormedRing α] (a b : α), ‖a * b‖ ≤ ‖a‖ * ‖b‖The norm is submultiplicative.
- Defined in
- Mathlib.Analysis.Normed.Ring.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Norm.normstatement · cited by 5,413
- SeminormedRingstatement and proof · cited by 446
Cited by1
Results whose statement or proof uses this declaration.
- SeminormedRing.toRingSeminormproof · cited by 10