Theorems · Theorem · functional analysis
NormMulClass.norm_mul
∀ {α : Type u_5} {inst : Norm α} {inst_1 : Mul α} [self : NormMulClass α] (a b : α), ‖a * b‖ = ‖a‖ * ‖b‖The norm is multiplicative.
- Defined in
- Mathlib.Analysis.Normed.Ring.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormMulClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- Normstatement and proof · cited by 512
- NormMulClassstatement and proof · cited by 66
Cited by1
Results whose statement or proof uses this declaration.
- norm_mulproof · cited by 171