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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.