Theorems · Theorem · functional analysis
nnnorm_mul_le
∀ {α : Type u_2} [inst : NonUnitalSeminormedRing α] (a b : α), ‖a * b‖₊ ≤ ‖a‖₊ * ‖b‖₊- Defined in
- Mathlib.Analysis.Normed.Ring.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NonUnitalSeminormedRing
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.
- NNRealstatement · cited by 4,310
- NNNorm.nnnormstatement · cited by 952
- NonUnitalSeminormedRingstatement and proof · cited by 44
- norm_mul_leproof · cited by 31
Cited by4
Results whose statement or proof uses this declaration.
- DoubleCentralizer.norm_fst_eq_sndproof · cited by 3
- ContinuousMap.idealOfSet_ofIdeal_eq_closureproof · cited by 2
- Matrix.linfty_opNNNorm_mulproof · cited by 2
- nnnorm_mul_le_of_leproof · cited by 1