Theorems · Theorem · functional analysis
nnnorm_mul
∀ {α : Type u_2} [inst : SeminormedAddCommGroup α] [inst_1 : Mul α] [NormMulClass α] (a b : α), ‖a * b‖₊ = ‖a‖₊ * ‖b‖₊- Defined in
- Mathlib.Analysis.Normed.Ring.Basic
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NNRealstatement · cited by 4,310
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- NNNorm.nnnormstatement · cited by 952
- NNReal.eqproof · cited by 201
- norm_mulproof · cited by 171
- NormMulClassstatement and proof · cited by 66
Cited by10
Results whose statement or proof uses this declaration.
- enorm_mulproof · cited by 4
- NumberField.mixedEmbedding.volume_fundamentalDomain_latticeBasisproof · cited by 4
- MeasureTheory.eLpNorm'_le_eLpNorm'_mul_eLpNorm'proof · cited by 2
- Real.toNNReal_mul_nnnormproof · cited by 1
- le_egauge_smul_rightproof · cited by 1
- Polynomial.mahlerMeasure_C_mul_X_add_Cproof · cited by 1
- lipschitzWith_circleMapproof · cited by 0
- NumberField.house_nat_mulproof · cited by 0
- Polynomial.cauchyBound_smulproof · cited by 0
- Polynomial.IsRoot.norm_lt_cauchyBoundproof · cited by 0