Theorems · Theorem · functional analysis
norm_norm
∀ {E : Type u_5} [inst : SeminormedAddCommGroup E] (x : E), ‖‖x‖‖ = ‖x‖- Defined in
- Mathlib.Analysis.Normed.Group.Real
- Cited by
- 113 results in Mathlib
- Foundations
- Depth 113 from the axioms, rests on 2,432 definitions · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedAddCommGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- norm_nonnegproof · cited by 725
- Real.norm_of_nonnegproof · cited by 135
Cited by113
Results whose statement or proof uses this declaration.
- SchwartzMap.integrableproof · cited by 10
- summable_norm_iffproof · cited by 8
- nnnorm_normproof · cited by 7
- MeasureTheory.hasFiniteIntegral_norm_iffproof · cited by 6
- Asymptotics.isBigOWith_norm_leftproof · cited by 6
- Asymptotics.isBigOWith_norm_rightproof · cited by 6
- norm_smul_inv_normproof · cited by 5
- MeasureTheory.eLpNorm_normproof · cited by 5
- RCLike.norm_coe_normproof · cited by 4
- exists_norm_eqproof · cited by 4
- MvPowerSeries.isRestricted_abs_iffproof · cited by 4
- MeasureTheory.MemLp.normproof · cited by 3