Theorems · Theorem · functional analysis
norm_toNNReal
∀ {E : Type u_5} [inst : SeminormedAddGroup E] {a : E}, ‖a‖.toNNReal = ‖a‖₊- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedAddGroup
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.
- Norm.normstatement · cited by 5,413
- NNRealstatement · cited by 4,310
- NNNorm.nnnormstatement · cited by 952
- SeminormedAddGroupstatement and proof · cited by 331
- Real.toNNRealstatement · cited by 267
- Real.toNNReal_coeproof · cited by 36
Cited by8
Results whose statement or proof uses this declaration.
- NumberField.mixedEmbedding.volume_fundamentalDomain_latticeBasisproof · cited by 4
- IsGreatest.nnnorm_cfcₙproof · cited by 3
- SchwartzMap.eLpNorm_le_seminormproof · cited by 2
- IsGreatest.nnnorm_cfcproof · cited by 2
- spectrum.hasFPowerSeriesOnBall_inverse_one_sub_smulproof · cited by 1
- spectrum.spectralRadius_le_pow_nnnorm_pow_one_divproof · cited by 1
- spectrum.limsup_pow_nnnorm_pow_one_div_le_spectralRadiusproof · cited by 1
- spectrum.differentiableOn_inverse_one_sub_smulproof · cited by 1