Theorems · Theorem · functional analysis
abs_norm
∀ {E : Type u_5} [inst : SeminormedAddGroup E] (z : E), |‖z‖| = ‖z‖- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 36 results in Mathlib
- Foundations
- Depth 113 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.
- Realstatement · cited by 25,697
- Norm.normstatement · cited by 5,413
- absstatement · cited by 1,814
- norm_nonnegproof · cited by 725
- SeminormedAddGroupstatement and proof · cited by 331
- abs_of_nonnegproof · cited by 279
Cited by36
Results whose statement or proof uses this declaration.
- innerSL_apply_normproof · cited by 5
- circleAverage_log_norm_sub_const_eq_posLogproof · cited by 4
- abs_real_inner_div_norm_mul_norm_le_oneproof · cited by 4
- FormalMultilinearSeries.isLittleO_of_lt_radiusproof · cited by 3
- ZLattice.exists_forall_abs_repr_le_normproof · cited by 2
- hasFDerivAt_of_tendstoUniformlyOnFilterproof · cited by 2
- summable_norm_mul_geometric_of_norm_lt_oneproof · cited by 2
- lp.hasSum_singleproof · cited by 2
- summableLocallyUniformlyOn_iteratedDerivWithin_smul_cexpproof · cited by 2
- Complex.isCauSeq_norm_expproof · cited by 2
- ModularGroup.exists_one_half_le_im_smul_and_norm_denom_leproof · cited by 1
- OpenPartialHomeomorph.contDiffOn_univUnitBall_symmproof · cited by 1