Theorems · Theorem · functional analysis
norm_sub_le
∀ {E : Type u_5} [inst : SeminormedAddGroup E] (a b : E), ‖a - b‖ ≤ ‖a‖ + ‖b‖- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 26 results in Mathlib
- Foundations
- Depth 98 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 and proof · cited by 5,413
- sub_eq_add_negproof · cited by 1,023
- SeminormedAddGroupstatement and proof · cited by 331
- norm_negproof · cited by 190
- norm_add_leproof · cited by 68
Cited by26
Results whose statement or proof uses this declaration.
- norm_sub_le_of_leproof · cited by 4
- norm_le_add_norm_addproof · cited by 3
- ApproximatesLinearOn.norm_fderiv_sub_leproof · cited by 3
- tendsto_tsum_of_dominated_convergenceproof · cited by 2
- MeasureTheory.tendsto_lintegral_norm_of_dominated_convergenceproof · cited by 2
- norm_commutator_units_sub_one_leproof · cited by 2
- nnnorm_sub_leproof · cited by 2
- NumberField.mixedEmbedding.convexBodySum_isBoundedproof · cited by 1
- ContinuousLinearMap.exists_approx_preimage_norm_leproof · cited by 1
- dist_vsub_vsub_leproof · cited by 1
- RightDerivMeasurableAux.mem_A_of_differentiableproof · cited by 1
- RightDerivMeasurableAux.norm_sub_le_of_mem_Aproof · cited by 1