Theorems · Theorem · functional analysis
abs_norm_sub_norm_le_norm_neg_add
∀ {E : Type u_5} [inst : SeminormedAddGroup E] (a b : E), |‖a‖ - ‖b‖| ≤ ‖-a + b‖- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 107 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.
Cites8
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
- add_zeroproof · cited by 2,707
- absstatement and proof · cited by 1,814
- SeminormedAddGroupstatement and proof · cited by 331
- norm_negproof · cited by 190
- dist_eq_norm_neg_addproof · cited by 46
- abs_dist_sub_leproof · cited by 8
Cited by3
Results whose statement or proof uses this declaration.
- abs_norm_sub_norm_leproof · cited by 7
- dist_norm_norm_le_norm_neg_addproof · cited by 1
- norm_sub_norm_le_norm_neg_addproof · cited by 0