Theorems · Theorem · functional analysis
abs_norm_sub_norm_le
∀ {E : Type u_5} [inst : SeminormedAddCommGroup E] (a b : E), |‖a‖ - ‖b‖| ≤ ‖a - b‖- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedAddCommGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- absstatement · cited by 1,814
- LE.le.trans_eqproof · cited by 328
- norm_neg_addproof · cited by 12
- abs_norm_sub_norm_le_norm_neg_addproof · cited by 3
Cited by7
Results whose statement or proof uses this declaration.
- norm_sub_norm_leproof · cited by 15
- Complex.lim_normproof · cited by 4
- dist_norm_norm_leproof · cited by 1
- multipliable_norm_one_add_of_summable_normproof · cited by 1
- RCLike.isCauSeq_normproof · cited by 0
- not_sameRay_iff_abs_lt_norm_subproof · cited by 0
- Complex.isCauSeq_normproof · cited by 0