Theorems · Theorem · functional analysis
norm_le_norm_add_norm_neg_add
∀ {E : Type u_5} [inst : SeminormedAddGroup E] (u v : E), ‖u‖ ≤ ‖v‖ + ‖-u + v‖- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 3 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.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Norm.normstatement and proof · cited by 5,413
- add_zeroproof · cited by 2,707
- add_commproof · cited by 1,535
- SeminormedAddGroupstatement and proof · cited by 331
- neg_add_cancelproof · cited by 256
- norm_negproof · cited by 190
- norm_add_leproof · cited by 68
- LE.le.trans_eq'proof · cited by 21
- zero_zsmulproof · cited by 19
- neg_one_zsmulproof · cited by 14
Cited by3
Results whose statement or proof uses this declaration.
- norm_le_of_mem_closedBallproof · cited by 2
- norm_lt_of_mem_ballproof · cited by 1
- CauchySeq.norm_bddAboveproof · cited by 1