Theorems · Theorem · functional analysis
norm_le_norm_add_norm_inv_mul
∀ {E : Type u_5} [inst : SeminormedGroup E] (u v : E), ‖u‖ ≤ ‖v‖ + ‖u⁻¹ * 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
- SeminormedGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- mul_oneproof · cited by 3,885
- add_commproof · cited by 1,535
- neg_add_cancelproof · cited by 256
- SeminormedGroupstatement and proof · cited by 250
- zpow_zeroproof · cited by 52
- norm_inv'proof · cited by 23
- LE.le.trans_eq'proof · cited by 21
- norm_mul_le'proof · cited by 15
Cited by3
Results whose statement or proof uses this declaration.
- norm_le_of_mem_closedBall'proof · cited by 1
- CauchySeq.mul_norm_bddAboveproof · cited by 0
- norm_lt_of_mem_ball'proof · cited by 0