Theorems · Theorem · functional analysis
NormedAddGroupHom.norm_id
∀ (V : Type u_1) [inst : SeminormedAddCommGroup V] [NontrivialTopology V], ‖NormedAddGroupHom.id V‖ = 1
If a normed space is non-trivial, then the norm of the identity equals 1.
- Defined in
- Mathlib.Analysis.Normed.Group.Hom
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 152 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realstatement and proof · cited by 25,697
- Norm.normstatement and proof · cited by 5,413
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- le_antisymmproof · cited by 2,068
- div_selfproof · cited by 237
- NormedAddGroupHomstatement · cited by 216
- NontrivialTopologystatement and proof · cited by 46
- NormedAddGroupHom.idstatement and proof · cited by 12
- exists_norm_ne_zeroproof · cited by 6
- NormedAddGroupHom.id_applyproof · cited by 6
- NormedAddGroupHom.ratio_le_opNormproof · cited by 1
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.