Theorems · Definition · functional analysis
NormedAddGroupHom.NormNoninc
{V : Type u_1} →
{W : Type u_2} →
[inst : SeminormedAddCommGroup V] → [inst_1 : SeminormedAddCommGroup W] → NormedAddGroupHom V W → PropA NormedAddGroupHom is norm-nonincreasing if ‖f v‖ ≤ ‖v‖ for all v.
- Defined in
- Mathlib.Analysis.Normed.Group.Hom
- Cited by
- 41 results in Mathlib
- Foundations
- Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Norm.normproof · cited by 5,413
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- NormedAddGroupHomstatement and proof · cited by 216
Cited by49
Results whose statement or proof uses this declaration.
- SemiNormedGrp₁.Hom.homstatement · cited by 18
- SemiNormedGrp₁.mkHomstatement and proof · cited by 8
- NormedAddGroupHom.NormNoninc.normNoninc_iff_norm_le_onestatement and proof · cited by 4
- SemiNormedGrp₁.comp_applystatement · cited by 3
- SemiNormedGrp₁.hom_extstatement · cited by 2
- SemiNormedGrp₁.Hom.extproof · cited by 2
- SemiNormedGrp₁.Hom.normNonincstatement · cited by 2
- SemiNormedGrp₁.mkIsostatement and proof · cited by 2
- SemiNormedGrp₁.extstatement · cited by 1
- SemiNormedGrp₁.id_applystatement · cited by 1
- SemiNormedGrp₁.Hom.mk.injstatement and proof · cited by 1
- SemiNormedGrp₁.Hom.mk.noConfusionstatement and proof · cited by 1