Theorems · Theorem · functional analysis
NormedAddGroupHom.opNorm_nonneg
∀ {V₁ : Type u_2} {V₂ : Type u_3} [inst : SeminormedAddCommGroup V₁] [inst_1 : SeminormedAddCommGroup V₂]
(f : NormedAddGroupHom V₁ V₂), 0 ≤ ‖f‖- Defined in
- Mathlib.Analysis.Normed.Group.Hom
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Set.ofPredproof · cited by 6,101
- Norm.normstatement and proof · cited by 5,413
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- NormedAddGroupHomstatement and proof · cited by 216
- le_csInfproof · cited by 36
- NormedAddGroupHom.bounds_nonemptyproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- NormedAddGroupHom.lipschitzstatement and proof · cited by 1
- NormedAddGroupHom.opNorm_zeroproof · cited by 1
- NormedAddGroupHom.ratio_le_opNormproof · cited by 1
- NormedAddGroupHom.opNorm_add_leproof · cited by 0
- NormedAddGroupHom.le_opNorm_of_leproof · cited by 0