Theorems · Theorem · functional analysis
NormedAddGroupHom.le_opNorm_of_le
∀ {V₁ : Type u_2} {V₂ : Type u_3} [inst : SeminormedAddCommGroup V₁] [inst_1 : SeminormedAddCommGroup V₂]
(f : NormedAddGroupHom V₁ V₂) {c : ℝ} {x : V₁}, ‖x‖ ≤ c → ‖f x‖ ≤ ‖f‖ * c- Defined in
- Mathlib.Analysis.Normed.Group.Hom
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 118 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · 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_transproof · cited by 985
- mul_le_mul_of_nonneg_leftproof · cited by 361
- NormedAddGroupHomstatement and proof · cited by 216
- NormedAddGroupHom.le_opNormproof · cited by 9
- NormedAddGroupHom.opNorm_nonnegproof · cited by 5
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.