Theorems · Theorem · functional analysis
NormedAddGroupHom.le_of_opNorm_le
∀ {V₁ : Type u_2} {V₂ : Type u_3} [inst : SeminormedAddCommGroup V₁] [inst_1 : SeminormedAddCommGroup V₂]
(f : NormedAddGroupHom V₁ V₂) {c : ℝ}, ‖f‖ ≤ c → ∀ (x : V₁), ‖f x‖ ≤ c * ‖x‖- Defined in
- Mathlib.Analysis.Normed.Group.Hom
- Cited by
- 2 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
- LE.le.transproof · cited by 3,151
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- norm_nonnegproof · cited by 725
- mul_le_mul_of_nonneg_rightproof · cited by 301
- NormedAddGroupHomstatement and proof · cited by 216
- NormedAddGroupHom.le_opNormproof · cited by 9
Cited by2
Results whose statement or proof uses this declaration.
- NormedAddGroupHom.NormNoninc.normNoninc_iff_norm_le_oneproof · cited by 4
- NormedAddGroupHom.lift_normNonincproof · cited by 0