Theorems · Theorem · functional analysis
NormedAddGroupHom.norm_comp_le
∀ {V₁ : Type u_2} {V₂ : Type u_3} {V₃ : Type u_4} [inst : SeminormedAddCommGroup V₁]
[inst_1 : SeminormedAddCommGroup V₂] [inst_2 : SeminormedAddCommGroup V₃] (g : NormedAddGroupHom V₂ V₃)
(f : NormedAddGroupHom V₁ V₂), ‖g.comp f‖ ≤ ‖g‖ * ‖f‖- Defined in
- Mathlib.Analysis.Normed.Group.Hom
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 167 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Norm.normstatement · cited by 5,413
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- norm_nonnegproof · cited by 725
- mul_nonnegproof · cited by 397
- AddMonoidHom.compproof · cited by 339
- NormedAddGroupHomstatement and proof · cited by 216
- NormedAddGroupHom.compstatement · cited by 39
- NormedAddGroupHom.toAddMonoidHomproof · cited by 13
- NormedAddGroupHom.mkNormedAddGroupHom_norm_leproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- NormedAddGroupHom.norm_comp_le_of_leproof · cited by 1