Theorems · Theorem · functional analysis
ContinuousAffineMap.norm_comp_le
∀ {𝕜 : Type u_1} {V : Type u_3} {W : Type u_4} {W₂ : Type u_5} [inst : SeminormedAddCommGroup V]
[inst_1 : SeminormedAddCommGroup W] [inst_2 : SeminormedAddCommGroup W₂] [inst_3 : NontriviallyNormedField 𝕜]
[inst_4 : NormedSpace 𝕜 V] [inst_5 : NormedSpace 𝕜 W] [inst_6 : NormedSpace 𝕜 W₂] (f : V →ᴬ[𝕜] W) (g : W₂ →ᴬ[𝕜] V),
‖f.comp g‖ ≤ ‖f‖ * ‖g‖ + ‖f 0‖- Cited by
- 0 results in Mathlib
- Foundations
- Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites29
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Norm.normstatement and proof · cited by 5,413
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- zero_addproof · cited by 2,366
- le_reflproof · cited by 2,061
- map_zeroproof · cited by 1,614
- norm_nonnegproof · cited by 725
- add_le_addproof · cited by 666
- le_imp_le_of_le_of_leproof · cited by 576
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