Theorems · Theorem · functional analysis
pi_norm_comp_le
∀ {ι : Type u_1} {E : Type u_2} {F : Type u_3} [inst : Fintype ι] [inst_1 : SeminormedAddGroup E] [inst_2 : Fintype F]
(g : ι → E) (f : F → ι), ‖g ∘ f‖ ≤ ‖g‖- Cited by
- 1 results in Mathlib
- Foundations
- Depth 157 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Fintypestatement and proof · cited by 7,736
- Norm.normstatement · cited by 5,413
- norm_nonnegproof · cited by 725
- SeminormedAddGroupstatement and proof · cited by 331
- pi_norm_le_iff_of_nonnegproof · cited by 18
- norm_le_pi_normproof · cited by 17
Cited by1
Results whose statement or proof uses this declaration.
- Function.Surjective.pi_norm_compproof · cited by 0