Theorems · Theorem · functional analysis
Seminorm.abs_le_of_le
∀ {E : Type u_6} [inst : AddCommGroup E] [inst_1 : Module ℝ E] {p : Seminorm ℝ E} {f : E →ₗ[ℝ] ℝ},
(∀ (x : E), f x ≤ p x) → ∀ (x : E), |f x| ≤ p x- Cited by
- 2 results in Mathlib
- Foundations
- Depth 157 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommGroupModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement and proof · cited by 10,215
- absstatement · cited by 1,814
- map_negproof · cited by 378
- Seminormstatement and proof · cited by 272
- abs_leproof · cited by 64
- neg_leproof · cited by 27
- AddGroupSeminormClass.map_neg_eq_mapproof · cited by 23
Cited by2
Results whose statement or proof uses this declaration.
- Module.Dual.exists_extension_of_le_seminorm_realproof · cited by 2
- WithSeminorms.continuous_real_rngproof · cited by 1