Theorems · Theorem · functional analysis
Submodule.norm_subtypeL_le
∀ {𝕜 : Type u_1} {E : Type u_4} [inst : SeminormedAddCommGroup E] [inst_1 : NontriviallyNormedField 𝕜]
[inst_2 : NormedSpace 𝕜 E] (K : Submodule 𝕜 E), ‖K.subtypeL‖ ≤ 1- Defined in
- Mathlib.Analysis.Normed.Operator.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 160 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- RingHom.idstatement · cited by 18,349
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Submodulestatement and proof · cited by 7,192
- Norm.normstatement · cited by 5,413
- ContinuousLinearMapstatement · cited by 5,352
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- Submodule.subtypeLstatement · cited by 53
- Submodule.subtypeₗᵢproof · cited by 42
- LinearIsometry.norm_toContinuousLinearMap_leproof · cited by 5
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