Theorems · Theorem · functional analysis
Submodule.norm_projection_orthogonal_le
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
(K : Submodule 𝕜 E) [inst_3 : K.HasOrthogonalProjection] (x : E), ‖(K.projection Kᗮ ⋯) x‖ ≤ ‖x‖- Cited by
- 1 results in Mathlib
- Foundations
- Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
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
- RingHom.idstatement · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- LinearMapstatement · cited by 10,215
- Submodulestatement and proof · cited by 7,192
- Norm.normstatement and proof · cited by 5,413
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- norm_nonnegproof · cited by 725
- SeminormedAddGroupproof · cited by 331
- sqproof · cited by 280
Cited by1
Results whose statement or proof uses this declaration.
- Submodule.isTopCompl_orthogonalproof · cited by 1