Theorems · Theorem · functional analysis
Submodule.le_orthogonal_orthogonal
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
(K : Submodule 𝕜 E), K ≤ KᗮᗮK is contained in Kᗮᗮ.
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 166 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.
- NormedAddCommGroupstatement and proof · cited by 15,752
- Submodulestatement and proof · cited by 7,192
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- Submodule.orthogonalstatement · cited by 257
- GaloisConnection.le_u_lproof · cited by 52
- Submodule.orthogonal_gcproof · cited by 6
Cited by7
Results whose statement or proof uses this declaration.
- Submodule.IsOrtho.symmproof · cited by 8
- Submodule.starProjection_orthogonal_valproof · cited by 7
- Submodule.bot_orthogonal_eq_topproof · cited by 4
- Submodule.isOrtho_orthogonal_rightproof · cited by 4
- Submodule.orthogonalProjectionOnto_orthogonal_apply_eq_zeroproof · cited by 3
- Submodule.orthogonal_orthogonal_eq_closureproof · cited by 3
- Submodule.reflection_mem_subspace_orthogonal_precomplement_eq_negproof · cited by 1