Theorems · Theorem · functional analysis
Submodule.isTopCompl_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.HasOrthogonalProjection], Submodule.IsTopCompl K Kᗮ- Cited by
- 1 results in Mathlib
- Foundations
- Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realproof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- Submodulestatement and proof · cited by 7,192
- Norm.normproof · cited by 5,413
- InnerProductSpacestatement and proof · cited by 3,523
- one_mulproof · cited by 2,841
- RCLikestatement and proof · cited by 2,829
- le_reflproof · cited by 2,061
- le_imp_le_of_le_of_leproof · cited by 576
- Submodule.orthogonalstatement and proof · cited by 257
- Submodule.HasOrthogonalProjectionstatement and proof · cited by 245
- Submodule.IsTopComplstatement · cited by 89
Cited by2
Results whose statement or proof uses this declaration.
- Submodule.orthogonalProjectionOntoproof · cited by 103
- Submodule.orthogonalProjectionOnto_norm_leproof · cited by 6