Theorems · Theorem · functional analysis
Submodule.orthogonal_disjoint
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
(K : Submodule 𝕜 E), Disjoint K KᗮK and Kᗮ have trivial intersection.
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Bot.botproof · cited by 4,720
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- Disjointstatement · cited by 2,201
- Submodule.orthogonalstatement · cited by 257
- Submodule.inf_orthogonal_eq_botproof · cited by 6
Cited by6
Results whose statement or proof uses this declaration.
- Submodule.isCompl_orthogonalproof · cited by 24
- Submodule.finrank_add_inf_finrank_orthogonalproof · cited by 3
- Submodule.IsOrtho.disjointproof · cited by 1
- Affine.Simplex.eq_mongePoint_of_forall_mem_mongePlaneproof · cited by 1
- LinearIsometryEquiv.reflections_generate_dim_auxproof · cited by 1
- Submodule.orthogonal_eq_top_iffproof · cited by 0