Theorems · Theorem · functional analysis
ClosedSubmodule.inf_orthogonal
∀ {𝕜 : Type u_4} {E : Type u_5} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
(K₁ K₂ : ClosedSubmodule 𝕜 E), K₁ᗮ ⊓ K₂ᗮ = (K₁ ⊔ K₂)ᗮThe inf of two orthogonal subspaces equals the subspace orthogonal to the sup.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 182 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
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- ClosedSubmodulestatement and proof · cited by 123
- GaloisConnection.l_supproof · cited by 81
- ClosedSubmodule.orthogonalstatement · cited by 32
- ClosedSubmodule.orthogonal_gcproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- ClosedSubmodule.sup_orthogonalproof · cited by 1
- ClosedSubmodule.symplComp_supproof · cited by 0