Theorems · Theorem · functional analysis
ClosedSubmodule.mem_orthogonal_toSubmodule_iff
∀ {𝕜 : Type u_4} {E : Type u_5} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
(K : ClosedSubmodule 𝕜 E) (v : E), v ∈ (↑K)ᗮ ↔ v ∈ Kᗮ- Cited by
- 1 results in Mathlib
- Foundations
- Depth 181 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 · cited by 7,192
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- Submodule.orthogonalstatement · cited by 257
- ClosedSubmodulestatement and proof · cited by 123
- ClosedSubmodule.toSubmodulestatement · cited by 51
- ClosedSubmodule.orthogonalstatement · cited by 32
Cited by1
Results whose statement or proof uses this declaration.
- ClosedSubmodule.mem_orthogonal_iffproof · cited by 0