Theorems · Theorem · functional analysis
ClosedSubmodule.orthogonal_toSubmodule_eq
Deprecated since 2026-01-18Use ClosedSubmodule.toSubmodule_orthogonal_eq instead.
∀ {𝕜 : Type u_4} {E : Type u_5} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
(K : ClosedSubmodule 𝕜 E), ↑Kᗮ = (↑K)ᗮAlias of ClosedSubmodule.toSubmodule_orthogonal_eq.
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- Foundations
- Depth 182 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NormedAddCommGroupstatement · cited by 15,752
- Submodulestatement · cited by 7,192
- InnerProductSpacestatement · cited by 3,523
- RCLikestatement · cited by 2,829
- Submodule.orthogonalstatement · cited by 257
- ClosedSubmodulestatement · cited by 123
- ClosedSubmodule.toSubmodulestatement · cited by 51
- ClosedSubmodule.orthogonalstatement · cited by 32
- ClosedSubmodule.toSubmodule_orthogonal_eqproof · cited by 1
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