Theorems · Theorem · functional analysis
ClosedSubmodule.sInf_orthogonal
∀ {𝕜 : Type u_4} {E : Type u_5} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
(s : Set (ClosedSubmodule 𝕜 E)), ⨅ K ∈ s, Kᗮ = (sSup s)ᗮThe inf of a set of orthogonal subspaces equals the subspace orthogonal to the sup.
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- Foundations
- Depth 182 from the axioms · uses propext, Classical.choice, Quot.sound
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- Setstatement and proof · cited by 53,352
- NormedAddCommGroupstatement and proof · cited by 15,752
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- iInfstatement · cited by 1,690
- SupSet.sSupstatement · cited by 954
- ClosedSubmodulestatement and proof · cited by 123
- ClosedSubmodule.orthogonalstatement · cited by 32
- GaloisConnection.l_sSupproof · cited by 19
- ClosedSubmodule.orthogonal_gcproof · cited by 4
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