Theorems · Theorem · functional analysis
Submodule.orthogonal_eq_top_iff
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
(K : Submodule 𝕜 E), Kᗮ = ⊤ ↔ K = ⊥- Cited by
- 0 results in Mathlib
- Foundations
- Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites12
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
- Top.topstatement and proof · cited by 9,680
- Submodulestatement and proof · cited by 7,192
- Bot.botstatement and proof · cited by 4,720
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- Submodule.orthogonalstatement and proof · cited by 257
- inf_commproof · cited by 139
- Disjoint.eq_botproof · cited by 52
- top_inf_eqproof · cited by 30
- Submodule.orthogonal_disjointproof · cited by 6
- Submodule.bot_orthogonal_eq_topproof · cited by 4
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