Theorems · Theorem · functional analysis
Submodule.le_orthogonal_iff_le_orthogonal
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
{K₀ K₁ : Submodule 𝕜 E} [K₀.HasOrthogonalProjection] [K₁.HasOrthogonalProjection], K₀ ≤ K₁ᗮ ↔ K₁ ≤ K₀ᗮ- Cited by
- 0 results in Mathlib
- Foundations
- Depth 182 from the axioms · uses propext, Classical.choice, Quot.sound
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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 and proof · cited by 7,192
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- Submodule.orthogonalstatement and proof · cited by 257
- Submodule.HasOrthogonalProjectionstatement and proof · cited by 245
- Submodule.orthogonal_orthogonalproof · cited by 14
- Submodule.orthogonal_le_orthogonal_iffproof · cited by 2
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