Theorems · Theorem · functional analysis
Submodule.orthogonal_le_orthogonal_iff
∀ {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], K₀ᗮ ≤ K₁ᗮ ↔ K₁ ≤ K₀- Cited by
- 2 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 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_leproof · cited by 12
Cited by2
Results whose statement or proof uses this declaration.
- Submodule.orthogonal_le_iff_orthogonal_leproof · cited by 0
- Submodule.le_orthogonal_iff_le_orthogonalproof · cited by 0