Theorems · Theorem · functional analysis
Submodule.IsOrtho.symm
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
{U V : Submodule 𝕜 E}, U ⟂ V → V ⟂ U- Cited by
- 8 results in Mathlib
- Foundations
- Depth 167 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
- LE.le.transproof · cited by 3,151
- RCLikestatement and proof · cited by 2,829
- Submodule.IsOrthostatement and proof · cited by 50
- Submodule.orthogonal_leproof · cited by 12
- Submodule.le_orthogonal_orthogonalproof · cited by 7
Cited by8
Results whose statement or proof uses this declaration.
- Submodule.isOrtho_commproof · cited by 4
- Submodule.IsOrtho.orthogonalProjectionOnto_comp_subtypeLproof · cited by 3
- Submodule.IsOrtho.mono_rightproof · cited by 2
- Submodule.IsOrtho.disjointproof · cited by 1
- Submodule.IsOrtho.geproof · cited by 1
- Submodule.IsOrtho.inner_eqproof · cited by 0
- Submodule.isOrtho_bot_rightproof · cited by 0
- Submodule.isOrtho_orthogonal_leftproof · cited by 0