Theorems · Theorem · functional analysis
Submodule.sub_mem_orthogonal_of_inner_right
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
{K : Submodule 𝕜 E} {x y : E}, (∀ (v : ↥K), inner 𝕜 (↑v) x = inner 𝕜 (↑v) y) → x - y ∈ Kᗮ- Cited by
- 1 results in Mathlib
- Foundations
- Depth 162 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
- Inner.innerstatement and proof · cited by 1,089
- sub_eq_zeroproof · cited by 407
- Submodule.orthogonalstatement · cited by 257
- inner_sub_rightproof · cited by 19
Cited by1
Results whose statement or proof uses this declaration.
- ClosedSubmodule.sub_mem_orthogonal_of_inner_rightproof · cited by 0