Mathlib Map

Theorems · Theorem · functional analysis

Submodule.isOrtho_sSup_left

∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
  {U : Set (Submodule 𝕜 E)} {V : Submodule 𝕜 E}, sSup U ⟂ V ↔ ∀ Uᵢ ∈ U, Uᵢ ⟂ V
Defined in
Mathlib.Analysis.InnerProductSpace.Orthogonal
Cited by
1 results in Mathlib
Foundations
Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
RCLikeNormedAddCommGroupInnerProductSpace
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Submodule.isOrtho_sSup_right · cited by 0Submodule.isOrtho_sSup_ri…Set · cited by 53352SetNormedAddCommGroup · cited by 15752NormedAddCommGroupSubmodule · cited by 7192SubmoduleInnerProductSpace · cited by 3523InnerProductSpaceRCLike · cited by 2829RCLikeSupSet.sSup · cited by 954SupSet.sSupSubmodule.IsOrtho · cited by 50Submodule.IsOrthosSup_le_iff · cited by 8sSup_le_iffSubmodule.isOrtho_sSup_leftCITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.