Theorems · Theorem · functional analysis

Submodule.IsOrtho.disjoint

∀ {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 → Disjoint U V

Orthogonal submodules are disjoint.

Defined in

Mathlib.Analysis.InnerProductSpace.Orthogonal

Cited by

1 results in Mathlib

Foundations

Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpace