Theorems · Theorem · nonassociative algebras

RootPairing.invtRootSubmodule.eq_span_root

∀ {ι : Type u_1} {M : Type u_3} {N : Type u_4} [inst : AddCommGroup M] [inst_1 : AddCommGroup N] {K : Type u_5}
  [inst_2 : Field K] [NeZero 2] [inst_4 : Module K M] [inst_5 : Module K N] {P : RootPairing ι K M N} [P.IsRootSystem]
  (q : ↥P.invtRootSubmodule), ↑q = Submodule.span K (⇑P.root '' {i | P.root i ∈ ↑q})

Defined in

Mathlib.LinearAlgebra.RootSystem.Irreducible

Cited by

1 results in Mathlib

Foundations

Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupAddCommGroupFieldNeZeroModuleModuleRootPairing.IsRootSystem