Theorems · Theorem · nonassociative algebras

RootPairing.IsReduced.eq_or_eq_neg

∀ {ι : Type u_1} {R : Type u_2} {M : Type u_3} {N : Type u_4} {inst : CommRing R} {inst_1 : AddCommGroup M}
  {inst_2 : Module R M} {inst_3 : AddCommGroup N} {inst_4 : Module R N} {P : RootPairing ι R M N} [self : P.IsReduced]
  (i j : ι), ¬LinearIndependent R ![P.root i, P.root j] → P.root i = P.root j ∨ P.root i = -P.root j

Defined in

Mathlib.LinearAlgebra.RootSystem.Reduced

Cited by

1 results in Mathlib

Foundations

Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RootPairing.IsReduced