Theorems · Theorem · nonassociative algebras

RootPairing.coroot_eq_coreflection_of_root_eq

∀ {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) {i j k : ι},
  P.root k = (P.reflection i) (P.root j) → P.coroot k = (P.coreflection i) (P.coroot j)

Defined in

Mathlib.LinearAlgebra.RootSystem.Defs

Cited by

0 results in Mathlib

Foundations

Depth 43 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModule