Theorems · Theorem · nonassociative algebras

RootPairing.smul_coroot_eq_of_root_eq_smul

∀ {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} [Finite ι]
  [IsAddTorsionFree N] (i j : ι) (t : R), P.root j = t • P.root i → t • P.coroot j = P.coroot i

Defined in

Mathlib.LinearAlgebra.RootSystem.Defs

Cited by

1 results in Mathlib

Foundations

Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModuleFiniteIsAddTorsionFree