Theorems · Theorem · nonassociative algebras

RootPairing.IsG2.span_eq_rootSpan_int

∀ {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} [P.IsG2] {b : P.Base}
  [Finite ι] [CharZero R] [IsDomain R] {i j : ι},
  i ∈ b.support → j ∈ b.support → i ≠ j → Submodule.span ℤ {P.root i, P.root j} = P.rootSpan ℤ

Defined in

Mathlib.LinearAlgebra.RootSystem.Finite.G2

Cited by

1 results in Mathlib

Foundations

Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModuleRootPairing.IsG2FiniteCharZeroIsDomain