Theorems · Theorem · nonassociative algebras

RootPairing.Base.exists_root_eq_sum_nat_or_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} (b : P.Base) (i : ι),
  ∃ f,
    Function.support f ⊆ ↑b.support ∧
      (P.root i = ∑ j ∈ b.support, f j • P.root j ∨ P.root i = -∑ j ∈ b.support, f j • P.root j)

Defined in

Mathlib.LinearAlgebra.RootSystem.Base

Cited by

1 results in Mathlib

Foundations

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

Assumes

CommRingAddCommGroupModuleAddCommGroupModule