Theorems · Theorem · nonassociative algebras

RootPairing.Base.pos_or_neg_of_sum_smul_root_mem

∀ {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)
  [CharZero R] (f : ι → ℤ),
  ∑ j ∈ b.support, f j • P.root j ∈ Set.range ⇑P.root → Function.support f ⊆ ↑b.support → 0 < f ∨ f < 0

Defined in

Mathlib.LinearAlgebra.RootSystem.Base

Cited by

2 results in Mathlib

Foundations

Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModuleCharZero