Theorems · Theorem · nonassociative algebras

RootPairing.Base.root_ne_neg_of_ne

∀ {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)
  [Nontrivial R] {i j : ι}, i ∈ b.support → j ∈ b.support → i ≠ j → P.root i ≠ -P.root j

Defined in

Mathlib.LinearAlgebra.RootSystem.Base

Cited by

1 results in Mathlib

Foundations

Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModuleNontrivial