Theorems · Theorem · nonassociative algebras

RootPairing.Base.IsPos.add_zsmul

∀ {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}
  [inst_5 : CharZero R] [Finite ι] [IsDomain R] [P.IsCrystallographic] [P.IsReduced] {i j k : ι} {z : ℤ},
  i ≠ j → b.IsPos i → j ∈ b.support → P.root k = P.root i + z • P.root j → b.IsPos k

Defined in

Mathlib.LinearAlgebra.RootSystem.Base

Cited by

1 results in Mathlib

Foundations

Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModuleCharZeroFiniteIsDomainRootPairing.IsCrystallographicRootPairing.IsReduced