Theorems · Theorem · nonassociative algebras

RootPairing.root_add_nsmul_mem_range_iff_le_chainTopCoeff

∀ {ι : Type u_1} {R : Type u_2} {M : Type u_3} {N : Type u_4} [inst : Finite ι] [inst_1 : CommRing R]
  [inst_2 : CharZero R] [inst_3 : IsDomain R] [inst_4 : AddCommGroup M] [inst_5 : Module R M] [inst_6 : AddCommGroup N]
  [inst_7 : Module R N] {P : RootPairing ι R M N} [inst_8 : P.IsCrystallographic] {i j : ι},
  LinearIndependent R ![P.root i, P.root j] →
    ∀ {n : ℕ}, P.root j + n • P.root i ∈ Set.range ⇑P.root ↔ n ≤ RootPairing.chainTopCoeff i j

Defined in

Mathlib.LinearAlgebra.RootSystem.Chain

Cited by

7 results in Mathlib

Foundations

Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FiniteCommRingCharZeroIsDomainAddCommGroupModuleAddCommGroupModuleRootPairing.IsCrystallographic