Theorems · Theorem · nonassociative algebras

RootPairing.RootPositiveForm.rootLength_lt_of_pairingIn_notMem

∀ {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} [Finite ι]
  [inst_6 : CharZero R] [inst_7 : P.IsCrystallographic] [IsDomain R] (B : RootPairing.RootPositiveForm ℤ P) {i j : ι},
  P.root i ≠ P.root j → P.root i ≠ -P.root j → P.pairingIn ℤ i j ∉ {-1, 0, 1} → B.rootLength j < B.rootLength i

Defined in

Mathlib.LinearAlgebra.RootSystem.Finite.Lemmas

Cited by

0 results in Mathlib

Foundations

Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModuleFiniteCharZeroRootPairing.IsCrystallographicIsDomain