Theorems · Theorem · nonassociative algebras

RootPairing.Base.injective_pairingIn

∀ {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] [CharZero R] [IsDomain R] [Finite ι]
  {P : RootPairing ι R M N} [P.IsRootSystem] [inst_9 : P.IsCrystallographic] (b : P.Base),
  Function.Injective fun i k => P.pairingIn ℤ i ↑k

Defined in

Mathlib.LinearAlgebra.RootSystem.CartanMatrix

Cited by

1 results in Mathlib

Foundations

Depth 132 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModuleCharZeroIsDomainFiniteRootPairing.IsRootSystemRootPairing.IsCrystallographic