Theorems · Theorem · nonassociative algebras

RootPairing.pairing_two_two_iff

∀ {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) (i j : ι) [Finite ι]
  [CharZero R] [IsDomain R] [Module.IsTorsionFree R M], P.pairing i j = 2 ∧ P.pairing j i = 2 ↔ i = j

See also RootPairing.pairingIn_two_two_iff.

Defined in

Mathlib.LinearAlgebra.RootSystem.Reduced

Cited by

2 results in Mathlib

Foundations

Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModuleFiniteCharZeroIsDomainModule.IsTorsionFree