Theorems · Theorem · nonassociative algebras

RootPairing.RootPositiveForm.pairingIn_mul_eq_pairingIn_mul_swap

∀ {ι : Type u_1} {R : Type u_2} {S : Type u_3} {M : Type u_4} {N : Type u_5} [inst : CommRing S]
  [inst_1 : LinearOrder S] [inst_2 : CommRing R] [inst_3 : Algebra S 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.IsValuedIn S]
  (B : RootPairing.RootPositiveForm S P) (i j : ι) [inst_9 : FaithfulSMul S R] [inst_10 : Module S M]
  [inst_11 : IsScalarTower S R M], P.pairingIn S j i * B.rootLength i = P.pairingIn S i j * B.rootLength j

Defined in

Mathlib.LinearAlgebra.RootSystem.RootPositive

Cited by

2 results in Mathlib

Foundations

Depth 45 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLinearOrderCommRingAlgebraAddCommGroupModuleAddCommGroupModuleRootPairing.IsValuedInFaithfulSMulModuleIsScalarTower