Theorems · Theorem · nonassociative algebras

RootPairing.RootPositiveForm.two_mul_apply_root_root

∀ {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) [FaithfulSMul S R],
  2 * (B.form (P.root i)) (P.root j) = P.pairing i j * (B.form (P.root j)) (P.root j)

Defined in

Mathlib.LinearAlgebra.RootSystem.RootPositive

Cited by

0 results in Mathlib

Foundations

Depth 44 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLinearOrderCommRingAlgebraAddCommGroupModuleAddCommGroupModuleRootPairing.IsValuedInFaithfulSMul