Theorems · Theorem · nonassociative algebras

RootPairing.RootPositiveForm.exists_pos_eq

∀ {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]
  (self : RootPairing.RootPositiveForm S P) (i : ι), ∃ s > 0, (algebraMap S R) s = (self.form (P.root i)) (P.root i)

Defined in

Mathlib.LinearAlgebra.RootSystem.RootPositive

Cited by

3 results in Mathlib

Foundations

Depth 35 from the axioms · uses propext, Quot.sound

Assumes

CommRingLinearOrderCommRingAlgebraAddCommGroupModuleAddCommGroupModuleRootPairing.IsValuedIn