Theorems · Theorem · nonassociative algebras

RootPairing.IsValuedIn.exists_value

∀ {ι : Type u_1} {R : Type u_2} {M : Type u_4} {N : Type u_5} {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} {S : Type u_6}
  {inst_5 : CommRing S} {inst_6 : Algebra S R} [self : P.IsValuedIn S] (i j : ι),
  ∃ s, (algebraMap S R) s = P.pairing i j

Defined in

Mathlib.LinearAlgebra.RootSystem.IsValuedIn

Cited by

1 results in Mathlib

Foundations

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

Assumes

RootPairing.IsValuedIn