Theorems · Theorem · nonassociative algebras

RootPairing.prod_rootForm_smul_coroot_mem_range_domRestrict

∀ {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) [inst_5 : Fintype ι]
  (i : ι), (∏ a, (P.RootForm (P.root a)) (P.root a)) • P.coroot i ∈ (P.Polarization.domRestrict (P.rootSpan R)).range

Defined in

Mathlib.LinearAlgebra.RootSystem.Finite.CanonicalBilinear

Cited by

0 results in Mathlib

Foundations

Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModuleFintype