Theorems · Theorem · nonassociative algebras

RootPairing.EmbeddedG2.setOfPred_index_eq_univ

∀ {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 : P.EmbeddedG2] [Finite ι] [CharZero R] [IsDomain R] [P.IsIrreducible],
  {RootPairing.EmbeddedG2.long P, -RootPairing.EmbeddedG2.long P, RootPairing.EmbeddedG2.short P,
      -RootPairing.EmbeddedG2.short P, RootPairing.EmbeddedG2.shortAddLong P, -RootPairing.EmbeddedG2.shortAddLong P,
      RootPairing.EmbeddedG2.twoShortAddLong P, -RootPairing.EmbeddedG2.twoShortAddLong P,
      RootPairing.EmbeddedG2.threeShortAddLong P, -RootPairing.EmbeddedG2.threeShortAddLong P,
      RootPairing.EmbeddedG2.threeShortAddTwoLong P, -RootPairing.EmbeddedG2.threeShortAddTwoLong P} =
    Set.univ

Defined in

Mathlib.LinearAlgebra.RootSystem.Finite.G2

Cited by

1 results in Mathlib

Foundations

Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModuleRootPairing.EmbeddedG2FiniteCharZeroIsDomainRootPairing.IsIrreducible