Theorems · Theorem · nonassociative algebras

RootPairing.EmbeddedG2.indexEquivAllRoots_symm_apply

∀ {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] [inst_6 : Finite ι] [inst_7 : CharZero R] [inst_8 : IsDomain R] [inst_9 : P.IsIrreducible]
  (x : ↥(RootPairing.EmbeddedG2.allRoots P).toFinset),
  (RootPairing.EmbeddedG2.indexEquivAllRoots P).symm x = Exists.choose ⋯

Defined in: Mathlib.LinearAlgebra.RootSystem.Finite.G2
Cited by: 0 results in Mathlib
Foundations: Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing AddCommGroup Module AddCommGroup Module RootPairing.EmbeddedG2 Finite CharZero IsDomain RootPairing.IsIrreducible

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites18

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement and proof · cited by 62,936
Modulestatement and proof · cited by 20,661
CommRingstatement and proof · cited by 17,173
Finsetstatement · cited by 13,712
AddCommGroupstatement and proof · cited by 12,871
Equivstatement · cited by 8,337
Equiv.symmstatement and proof · cited by 3,681
Finitestatement and proof · cited by 3,029
IsDomainstatement and proof · cited by 2,196
Function.Embeddingstatement · cited by 988
CharZerostatement and proof · cited by 932
RootPairingstatement and proof · cited by 710

Cited by0

Results whose statement or proof uses this declaration.

Nothing cites this yet.