Theorems · Theorem · nonassociative algebras

RootPairing.forall_pairing_eq_swap_or

∀ {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) [Finite ι]
  [CharZero R] [P.IsCrystallographic] [IsDomain R] [P.IsReduced] [P.IsIrreducible],
  (∀ (i j : ι), P.pairing i j = P.pairing j i ∨ P.pairing i j = 2 * P.pairing j i ∨ P.pairing j i = 2 * P.pairing i j) ∨
    ∀ (i j : ι), P.pairing i j = P.pairing j i ∨ P.pairing i j = 3 * P.pairing j i ∨ P.pairing j i = 3 * P.pairing i j

Defined in: Mathlib.LinearAlgebra.RootSystem.Finite.Lemmas
Cited by: 1 results in Mathlib
Foundations: Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing AddCommGroup Module AddCommGroup Module Finite CharZero RootPairing.IsCrystallographic IsDomain RootPairing.IsReduced RootPairing.IsIrreducible

Mathlib docs Source Loogle LeanSearch

Around this declaration

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

Cites26

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

DFunLike.coeproof · cited by 62,936
Modulestatement and proof · cited by 20,661
CommRingstatement and proof · cited by 17,173
AddCommGroupstatement and proof · cited by 12,871
Fintypeproof · cited by 7,736
Finitestatement and proof · cited by 3,029
mul_commproof · cited by 2,262
IsDomainstatement and proof · cited by 2,196
CharZerostatement and proof · cited by 932
RootPairingstatement and proof · cited by 710
RootPairing.rootproof · cited by 326
Fintype.ofFiniteproof · cited by 255

Cited by1

Results whose statement or proof uses this declaration.

RootPairing.forall_pairingIn_eq_swap_orproof · cited by 1