Theorems · Theorem · nonassociative algebras
RootPairing.not_isG2_iff_isNotG2
∀ {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) [P.IsCrystallographic]
[P.IsReduced] [P.IsIrreducible] [Finite ι] [CharZero R] [IsDomain R], ¬P.IsG2 ↔ P.IsNotG2- Cited by
- 1 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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
- Finitestatement and proof · cited by 3,029
- IsDomainstatement and proof · cited by 2,196
- CharZerostatement and proof · cited by 932
- RootPairingstatement and proof · cited by 710
- RootPairing.IsCrystallographicstatement and proof · cited by 160
- RootPairing.pairingInproof · cited by 100
- RootPairing.reflectionPermproof · cited by 87
- RootPairing.IsReducedstatement and proof · cited by 48
Cited by1
Results whose statement or proof uses this declaration.
- RootPairing.chainBotCoeff_mul_chainTopCoeff.isNotG2proof · cited by 1