Theorems · Theorem · nonassociative algebras
RootPairing.isG2_iff
∀ {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.IsCrystallographic] [P.IsReduced] [P.IsIrreducible], P.IsG2 ↔ ∃ i j, P.pairingIn ℤ i j = -3- Cited by
- 0 results in Mathlib
- Foundations
- Depth 43 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- RootPairingstatement and proof · cited by 710
- RootPairing.IsCrystallographicstatement and proof · cited by 160
- RootPairing.pairingInstatement and proof · cited by 100
- RootPairing.IsReducedstatement and proof · cited by 48
- RootPairing.IsIrreduciblestatement and proof · cited by 35
- RootPairing.IsG2statement and proof · cited by 8
- RootPairing.IsG2.exists_pairingIn_neg_threeproof · cited by 3
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