Theorems · Theorem · nonassociative algebras
RootPairing.EmbeddedG2.pairingIn_short_long
∀ {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.pairingIn ℤ (RootPairing.EmbeddedG2.short P) (RootPairing.EmbeddedG2.long P) = -1- Cited by
- 2 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.
Cites13
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
- 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.pairingInstatement and proof · cited by 100
- RootPairing.EmbeddedG2statement and proof · cited by 35
- RootPairing.EmbeddedG2.longstatement and proof · cited by 28
- RootPairing.EmbeddedG2.shortstatement and proof · cited by 28
- RootPairing.pairingIn_pairingIn_mem_set_of_isCrystal_of_isRedproof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- RootPairing.EmbeddedG2.pairing_short_longproof · cited by 4
- RootPairing.EmbeddedG2.linearIndependent_short_longproof · cited by 1