Theorems · Theorem · nonassociative algebras
RootPairing.EmbeddedG2.pairing_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.pairing (RootPairing.EmbeddedG2.short P) (RootPairing.EmbeddedG2.long P) = -1- Cited by
- 4 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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
- Algebra.algebraMapproof · cited by 4,706
- 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
- Int.cast_oneproof · cited by 371
- Int.castRingHomproof · cited by 254
- Int.cast_negproof · cited by 224
Cited by4
Results whose statement or proof uses this declaration.
- RootPairing.EmbeddedG2.long_eq_three_mul_shortproof · cited by 4
- RootPairing.EmbeddedG2.twoShortAddLongRoot_eqproof · cited by 3
- RootPairing.EmbeddedG2.shortAddLongRoot_eqproof · cited by 3
- RootPairing.EmbeddedG2.threeShortAddTwoLongRoot_eqproof · cited by 3