Theorems · Theorem · nonassociative algebras
RootPairing.EmbeddedG2.threeShortAddTwoLongRoot_eq
∀ {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],
RootPairing.EmbeddedG2.threeShortAddTwoLongRoot P =
3 • RootPairing.EmbeddedG2.shortRoot P + 2 • RootPairing.EmbeddedG2.longRoot P- Cited by
- 3 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites35
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
- add_zeroproof · cited by 2,707
- Nat.cast_oneproof · cited by 2,501
- zero_addproof · cited by 2,366
- IsDomainstatement and proof · cited by 2,196
- one_smulproof · cited by 1,374
- map_addproof · cited by 964
Cited by3
Results whose statement or proof uses this declaration.
- RootPairing.EmbeddedG2.allRoots_eq_map_allCoeffsproof · cited by 2
- RootPairing.EmbeddedG2.pairingIn_threeShortAddTwoLong_leftproof · cited by 1
- RootPairing.EmbeddedG2.pairingIn_threeShortAddTwoLong_rightproof · cited by 1