Theorems · Theorem · nonassociative algebras
RootPairing.EmbeddedG2.isOrthogonal_short_and_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] {i : ι},
P.root i ∉ RootPairing.EmbeddedG2.allRoots P →
P.IsOrthogonal i (RootPairing.EmbeddedG2.short P) ∧ P.IsOrthogonal i (RootPairing.EmbeddedG2.long P)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites41
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · 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
- Function.Embeddingstatement · cited by 988
- CharZerostatement and proof · cited by 932
- RootPairingstatement and proof · cited by 710
- RootPairing.rootstatement and proof · cited by 326
- Int.castRingHomproof · cited by 254
- eq_intCastproof · cited by 127
Cited by2
Results whose statement or proof uses this declaration.
- RootPairing.EmbeddedG2.span_eq_topproof · cited by 1
- RootPairing.EmbeddedG2.mem_allRootsproof · cited by 1