Theorems · Theorem · nonassociative algebras
RootPairing.EmbeddedG2.mem_allRoots
∀ {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.IsIrreducible] (i : ι),
P.root i ∈ RootPairing.EmbeddedG2.allRoots P- Cited by
- 1 results in Mathlib
- Foundations
- Depth 101 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
- Fintypeproof · cited by 7,736
- Finitestatement and proof · cited by 3,029
- add_zeroproof · cited by 2,707
- IsDomainstatement and proof · cited by 2,196
- MulZeroClass.mul_zeroproof · cited by 2,091
- map_zeroproof · cited by 1,614
- Submodule.spanproof · cited by 1,504
- Function.Embeddingstatement · cited by 988
Cited by1
Results whose statement or proof uses this declaration.
- RootPairing.EmbeddedG2.setOfPred_index_eq_univproof · cited by 1