Theorems · Theorem · nonassociative algebras
RootPairing.rootForm_nondegenerate
∀ {ι : Type u_1} {R : Type u_2} {M : Type u_3} {N : Type u_4} [inst : Fintype ι] [inst_1 : AddCommGroup M]
[inst_2 : AddCommGroup N] [inst_3 : CommRing R] [IsDomain R] [inst_5 : Module R M] [inst_6 : Module R N]
(P : RootPairing ι R M N) [P.IsAnisotropic] [P.IsRootSystem], P.RootForm.Nondegenerate- Cited by
- 1 results in Mathlib
- Foundations
- Depth 125 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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
- Fintypestatement and proof · cited by 7,736
- Disjointproof · cited by 2,201
- IsDomainstatement and proof · cited by 2,196
- LinearMap.kerproof · cited by 848
- RootPairingstatement and proof · cited by 710
- LinearMap.BilinForm.Nondegeneratestatement · cited by 77
- RootPairing.IsRootSystemstatement and proof · cited by 50
- RootPairing.RootFormstatement and proof · cited by 41
- RootPairing.IsAnisotropicstatement and proof · cited by 31
Cited by1
Results whose statement or proof uses this declaration.
- RootPairing.Base.cartanMatrixIn_nondegenerateproof · cited by 1