Theorems · Theorem · nonassociative algebras
RootPairing.posRootForm_rootFormIn_posDef
∀ {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] [inst_4 : Module R M] [inst_5 : Module R N] (P : RootPairing ι R M N)
(S : Type u_5) [inst_6 : CommRing S] [inst_7 : LinearOrder S] [IsStrictOrderedRing S] [IsDomain R]
[inst_10 : Algebra S R] [inst_11 : FaithfulSMul S R] [inst_12 : P.IsValuedIn S] [inst_13 : Module S M]
[inst_14 : IsScalarTower S R M] [inst_15 : Module S N] [IsScalarTower S R N],
(LinearMap.BilinMap.toQuadraticMap (P.RootFormIn S)).PosDef- Cited by
- 2 results in Mathlib
- Foundations
- Depth 126 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
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
- Algebrastatement and proof · cited by 11,388
- LinearOrderstatement and proof · cited by 8,572
- Fintypestatement and proof · cited by 7,736
- Submodulestatement · cited by 7,192
- IsScalarTowerstatement and proof · cited by 3,896
- IsStrictOrderedRingstatement and proof · cited by 2,490
- IsDomainstatement and proof · cited by 2,196
- RootPairingstatement and proof · cited by 710
Cited by2
Results whose statement or proof uses this declaration.
- RootPairing.Base.exists_cartanMatrix_mul_diagaonal_posDefproof · cited by 1
- RootPairing.linearIndepOn_root_baseOf'proof · cited by 1