Theorems · Theorem · nonassociative algebras
RootPairing.RootPositiveForm.isSymm_posForm
∀ {ι : Type u_1} {R : Type u_2} {S : Type u_3} {M : Type u_4} {N : Type u_5} [inst : CommRing S]
[inst_1 : LinearOrder S] [inst_2 : CommRing R] [inst_3 : Algebra S R] [inst_4 : AddCommGroup M] [inst_5 : Module R M]
[inst_6 : AddCommGroup N] [inst_7 : Module R N] {P : RootPairing ι R M N} [inst_8 : P.IsValuedIn S]
(B : RootPairing.RootPositiveForm S P) [inst_9 : FaithfulSMul S R] [inst_10 : Module S M]
[inst_11 : IsScalarTower S R M], LinearMap.IsSymm B.posForm- Cited by
- 2 results in Mathlib
- Foundations
- Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
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
- RingHom.idstatement and proof · cited by 18,349
- 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
- Submodulestatement · cited by 7,192
- Set.rangestatement and proof · cited by 4,705
- IsScalarTowerstatement and proof · cited by 3,896
- Submodule.spanstatement and proof · cited by 1,504
- Function.Embeddingstatement · cited by 988
Cited by2
Results whose statement or proof uses this declaration.
- RootPairing.zero_lt_pairingIn_iffproof · cited by 2
- RootPairing.coxeterWeightIn_le_fourproof · cited by 1