Theorems · Theorem · nonassociative algebras
RootPairing.pairing_reflectionPerm
∀ {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) (i j k : ι),
P.pairing j ((P.reflectionPerm i) k) = P.pairing ((P.reflectionPerm i) j) k- Defined in
- Mathlib.LinearAlgebra.RootSystem.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 44 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- Equivstatement · cited by 8,337
- mul_commproof · cited by 2,262
- RootPairingstatement and proof · cited by 710
- map_smulproof · cited by 566
- map_subproof · cited by 565
- RootPairing.rootproof · cited by 326
- RootPairing.corootproof · cited by 123
- RootPairing.toLinearMapproof · cited by 108
Cited by2
Results whose statement or proof uses this declaration.
- RootPairing.pairingIn_reflectionPermproof · cited by 1
- LieIdeal.reflectionPerm_mem_rootSet_iffproof · cited by 1