Theorems · Theorem · nonassociative algebras
RootPairing.toPerfPair_conj_reflection
∀ {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 : ι),
P.toPerfPair.conj ↑(P.reflection i) = (↑(P.coreflection i)).dualMap- 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.
Cites25
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 · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- LinearEquivstatement · cited by 3,317
- mul_commproof · cited by 2,262
- LinearEquiv.symmproof · cited by 1,461
- LinearEquiv.toLinearMapstatement · cited by 1,171
- LinearMap.extproof · cited by 844
- Module.Endstatement · cited by 774
- RootPairingstatement and proof · cited by 710
Cited by2
Results whose statement or proof uses this declaration.
- RootPairing.invtSubmodule_reflection_of_invtSubmodule_coreflectionproof · cited by 1
- RootPairing.toPerfPair_flip_conj_coreflectionproof · cited by 0