Theorems · Theorem · nonassociative algebras
RootPairing.coroot_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 : ι),
P.coroot ((P.reflectionPerm i) j) = (P.coreflection i) (P.coroot j)- Defined in
- Mathlib.LinearAlgebra.RootSystem.Defs
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · 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
- Equivstatement · cited by 8,337
- LinearEquivstatement · cited by 3,317
- Function.Embeddingstatement · cited by 988
- RootPairingstatement and proof · cited by 710
- RootPairing.corootstatement · cited by 123
- RootPairing.reflectionPermstatement · cited by 87
- RootPairing.coreflectionstatement · cited by 28
Cited by9
Results whose statement or proof uses this declaration.
- RootPairing.pairing_reflectionPermproof · cited by 2
- RootPairing.reflection_reflectionPermproof · cited by 1
- RootPairing.coroot'_reflectionPermproof · cited by 1
- RootPairing.mapsTo_coreflection_corootproof · cited by 1
- RootPairing.Base.forall_mem_support_invtSubmodule_iffproof · cited by 1
- RootPairing.corootSpanMem_reflectionPerm_selfproof · cited by 0
- RootPairing.coroot_eq_coreflection_of_root_eqproof · cited by 0
- RootPairing.coroot_mem_or_neg_mem_closure_of_rootproof · cited by 0