Theorems · Theorem · nonassociative algebras
RootPairing.reflection_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.reflection ((P.reflectionPerm j) i) = P.reflection j * P.reflection i * P.reflection j- Defined in
- Mathlib.LinearAlgebra.RootSystem.Defs
- Cited by
- 1 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.
Cites26
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
- Equivstatement · cited by 8,337
- Algebra.algebraMapproof · cited by 4,706
- LinearEquivstatement · cited by 3,317
- Nat.cast_oneproof · cited by 2,501
- sub_zeroproof · cited by 938
- RootPairingstatement and proof · cited by 710
- map_smulproof · cited by 566
Cited by1
Results whose statement or proof uses this declaration.
- RootPairing.Base.forall_mem_support_invtSubmodule_iffproof · cited by 1