Theorems · Theorem · group theory
RootPairing.reflection_mem_weylGroup
∀ {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),
RootPairing.Equiv.reflection P i ∈ P.weylGroup- Cited by
- 7 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- Subgroupstatement · cited by 3,593
- RootPairingstatement and proof · cited by 710
- Set.mem_range_selfproof · cited by 328
- Subgroup.subset_closureproof · cited by 53
- RootPairing.Autstatement · cited by 30
- RootPairing.Equiv.reflectionstatement and proof · cited by 15
- RootPairing.weylGroupstatement · cited by 14
Cited by8
Results whose statement or proof uses this declaration.
- RootPairing.weylGroup.inductionstatement and proof · cited by 3
- RootPairing.span_orbit_eq_topproof · cited by 1
- RootPairing.weylGroup.ofIdxproof · cited by 1
- RootPairing.isSimpleModule_weylGroupRootRep_iffproof · cited by 1
- RootPairing.range_weylGroupToPermproof · cited by 0
- RootPairing.range_weylGroup_coweightHomproof · cited by 0
- RootPairing.range_weylGroup_weightHomproof · cited by 0
- RootPairing.weylGroup.induction'statement and proof · cited by 0