Theorems · Theorem · nonassociative algebras
LieSubmodule.mem_top
∀ {R : Type u} {L : Type v} {M : Type w} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : AddCommGroup M]
[inst_3 : Module R M] [inst_4 : LieRingModule L M] (x : M), x ∈ ⊤- Defined in
- Mathlib.Algebra.Lie.Submodule
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Top.topstatement · cited by 9,680
- LieRingstatement and proof · cited by 1,548
- LieRingModulestatement and proof · cited by 727
- LieSubmodulestatement · cited by 489
- Set.mem_univproof · cited by 416
Cited by11
Results whose statement or proof uses this declaration.
- LieModule.iterate_toEnd_mem_lowerCentralSeriesproof · cited by 2
- coe_lowerCentralSeries_ideal_quot_eqproof · cited by 1
- LieAlgebra.hasCentralRadical_and_of_isIrreducible_of_isFaithfulproof · cited by 1
- LieModule.isTrivial_iff_max_triv_eq_topproof · cited by 1
- LieModule.iterate_toEnd_mem_lowerCentralSeries₂proof · cited by 1
- LieModule.le_max_triv_iff_bracket_eq_botproof · cited by 1
- LieAlgebra.killingCompl_top_le_radicalproof · cited by 0
- LieModule.coe_lowerCentralSeries_ideal_leproof · cited by 0
- LieModule.posFittingCompOf_le_lowerCentralSeriesproof · cited by 0
- LieHom.mem_idealRangeproof · cited by 0
- LieAlgebra.IsSemisimple.isSimple_of_isAtomproof · cited by 0