Theorems · Theorem · nonassociative algebras
LieSubmodule.subset_lieSpan
∀ {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] {s : Set M}, s ⊆ ↑(LieSubmodule.lieSpan R L s)- Defined in
- Mathlib.Algebra.Lie.Submodule
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Modulestatement and proof · cited by 20,661
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- SetLike.coestatement and proof · cited by 8,199
- LieRingstatement and proof · cited by 1,548
- LieRingModulestatement and proof · cited by 727
- LieSubmodulestatement and proof · cited by 489
- SetLike.mem_coeproof · cited by 302
- LieSubmodule.lieSpanstatement · cited by 22
- LieSubmodule.mem_lieSpanproof · cited by 3
Cited by14
Results whose statement or proof uses this declaration.
- LieSubmodule.lieSpan_leproof · cited by 17
- LieSubmodule.lie_coe_mem_lieproof · cited by 5
- LieIdeal.mem_mapproof · cited by 3
- LieSubmodule.coe_lieSpan_submodule_eq_iffproof · cited by 3
- LieSubmodule.lieSpan_monoproof · cited by 2
- LieModule.trivial_iff_lower_central_eq_botproof · cited by 1
- LieSubmodule.lieSpan_eqproof · cited by 1
- LieSubmodule.submodule_span_le_lieSpanproof · cited by 1
- LieSubmodule.isCompactElement_lieSpan_singletonproof · cited by 0
- LieIdeal.map_of_imageproof · cited by 0
- LieHom.range_subset_idealRangeproof · cited by 0
- LieSubmodule.sSup_image_lieSpan_singletonproof · cited by 0