Theorems · Theorem · nonassociative algebras
LieSubmodule.mem_toSubmodule
∀ {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] (N : LieSubmodule R L M) {x : M}, x ∈ ↑N ↔ x ∈ N- 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
- Submodulestatement · cited by 7,192
- LieRingstatement and proof · cited by 1,548
- LieRingModulestatement and proof · cited by 727
- LieSubmodulestatement and proof · cited by 489
- LieSubmodule.toSubmodulestatement · cited by 150
Cited by11
Results whose statement or proof uses this declaration.
- LieSubmodule.mem_supproof · cited by 5
- LieSubmodule.coe_lieSpan_submodule_eq_iffproof · cited by 3
- LieSubmodule.iSup_inductionproof · cited by 2
- LieAlgebra.IsKilling.traceForm_eq_zero_of_mem_ker_of_mem_span_corootproof · cited by 2
- LieModule.coe_lcs_range_toEnd_eqproof · cited by 1
- coe_lowerCentralSeries_ideal_quot_eqproof · cited by 1
- LieIdeal.coe_lcs_eqproof · cited by 1
- LieIdeal.mem_map_of_surjectiveproof · cited by 1
- LieModule.trace_toEnd_eq_zero_of_mem_lcsproof · cited by 1
- LieAlgebra.lieCharacter_apply_of_mem_derivedproof · cited by 0
- LieSubmodule.mem_infproof · cited by 0