Theorems · Theorem · nonassociative algebras
LieSubmodule.range_incl
∀ {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), N.incl.range = N- Defined in
- Mathlib.Algebra.Lie.Submodule
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, 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.
- Modulestatement and proof · cited by 20,661
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- Submoduleproof · cited by 7,192
- LieRingstatement and proof · cited by 1,548
- LieRingModulestatement and proof · cited by 727
- LieSubmodulestatement and proof · cited by 489
- LieSubmodule.toSubmoduleproof · cited by 150
- Submodule.range_subtypeproof · cited by 82
- LieSubmodule.inclstatement and proof · cited by 29
- LieModuleHom.rangestatement and proof · cited by 14
Cited by5
Results whose statement or proof uses this declaration.
- LieSubmodule.lowerCentralSeries_eq_lcs_comapproof · cited by 3
- LieSubmodule.map_incl_topproof · cited by 2
- LieSubmodule.map_incl_lt_iff_lt_topproof · cited by 1
- LieModule.genWeightSpace_genWeightSpaceOf_map_inclproof · cited by 0
- LieAlgebra.IsKilling.biSup_corootSubmodule_eq_cartanproof · cited by 0