Theorems · Theorem · nonassociative algebras
LieSubmodule.subsingleton_iff
∀ (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], Subsingleton (LieSubmodule R L M) ↔ Subsingleton M
- Defined in
- Mathlib.Algebra.Lie.Submodule
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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.topproof · cited by 9,680
- Submoduleproof · cited by 7,192
- Bot.botproof · cited by 4,720
- LieRingstatement and proof · cited by 1,548
- LieRingModulestatement and proof · cited by 727
- LieSubmodulestatement and proof · cited by 489
- LieSubmodule.toSubmoduleproof · cited by 150
- LieSubmodule.toSubmodule_injproof · cited by 34
- subsingleton_iff_bot_eq_topproof · cited by 16
Cited by4
Results whose statement or proof uses this declaration.
- LieAlgebra.IsKilling.isLieAbelian_iff_subsingletonproof · cited by 1
- LieModule.nilpotencyLength_eq_zero_iffproof · cited by 1
- LieAlgebra.subsingleton_of_hasTrivialRadical_lie_abelianproof · cited by 0
- LieSubmodule.nontrivial_iffproof · cited by 0