Theorems · Theorem · nonassociative algebras
LieSubmodule.bot_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], ↑⊥ = ⊥- Defined in
- Mathlib.Algebra.Lie.Submodule
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Bot.botstatement · cited by 4,720
- LieRingstatement and proof · cited by 1,548
- LieRingModulestatement and proof · cited by 727
- LieSubmodulestatement · cited by 489
- LieSubmodule.toSubmodulestatement · cited by 150
Cited by8
Results whose statement or proof uses this declaration.
- LieSubmodule.subsingleton_iffproof · cited by 4
- LieHom.ker_eq_botproof · cited by 3
- LieSubmodule.disjoint_toSubmoduleproof · cited by 3
- LieModule.ideal_oper_maxTrivSubmodule_eq_botproof · cited by 2
- LieModuleHom.ker_eq_botproof · cited by 2
- LieSubmodule.toSubmodule_eq_botproof · cited by 1
- LieIdeal.comap_incl_eq_botproof · cited by 0
- LieSubmodule.mk_eq_bot_iffproof · cited by 0