Theorems · Theorem · nonassociative algebras
LieSubmodule.eq_bot_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] (N : LieSubmodule R L M), N = ⊥ ↔ ∀ m ∈ N, m = 0- Defined in
- Mathlib.Algebra.Lie.Submodule
- Cited by
- 6 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.
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
- Bot.botstatement · cited by 4,720
- LieRingstatement and proof · cited by 1,548
- LieRingModulestatement and proof · cited by 727
- LieSubmodulestatement and proof · cited by 489
- eq_bot_iffproof · cited by 159
Cited by6
Results whose statement or proof uses this declaration.
- LieSubmodule.nontrivial_iff_ne_botproof · cited by 6
- LieModule.trivial_iff_lower_central_eq_botproof · cited by 1
- LieSubalgebra.normalizer_eq_self_iffproof · cited by 1
- LieAlgebra.hasTrivialRadical_of_isIrreducible_of_isFaithfulproof · cited by 0
- LieDerivation.maxTrivSubmodule_eq_bot_of_center_eq_botproof · cited by 0
- LieSubmodule.lie_botproof · cited by 0