Theorems · Theorem · nonassociative algebras
LieSubmodule.nontrivial_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], Nontrivial (LieSubmodule R L M) ↔ Nontrivial M
- Defined in
- Mathlib.Algebra.Lie.Submodule
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
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
- Nontrivialstatement · cited by 2,416
- LieRingstatement and proof · cited by 1,548
- LieRingModulestatement and proof · cited by 727
- LieSubmodulestatement · cited by 489
- not_iff_notproof · cited by 159
- not_nontrivial_iff_subsingletonproof · cited by 23
- LieSubmodule.subsingleton_iffproof · cited by 4
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