Theorems · Theorem · nonassociative algebras
LieModule.Weight.isZero_iff_eq_zero
∀ {R : Type u_2} {L : Type u_3} {M : Type u_4} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L]
[inst_3 : AddCommGroup M] [inst_4 : Module R M] [inst_5 : LieRingModule L M] [inst_6 : LieModule R L M]
[inst_7 : LieRing.IsNilpotent L] [inst_8 : Nontrivial ↥(LieModule.genWeightSpace M 0)] {χ : LieModule.Weight R L M},
χ.IsZero ↔ χ = 0- Defined in
- Mathlib.Algebra.Lie.Weights.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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 and proof · cited by 2,416
- LieRingstatement and proof · cited by 1,548
- LieAlgebrastatement and proof · cited by 1,246
- LieRingModulestatement and proof · cited by 727
- LieSubmodulestatement · cited by 489
- LieModulestatement and proof · cited by 424
- LieRing.IsNilpotentstatement and proof · cited by 176
- LieModule.Weightstatement and proof · cited by 172
- LieModule.genWeightSpacestatement and proof · cited by 99
Cited by1
Results whose statement or proof uses this declaration.
- LieModule.Weight.isNonZero_iff_ne_zeroproof · cited by 0