Theorems · Theorem · nonassociative algebras
LieModule.Weight.coe_toLinear_ne_zero_iff
∀ {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 : LieModule.LinearWeights R L M] {χ : LieModule.Weight R L M},
LieModule.Weight.toLinear R L M χ ≠ 0 ↔ χ.IsNonZero- Defined in
- Mathlib.Algebra.Lie.Weights.Linear
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
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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
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement · cited by 10,215
- LieRingstatement and proof · cited by 1,548
- LieAlgebrastatement and proof · cited by 1,246
- LieRingModulestatement and proof · cited by 727
- LieModulestatement and proof · cited by 424
- LieRing.IsNilpotentstatement and proof · cited by 176
- LieModule.Weightstatement and proof · cited by 172
- LieModule.Weight.IsNonZerostatement and proof · cited by 47
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