Theorems · Definition · nonassociative algebras
LieAlgebra.HasCentralRadical.casesOn
{R : Type u_1} →
{L : Type u_2} →
[inst : CommRing R] →
[inst_1 : LieRing L] →
[inst_2 : LieAlgebra R L] →
{motive : LieAlgebra.HasCentralRadical R L → Sort u} →
(t : LieAlgebra.HasCentralRadical R L) →
((radical_eq_center : LieAlgebra.radical R L = LieAlgebra.center R L) → motive ⋯) → motive t- Defined in
- Mathlib.Algebra.Lie.Semisimple.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingLieRingLieAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- LieRingstatement and proof · cited by 1,548
- LieAlgebrastatement and proof · cited by 1,246
- LieIdealstatement · cited by 282
- LieAlgebra.centerstatement and proof · cited by 23
- LieAlgebra.radicalstatement and proof · cited by 13
- LieAlgebra.HasCentralRadicalstatement and proof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- LieAlgebra.hasCentralRadical_iffproof · cited by 1