Theorems · Theorem · nonassociative algebras
LieSubalgebra.self_mem_engel
∀ (R : Type u_1) {L : Type u_2} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L] (x : L),
x ∈ LieSubalgebra.engel R x- Defined in
- Mathlib.Algebra.Lie.EngelSubalgebra
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 79 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- LieRingstatement and proof · cited by 1,548
- LieAlgebrastatement and proof · cited by 1,246
- pow_oneproof · cited by 894
- LieSubalgebrastatement · cited by 418
- LieAlgebra.adproof · cited by 49
- LieSubalgebra.engelstatement · cited by 13
- lie_selfproof · cited by 6
Cited by4
Results whose statement or proof uses this declaration.
- LieAlgebra.engel_isBot_of_isMinproof · cited by 1
- LieSubalgebra.normalizer_engelproof · cited by 1
- LieAlgebra.exists_isCartanSubalgebra_engel_of_finrank_le_cardproof · cited by 1
- LieSubalgebra.normalizer_eq_self_of_engel_leproof · cited by 0