Theorems · Theorem · nonassociative algebras
LieAlgebra.exists_isCartanSubalgebra_engel_of_finrank_le_card
∀ (K : Type u_1) (L : Type u_2) [inst : Field K] [inst_1 : LieRing L] [inst_2 : LieAlgebra K L] [Module.Finite K L], ↑(Module.finrank K L) ≤ Cardinal.mk K → ∃ x, (LieSubalgebra.engel K x).IsCartanSubalgebra
- Defined in
- Mathlib.Algebra.Lie.CartanExists
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 141 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fieldstatement and proof · cited by 7,404
- Set.Elemproof · cited by 7,166
- Set.ofPredproof · cited by 6,101
- Cardinalstatement · cited by 2,598
- Module.finrankstatement and proof · cited by 1,770
- le_rflproof · cited by 1,558
- LieRingstatement and proof · cited by 1,548
- LieAlgebrastatement and proof · cited by 1,246
- Module.Finitestatement and proof · cited by 1,032
- Cardinal.mkstatement and proof · cited by 942
- LieSubalgebraproof · cited by 418
- Eq.geproof · cited by 375
Cited by1
Results whose statement or proof uses this declaration.
- LieAlgebra.exists_isCartanSubalgebra_engelproof · cited by 0