Theorems · Theorem · nonassociative algebras
LieDerivation.ad_apply_apply
∀ (R : Type u_1) (L : Type u_2) [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L] (a a_1 : L), ((LieDerivation.ad R L) a) a_1 = ⁅a, a_1⁆
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 55 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.coestatement · 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
- Bracket.bracketstatement · cited by 642
- LieHomstatement · cited by 382
- LieDerivationstatement · cited by 95
- lie_skewproof · cited by 26
- LieDerivation.adstatement · cited by 19
Cited by3
Results whose statement or proof uses this declaration.
- LieDerivation.ad_ker_eq_centerproof · cited by 3
- LieDerivation.coe_ad_apply_eq_ad_applyproof · cited by 1
- LieDerivation.lie_adproof · cited by 1