Theorems · Theorem · nonassociative algebras
LieDerivation.lie_ad
∀ {R : Type u_1} {L : Type u_2} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L] (x : L)
(D : LieDerivation R L L), ⁅(LieDerivation.ad R L) x, D⁆ = ⁅x, D⁆- Cited by
- 1 results in Mathlib
- Foundations
- Depth 56 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.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · 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 and proof · cited by 642
- LieHomstatement · cited by 382
- sub_sub_cancelproof · cited by 105
- LieDerivationstatement and proof · cited by 95
- LieDerivation.adstatement · cited by 19
- LieDerivation.extproof · cited by 7
- LieDerivation.apply_lie_eq_subproof · cited by 5
- LieDerivation.ad_apply_applyproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- LieDerivation.lie_der_ad_eq_ad_derproof · cited by 1