Theorems · Theorem · nonassociative algebras
neg_lie
∀ {L : Type v} {M : Type w} [inst : LieRing L] [inst_1 : AddCommGroup M] [inst_2 : LieRingModule L M] (x : L) (m : M),
⁅-x, m⁆ = -⁅x, m⁆- Defined in
- Mathlib.Algebra.Lie.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext
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.
- AddCommGroupstatement and proof · cited by 12,871
- LieRingstatement and proof · cited by 1,548
- LieRingModulestatement and proof · cited by 727
- Bracket.bracketstatement and proof · cited by 642
- sub_eq_zeroproof · cited by 407
- sub_neg_eq_addproof · cited by 264
- neg_add_cancelproof · cited by 256
- add_lieproof · cited by 20
- zero_lieproof · cited by 16
Cited by4
Results whose statement or proof uses this declaration.
- lie_mem_leftproof · cited by 6
- LieAlgebra.IsKilling.finrank_rootSpace_eq_oneproof · cited by 6
- sub_lieproof · cited by 5
- IsSl2Triple.symmproof · cited by 2