Theorems · Theorem · nonassociative algebras
IsSl2Triple.symm
∀ {L : Type u_2} [inst : LieRing L] {h e f : L}, IsSl2Triple h e f → IsSl2Triple (-h) f e- Defined in
- Mathlib.Algebra.Lie.Sl2
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext
- Assumes
- LieRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LieRingstatement and proof · cited by 1,548
- neg_injproof · cited by 85
- neg_eq_iff_eq_negproof · cited by 60
- IsSl2Triplestatement and proof · cited by 38
- lie_skewproof · cited by 26
- IsSl2Triple.lie_e_fproof · cited by 8
- IsSl2Triple.h_ne_zeroproof · cited by 4
- IsSl2Triple.lie_h_e_nsmulproof · cited by 4
- neg_lieproof · cited by 4
- IsSl2Triple.lie_h_f_nsmulproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- LieAlgebra.IsKilling.finrank_rootSpace_eq_oneproof · cited by 6
- IsSl2Triple.symm_iffproof · cited by 0