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Theorems · Theorem · nonassociative algebras

LieAlgebra.IsSimple.non_abelian

∀ (R : Type u_1) {L : Type u_2} {inst : CommRing R} {inst_1 : LieRing L} {inst_2 : LieAlgebra R L}
  [self : LieAlgebra.IsSimple R L], ¬IsLieAbelian L
Defined in
Mathlib.Algebra.Lie.Semisimple.Defs
Cited by
2 results in Mathlib
Foundations
Depth 13 from the axioms · uses propext
Assumes
LieAlgebra.IsSimple
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

LieAlgebra.not_isSimple_of_subsingleton · cited by 0LieAlgebra.not_isSimple_o…LieAlgebra.IsSimple.nontrivial · cited by 0IsSimple.nontrivialCommRing · cited by 17173CommRingLieRing · cited by 1548LieRingLieAlgebra · cited by 1246LieAlgebraIsLieAbelian · cited by 55IsLieAbelianLieAlgebra.IsSimple · cited by 10LieAlgebra.IsSimpleIsSimple.non_abelianCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.