Theorems · Theorem · nonassociative algebras

LieModule.range_traceForm_le_span_weight

∀ (K : Type u_2) (L : Type u_3) (M : Type u_4) [inst : LieRing L] [inst_1 : AddCommGroup M] [inst_2 : LieRingModule L M]
  [inst_3 : Field K] [inst_4 : LieAlgebra K L] [inst_5 : Module K M] [inst_6 : LieModule K L M] [FiniteDimensional K M]
  [inst_8 : LieRing.IsNilpotent L] [inst_9 : LieModule.LinearWeights K L M] [LieModule.IsTriangularizable K L M],
  LinearMap.range (LieModule.traceForm K L M) ≤ Submodule.span K (Set.range (LieModule.Weight.toLinear K L M))

Defined in: Mathlib.Algebra.Lie.TraceForm
Cited by: 1 results in Mathlib
Foundations: Depth 130 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: LieRing AddCommGroup LieRingModule Field LieAlgebra Module LieModule FiniteDimensional LieRing.IsNilpotent LieModule.LinearWeights LieModule.IsTriangularizable

Mathlib docs Source Loogle LeanSearch

Around this declaration

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

Cites36

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

DFunLike.coeproof · cited by 62,936
Modulestatement and proof · cited by 20,661
RingHom.idstatement and proof · cited by 18,349
AddCommGroupstatement and proof · cited by 12,871
AddCommMonoidproof · cited by 12,281
LinearMapstatement and proof · cited by 10,215
Fieldstatement and proof · cited by 7,404
Submodulestatement · cited by 7,192
Set.rangestatement and proof · cited by 4,705
Finset.univproof · cited by 3,473
FiniteDimensionalstatement and proof · cited by 1,854
Module.finrankproof · cited by 1,770

Cited by1

Results whose statement or proof uses this declaration.

LieAlgebra.IsKilling.span_weight_eq_topproof · cited by 2