Theorems · Theorem · nonassociative algebras

LieModule.genWeightSpaceChain.congr_simp

∀ {R : Type u_1} {L : Type u_2} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L] (M : Type u_3)
  [inst_3 : AddCommGroup M] [inst_4 : Module R M] [inst_5 : LieRingModule L M] [inst_6 : LieModule R L M]
  [inst_7 : LieRing.IsNilpotent L] (χ₁ χ₁_1 : L → R),
  χ₁ = χ₁_1 →
    ∀ (χ₂ χ₂_1 : L → R),
      χ₂ = χ₂_1 →
        ∀ (p p_1 : ℤ),
          p = p_1 →
            ∀ (q q_1 : ℤ),
              q = q_1 → LieModule.genWeightSpaceChain M χ₁ χ₂ p q = LieModule.genWeightSpaceChain M χ₁_1 χ₂_1 p_1 q_1

Defined in

Mathlib.Algebra.Lie.Weights.Chain

Cited by

0 results in Mathlib

Foundations

Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraAddCommGroupModuleLieRingModuleLieModuleLieRing.IsNilpotent