Theorems · Theorem · nonassociative algebras
LieEquiv.apply_symm_apply
∀ {R : Type u} {L₁ : Type v} {L₂ : Type w} [inst : CommRing R] [inst_1 : LieRing L₁] [inst_2 : LieRing L₂]
[inst_3 : LieAlgebra R L₁] [inst_4 : LieAlgebra R L₂] (e : L₁ ≃ₗ⁅R⁆ L₂) (x : L₂), e (e.symm x) = x- Defined in
- Mathlib.Algebra.Lie.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- LieRingstatement and proof · cited by 1,548
- LieAlgebrastatement and proof · cited by 1,246
- LinearEquiv.apply_symm_applyproof · cited by 108
- LieEquivstatement and proof · cited by 86
- LieEquiv.symmstatement · cited by 34
- LieEquiv.toLinearEquivproof · cited by 16
Cited by4
Results whose statement or proof uses this declaration.
- Equiv.lieModule_isNilpotent_iffproof · cited by 2
- LieAlgebra.isKilling_of_equivproof · cited by 1
- LieAlgebra.Extension.d₁₂_oneCochainOfTwoSplittingproof · cited by 0
- LieAlgebra.Extension.toKer_bracketproof · cited by 0