∀ {R : Type u_1} {L : Type u_2} {L' : Type u_3} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L]
  [inst_3 : LieRing L'] [inst_4 : LieAlgebra R L'] (toLinearMap toLinearMap_1 : L →ₗ[R] L')
  (e_toLinearMap : toLinearMap = toLinearMap_1)
  (map_lie' : ∀ {x y : L}, toLinearMap.toFun ⁅x, y⁆ = ⁅toLinearMap.toFun x, toLinearMap.toFun y⁆),
  { toLinearMap := toLinearMap, map_lie' := map_lie' } = { toLinearMap := toLinearMap_1, map_lie' := ⋯ }