∀ {R : Type u_2} {L₁ : Type u_1} [inst : CommRing R] [inst_1 : LieRing L₁] [inst_2 : LieAlgebra R L₁]
  (L₁' L₁'' : LieSubalgebra R L₁) (h : ↑L₁' = ↑L₁'') {x x_1 : ↥L₁'},
  (↑(LinearEquiv.ofEq L₁'.toSubmodule L₁''.toSubmodule ⋯)).toFun ⁅x, x_1⁆ =
    (↑(LinearEquiv.ofEq L₁'.toSubmodule L₁''.toSubmodule ⋯)).toFun ⁅x, x_1⁆