R : Type u_1
inst✝² : CommSemiring R
X : Type u_2
A : Type u_3
inst✝¹ : Semiring A
inst✝ : Algebra R A
g : FreeAlgebra R X →ₐ[R] A
⊢ ↑(lift R) (↑(lift R).symm g) = g
R : Type u_1
inst✝² : CommSemiring R
X : Type u_2
A : Type u_3
inst✝¹ : Semiring A
inst✝ : Algebra R A
g : FreeAlgebra R X →ₐ[R] A
⊢ ↑(lift R) (↑g ∘ ι R) = g
rw [← lift_symm_apply]
no goals
R : Type u_1
inst✝² : CommSemiring R
X : Type u_2
A : Type u_3
inst✝¹ : Semiring A
inst✝ : Algebra R A
g : FreeAlgebra R X →ₐ[R] A
⊢ ↑(lift R) (↑(lift R).symm g) = g
exact (lift R).apply_symm_apply g