no goals
ι : Type u_1
R : Type u_3
A : Type u_2
σ : Type ?u.286140
inst✝⁵ : DecidableEq ι
inst✝⁴ : AddMonoid ι
inst✝³ : CommSemiring R
inst✝² : Semiring A
inst✝¹ : Algebra R A
𝒜 : ι → Submodule R A
inst✝ : GradedAlgebra 𝒜
a : ⨁ (i : ι), { x // x ∈ 𝒜 i }
i : ι
⊢ ↑(proj 𝒜 i) (↑(decompose 𝒜).symm a) = ↑(decompose 𝒜).symm (↑(of (fun i => (fun i => { x // x ∈ 𝒜 i }) i) i) (↑a i))
rw [GradedAlgebra.proj_apply, decompose_symm_of, Equiv.apply_symm_apply]