From 804fd57037abd5312178ec102b7e2e63fb7efd4e Mon Sep 17 00:00:00 2001
From: chelseaandmadrid <53058005+chelseaandmadrid@users.noreply.github.com>
Date: Wed, 14 Jun 2023 21:53:35 -0700
Subject: [PATCH] a little standard graded

---
 HilbertFunction.lean | 5 +++--
 1 file changed, 3 insertions(+), 2 deletions(-)

diff --git a/HilbertFunction.lean b/HilbertFunction.lean
index ce68f8c..fccd2e4 100644
--- a/HilbertFunction.lean
+++ b/HilbertFunction.lean
@@ -109,7 +109,7 @@ instance {𝒜 : ℤ → Type _} [∀ i, AddCommGroup (𝒜 i)] [DirectSum.GComm
 
 
 
-class StandardGraded {𝒜 : ℤ → Type _} [∀ i, AddCommGroup (𝒜 i)] [DirectSum.GCommRing 𝒜] : Prop where
+class StandardGraded (𝒜 : ℤ → Type _) [∀ i, AddCommGroup (𝒜 i)] [DirectSum.GCommRing 𝒜] : Prop where
   gen_in_first_piece :
     Algebra.adjoin (𝒜 0) (DirectSum.of _ 1 : 𝒜 1 →+ ⨁ i, 𝒜 i).range = (⊤ : Subalgebra (𝒜 0) (⨁ i, 𝒜 i))
 
@@ -188,10 +188,11 @@ lemma Associated_prime_of_graded_is_graded
 -- If M is a finite graed R-Mod of dimension d ≥ 1, then the Hilbert function H(M, n) is of polynomial type (d - 1)
 theorem Hilbert_polynomial_d_ge_1 (d : ℕ) (d1 : 1 ≤ d) (𝒜 : ℤ → Type _) (𝓜 : ℤ → Type _) [∀ i, AddCommGroup (𝒜 i)] [∀ i, AddCommGroup (𝓜 i)]
 [DirectSum.GCommRing 𝒜]
-[DirectSum.Gmodule 𝒜 𝓜] (art: IsArtinianRing (𝒜 0)) (loc : LocalRing (𝒜 0)) 
+[DirectSum.Gmodule 𝒜 𝓜] (st: StandardGraded 𝒜) (art: IsArtinianRing (𝒜 0)) (loc : LocalRing (𝒜 0)) 
 (fingen : IsNoetherian (⨁ i, 𝒜 i) (⨁ i, 𝓜 i))
 (findim :  dimensionmodule (⨁ i, 𝒜 i) (⨁ i, 𝓜 i) = d)
 (hilb : ℤ → ℤ) (Hhilb: hilbert_function 𝒜 𝓜 hilb)
+
 : PolyType hilb (d - 1) := by
   sorry