feat(RingTheory): definition of Koszul cocomplex

[Thmoas-Guan]

Definition of Koszul cocomplex.

This PR have some proofs generated by LLM.

Co-authored-by: Wang Jingting wangjt2020@163.com

---

[github-actions]

PR summary 9be0e0b49e

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.RingTheory.KoszulComplex.Cocomplex (new file)	1984

---

Declarations diff (regex)

+ GradedAlgebra.linearGMul
+ GradedAlgebra.linearGMul_eq_mul
+ d_def
+ free
+ isZero_X_ofList_of_length_le
+ isZero_X_of_span_eq_top
+ isoOfEquiv
+ koszulCocomplex
+ koszulCocomplex.d
+ koszulCocomplex.d_apply_ιMulti
+ map
+ map_comp
+ map_f
+ map_id
+ map_id_refl
+ ofList

You can run this locally as follows

## from your `mathlib4` directory:
git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci

## summary with just the declaration names:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh <optional_commit>

## more verbose report:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh long <optional_commit>

The doc-module for scripts/pr_summary/declarations_diff.sh in the mathlib-ci repository contains some details about this script.

Declarations diff (Lean)

✅ Lean-aware diff — post-build, computed from the Lean environment (commit 9be0e0b).

• +21 new declarations
• −0 removed declarations

+GradedAlgebra.linearGMul
+GradedAlgebra.linearGMul.congr_simp
+GradedAlgebra.linearGMul_eq_mul
+koszulCocomplex
+koszulCocomplex.d
+koszulCocomplex.d_apply_ιMulti
+koszulCocomplex.d_def
+koszulCocomplex.free
+koszulCocomplex.isZero_X_ofList_of_length_le
+koszulCocomplex.isZero_X_of_span_eq_top
+koszulCocomplex.isoOfEquiv
+koszulCocomplex.map
+koszulCocomplex.map.congr_simp
+koszulCocomplex.map_comp
+koszulCocomplex.map_comp_assoc
+koszulCocomplex.map_f
+koszulCocomplex.map_id
+koszulCocomplex.map_id_assoc
+koszulCocomplex.map_id_refl
+koszulCocomplex.map_id_refl_assoc
+koszulCocomplex.ofList

---

No changes to strong technical debt.

Increase in weak tech debt: (relative, absolute) = (1.00, 0.00)

Current number	Change	Type (weak)
exposed public sections	5062	1

Current commit 9be0e0b49e
Reference commit 98b840bb29

This script lives in the mathlib-ci repository. To run it locally, from your mathlib4 directory:

git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci
../mathlib-ci/scripts/reporting/technical-debt-metrics.py pr_summary

• The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
• The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).