feat: q-analogs

[SashaIr]

An implementation of q-analogs, q-binomials, and counting results.

---

[github-actions]

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[github-actions]

PR summary bf1d33d12b

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.Combinatorics.QAnalog.Basic (new file)	833
Mathlib.Combinatorics.QAnalog.Binomial (new file)	850
Mathlib.Combinatorics.QAnalog.Counting (new file)	851
Mathlib.Combinatorics.QAnalog.Subspace (new file)	1781

---

Declarations diff (regex)

+ Commute.list_prod_one_add_pow_mul
+ Commute.qBinomial_left
+ Commute.qBinomial_right
+ Commute.qFactorial_left
+ Commute.qFactorial_right
+ Commute.qNat_left
+ Commute.qNat_right
+ Commute.qPochhammer_eq_sum_qBinomial
+ card_submodule_finrank_eq_qBinomial
+ filter_notMem_insert_zero_map
+ filter_notMem_map
+ inversions
+ inversions_empty
+ inversions_insert_zero_map
+ inversions_map_succ
+ map_qBinomial
+ map_qNat
+ one_sub_mul_qNat
+ prod_one_add_pow_mul_eq_sum_qBinomial
+ prod_pow_sub_pow_mul_qFactorial
+ qBinomial
+ qBinomial_commute
+ qBinomial_commute_pow
+ qBinomial_eq_zero_of_lt
+ qBinomial_mul_eq_mul
+ qBinomial_mul_prod_pow_sub_pow
+ qBinomial_mul_qFactorial_mul_qFactorial
+ qBinomial_mul_qNat_sub
+ qBinomial_one_left
+ qBinomial_one_right
+ qBinomial_self
+ qBinomial_succ_left
+ qBinomial_succ_right
+ qBinomial_succ_succ
+ qBinomial_succ_succ'
+ qBinomial_symm
+ qBinomial_symm_add
+ qBinomial_symm_of_eq_add
+ qBinomial_zero_right
+ qBinomial_zero_succ
+ qFactorial
+ qFactorial_commute
+ qFactorial_commute_qBinomial
+ qFactorial_commute_qFactorial
+ qFactorial_eq_prod_range
+ qFactorial_int_pos
+ qFactorial_one
+ qFactorial_one_left
+ qFactorial_succ
+ qFactorial_succ'
+ qFactorial_zero
+ qNat
+ qNat_add
+ qNat_commute
+ qNat_commute_pow
+ qNat_commute_qBinomial
+ qNat_commute_qFactorial
+ qNat_commute_qNat
+ qNat_eq_sum_range
+ qNat_mul
+ qNat_mul_one_sub
+ qNat_one
+ qNat_one_left
+ qNat_succ
+ qNat_succ'
+ qNat_two
+ qNat_zero
+ qPochhammer
+ qPochhammer_eq_prod_range
+ qPochhammer_eq_sum_qBinomial
+ qPochhammer_one
+ qPochhammer_self
+ qPochhammer_succ
+ qPochhammer_succ'
+ qPochhammer_zero
+ qPochhammer_zero_left
+ range_succ_eq_insert_map
+ spanEquiv
+ succEmb
+ succEmb_apply
+ sum_pow_inversions_eq_qBinomial
+ sum_pow_sum_eq_qBinomial
+ sum_powersetCard_succ

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 -- stale, waiting for the new build)

✅ Lean-aware diff — post-build, computed from the Lean environment (commit 016b867).

• +80 new declarations
• −0 removed declarations

+Commute.list_prod_one_add_pow_mul
+Commute.qBinomial_left
+Commute.qBinomial_right
+Commute.qFactorial_left
+Commute.qFactorial_right
+Commute.qNat_left
+Commute.qNat_right
+Commute.qPochhammer_eq_sum_qBinomial
+QAnalog.card_submodule_finrank_eq_qBinomial
+QAnalog.inversions
+QAnalog.inversions_empty
+QAnalog.inversions_insert_zero_map
+QAnalog.inversions_map_succ
+QAnalog.prod_pow_sub_pow_mul_qFactorial
+QAnalog.qBinomial_mul_prod_pow_sub_pow
+QAnalog.spanEquiv
+QAnalog.succEmb
+QAnalog.sum_pow_inversions_eq_qBinomial
+QAnalog.sum_pow_sum_eq_qBinomial
+QAnalog.«term[_;_]__»
+QAnalog.«term[_]__!»
+QAnalog.«term[_]__»
+map_qBinomial
+map_qNat
+one_sub_mul_qNat
+prod_one_add_pow_mul_eq_sum_qBinomial
+qBinomial
+qBinomial_commute
+qBinomial_commute_pow
+qBinomial_eq_zero_of_lt
+qBinomial_mul_eq_mul
+qBinomial_mul_qFactorial_mul_qFactorial
+qBinomial_mul_qNat_sub
+qBinomial_one_left
+qBinomial_one_right
+qBinomial_self
+qBinomial_succ_left
+qBinomial_succ_right
+qBinomial_succ_succ
+qBinomial_succ_succ'
+qBinomial_symm
+qBinomial_symm_add
+qBinomial_symm_of_eq_add
+qBinomial_zero_right
+qBinomial_zero_succ
+qFactorial
+qFactorial_commute
+qFactorial_commute_qBinomial
+qFactorial_commute_qFactorial
+qFactorial_eq_prod_range
+qFactorial_one
+qFactorial_one_left
+qFactorial_succ
+qFactorial_succ'
+qFactorial_zero
+qNat
+qNat_add
+qNat_commute
+qNat_commute_pow
+qNat_commute_qBinomial
+qNat_commute_qFactorial
+qNat_commute_qNat
+qNat_eq_sum_range
+qNat_mul
+qNat_mul_one_sub
+qNat_one
+qNat_one_left
+qNat_succ
+qNat_succ'
+qNat_two
+qNat_zero
+qPochhammer
+qPochhammer_eq_prod_range
+qPochhammer_eq_sum_qBinomial
+qPochhammer_one
+qPochhammer_self
+qPochhammer_succ
+qPochhammer_succ'
+qPochhammer_zero
+qPochhammer_zero_left

---

No changes to strong technical debt.

Increase in weak tech debt: (relative, absolute) = (4.00, 0.00)

Current number	Change	Type (weak)
exposed public sections	5070	4

Current commit bf1d33d12b
Reference commit 8d52ea9a14

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).

[b-mehta]

Can you comment on the use of AI in this PR?

[SashaIr]

Sure. The initial draft is human-written (by the listed authors), based on the existing implementation of Nat, factorials, and binomials. I fed Aristotle a few of these files to improve, restructure, and make Mathlib-ready.

Most of the code in Basic.lean and Binomial.lean is essentially human-written and AI-polished; Counting.lean is based on another human-written file but some proofs were originally provided by Aristotle in sorry-filling mode, if I recall correctly; Subspace.lean is pretty much entirely AI-generated, I did not even ask for it but Aristotle produced the file together with the others, so I included it in the PR as well.

[SashaIr]

The AI use was originally disclosed in the header, but then I got asked to remove Aristotle from the author list in a discussion in a different PR. It could (should?) be mentioned in the implementation details section.

[SnirBroshi]

The Authors list refers to humans responsible for the code, and AI usage disclosures belong in the PR description, per the contribution guidelines.

[SashaIr]

I'll make a revision pass and then update everything according to the guidelines.