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feat(Combinatorics/Schnirelmann): if sum of densities is at least one, the sumset covers the naturals#34227

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feat(Combinatorics/Schnirelmann): if sum of densities is at least one, the sumset covers the naturals#34227
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@stepan2698-cpu stepan2698-cpu commented Jan 21, 2026

Proves an outstanding TODO item from Mathlib.Combinatorics.Schnirelmann : shows that if the sum of two densities is at least one, the sumset covers the positive naturals.


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@github-actions github-actions bot added new-contributor This PR was made by a contributor with at most 5 merged PRs. Welcome to the community! merge-conflict The PR has a merge conflict with master, and needs manual merging. (this label is managed by a bot) t-combinatorics Combinatorics and removed merge-conflict The PR has a merge conflict with master, and needs manual merging. (this label is managed by a bot) labels Jan 21, 2026
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github-actions bot commented Jan 21, 2026

PR summary 6ef8cc2731

Import changes for modified files

Dependency changes

File Base Count Head Count Change
Mathlib.Combinatorics.Schnirelmann 800 802 +2 (+0.25%)
Import changes for all files
Files Import difference
Mathlib.Combinatorics.Schnirelmann 2

Declarations diff

+ zero_union_add_eq_univ_of_schirelmannDensity_ge_one
+ zero_union_add_eq_univ_of_schirelmannDensity_ge_one_of_zero_mem

You can run this locally as follows
## summary with just the declaration names:
./scripts/pr_summary/declarations_diff.sh <optional_commit>

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

The doc-module for scripts/pr_summary/declarations_diff.sh contains some details about this script.


No changes to technical debt.

You can run this locally as

./scripts/reporting/technical-debt-metrics.sh 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).

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Thanks! I've left a couple of style comments, but otherwise the proof looks good to me.

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Thanks! I've left a couple of style comments, but otherwise the proof looks good to me.

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cc @YaelDillies

@YaelDillies YaelDillies changed the title feat: If sum of densities is at least one, the sumset covers the naturals feat: if sum of densities is at least one, the sumset covers the naturals Mar 31, 2026
@YaelDillies YaelDillies changed the title feat: if sum of densities is at least one, the sumset covers the naturals feat(Combinatorics/Schnirelmann): if sum of densities is at least one, the sumset covers the naturals Mar 31, 2026
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