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[Merged by Bors] - feat: simplify ℵ₁ ≤ c to ℵ₀ < c#37024

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[Merged by Bors] - feat: simplify ℵ₁ ≤ c to ℵ₀ < c#37024
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@vihdzp vihdzp commented Mar 23, 2026

We simplify c < ℵ₁ to c ≤ ℵ₀ and ℵ₁ ≤ c to ℵ₀ < c, under the logic that there is more to be said about ℵ₀ (the least infinite cardinal, etc.) than there is about ℵ₁, characterized only by being the successor to ℵ₀.


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github-actions bot commented Mar 23, 2026

PR summary 47aa862678

Import changes for modified files

No significant changes to the import graph

Import changes for all files
Files Import difference

Declarations diff

+ aleph_one_le_iff
+ lt_aleph_one_iff

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).

@vihdzp vihdzp requested a review from YaelDillies March 27, 2026 09:04
@vihdzp vihdzp changed the title feat: improve simp set for ω₁ and ℵ₁ feat: simplify ℵ₁ ≤ c to ℵ₀ < c Mar 30, 2026
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Thanks! 🚀

maintainer merge

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🚀 Pull request has been placed on the maintainer queue by YaelDillies.


pull_request_review, wf_run

@mathlib-triage mathlib-triage bot added the maintainer-merge A reviewer has approved the changed; awaiting maintainer approval. label Mar 30, 2026
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Thanks!

bors merge

@mathlib-triage mathlib-triage bot added ready-to-merge This PR has been sent to bors. and removed maintainer-merge A reviewer has approved the changed; awaiting maintainer approval. labels Mar 31, 2026
mathlib-bors bot pushed a commit that referenced this pull request Mar 31, 2026
We simplify `c < ℵ₁` to `c ≤ ℵ₀` and `ℵ₁ ≤ c` to `ℵ₀ < c`, under the logic that there is more to be said about ℵ₀ (the least infinite cardinal, etc.) than there is about ℵ₁, characterized only by being the successor to ℵ₀.
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mathlib-bors bot commented Mar 31, 2026

Pull request successfully merged into master.

Build succeeded:

@mathlib-bors mathlib-bors bot changed the title feat: simplify ℵ₁ ≤ c to ℵ₀ < c [Merged by Bors] - feat: simplify ℵ₁ ≤ c to ℵ₀ < c Mar 31, 2026
@mathlib-bors mathlib-bors bot closed this Mar 31, 2026
aditya-ramabadran pushed a commit to aditya-ramabadran/mathlib4 that referenced this pull request Apr 1, 2026
We simplify `c < ℵ₁` to `c ≤ ℵ₀` and `ℵ₁ ≤ c` to `ℵ₀ < c`, under the logic that there is more to be said about ℵ₀ (the least infinite cardinal, etc.) than there is about ℵ₁, characterized only by being the successor to ℵ₀.
xroblot pushed a commit to xroblot/mathlib4 that referenced this pull request Apr 3, 2026
We simplify `c < ℵ₁` to `c ≤ ℵ₀` and `ℵ₁ ≤ c` to `ℵ₀ < c`, under the logic that there is more to be said about ℵ₀ (the least infinite cardinal, etc.) than there is about ℵ₁, characterized only by being the successor to ℵ₀.
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