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feat(Convex): the set of concave/convex functions on a given set is closed#37352

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dupuisf wants to merge 2 commits intoleanprover-community:masterfrom
dupuisf:isClosed_convexOn
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feat(Convex): the set of concave/convex functions on a given set is closed#37352
dupuisf wants to merge 2 commits intoleanprover-community:masterfrom
dupuisf:isClosed_convexOn

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@dupuisf dupuisf commented Mar 30, 2026

This PR proves that the set of concave/convex functions on a set s is closed.


AI use: this was my first attempt at using Aristotle. It found a proof in ~15 mins, but I had to generalise and clean it up quite a bit (it only did it for real vector spaces).

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@dupuisf dupuisf added the t-analysis Analysis (normed *, calculus) label Mar 30, 2026
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PR summary 34f85c5f24

Import changes for modified files

No significant changes to the import graph

Import changes for all files
Files Import difference
Mathlib.Analysis.Convex.FunctionTopology (new file) 1173

Declarations diff

+ OrderDual.instContinuousSMul_left
+ OrderDual.instContinuousSMul_right

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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