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feat (Algebra/Order/Quantale): isMulIdempotent, isMulLeftsided, isMulRightsided, isMulTwosided and strict versions#36896

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feat (Algebra/Order/Quantale): isMulIdempotent, isMulLeftsided, isMulRightsided, isMulTwosided and strict versions#36896
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@PieterCuijpers PieterCuijpers commented Mar 20, 2026

  • Adding definitions of quantale elements being idempotent, leftsided, rightsided, and twosided, and strict versions

I'd value some discussion on whether especially the definition of isMulIdempotent would belong here, since
it applies to semigroups in general. I only see definitions of IdempotentOp in the library so far, focussing on
operators that are fully idempotent, while in the study of Quantales it seems that subquantales of elements
that are idempotent in the original are also interesting. This argues the need for having definitions on
separate elements.

Also, should we include these definitions in the main Algebra/Order/Quantale.lean file, or start a separate file for them?
And I have a few basic theorems I would like to include, but invite suggestions.

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github-actions bot commented Mar 20, 2026 •
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PR summary 205a0ba54c

Import changes for modified files

No significant changes to the import graph

Import changes for all files
Files Import difference

Declarations diff

+ IsAddLeftsided
+ IsAddRightsided
+ IsAddTwosided
+ IsMulLeftsided
+ IsMulRightsided
+ IsMulTwosided
+ IsStrictAddLeftsided
+ IsStrictAddRightsided
+ IsStrictAddTwosided
+ IsStrictMulLeftsided
+ IsStrictMulRightsided
+ IsStrictMulTwosided

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).

@github-actions github-actions bot added the t-algebra Algebra (groups, rings, fields, etc) label Mar 20, 2026
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github-actions bot commented Mar 20, 2026 •
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@PieterCuijpers PieterCuijpers changed the title feat(Algebra/Order/Quantale) : isMulIdempotent, isMulLeftsided, isMulRightsided, isMulTwosided and strict versions feat (Algebra/Order/Quantale): isMulIdempotent, isMulLeftsided, isMulRightsided, isMulTwosided and strict versions Mar 20, 2026
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NoahW314 commented Mar 20, 2026

We do have idempotent elements, see IsIdempotentElem.

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