[Merged by Bors] - feat(Complex): reProdIm lemmas

[javierlcontreras]

From FLT

Co-authored-by: Yaël Dillies [email protected]

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[github-actions]

PR summary 1eb98d3a2f

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

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Declarations diff

+ _root_.IsCompact.reProdIm
+ reProdIm
+ reProdIm_eq_empty
+ reProdIm_nonempty
+ «exists»
+ «forall»

You can run this locally as follows

## summary with just the declaration names:
./scripts/declarations_diff.sh <optional_commit>

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

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

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No changes to technical debt.

You can run this locally as

./scripts/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).

[loefflerd]

This looks very reasonable to me. I guess the old name Complex.Set.reProdIm was a mistake, the new name is definitely better. Thanks!

maintainer delegate

[github-actions]

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

[mathlib-bors]

✌️ javierlcontreras can now approve this pull request. To approve and merge a pull request, simply reply with bors r+. More detailed instructions are available here.

[YaelDillies]

I guess the old name Complex.Set.reProdIm was a mistake

I can tell you what happened here: It was originally called set.re_prod_im, for dot notation. Then at some point notation was added and dot notation became redundant. Then mathport dropped all _root_ in declaration names, meaning that our definition was accidentally named Complex.Set.reProdIm (but nobody minded because dot notation wasn't used). Given that dot notation isn't useful here anymore, I think Complex.reProdIm has become the best option.

[leanprover-community-mathlib4-bot]

As this PR is labelled auto-merge-after-CI, we are now sending it to bors:

bors merge

[mathlib-bors]

Pull request successfully merged into master.

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