refactor(Combinatorics/SimpleGraph): no proof obligation in rotate

[YaelDillies]

If the walk doesn't go through the new vertex, return nil instead.

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[github-actions]

PR summary 28f63a901b

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

+ append_eq_nil
+ rotate_of_mem_support
+ rotate_of_not_mem_support

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.

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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).

[eric-wieser]

Could you elaborate on the tradeoff here in the description? The obvious downside is that the proof can no longer be found by unification in lemmas about the definition. Are there enough places where having a total (junk) function is beneficial to warrant this loss?

[SnirBroshi]

Doesn't this mean that goals with rotate have to give the proof obligation for every lemma in rw, rather than it being inferred from the rotate call?

[mathlib-merge-conflicts]

This pull request has conflicts, please merge master and resolve them.

[YaelDillies]

I understand the tradeoff. I do not have an application for removing the proof field and opened the PR solely because we do tend to prefer junk values over propositional arguments (eg integral doesn't carry around a proof of integrability of the function) and that @b-mehta agreed it could be a good idea. On the other hand, you can see that the proof obligations aren't provided more often with this new setup: they are merely provided at a different point in the proof.

[b-mehta]

Yeah I agree this definition feels nicer because it doesn't require a hypothesis in the def, but Eric's point about the unification is a good one. In the diff, it's true that proof obligations aren't provided more, but that could be because the places this def is used in mathlib are simple enough that the downside doesn't really appear. Maybe the sensible thing to do is shelve this PR until there's a more concrete signal that the junk value is useful, as Eric suggests

[YaelDillies]

Do we have a good way to "shelve" a PR?

[mathlib-merge-conflicts]

This pull request has conflicts, please merge master and resolve them.