Proved sorted permutations are equal

[MatthewDaggitt]

The main result. Would like to try and sneak this into v2.3 for @onestruggler.

Have also added an explanation of the choice of propositional permutation in SortingAlgorithm and a lemma that proves the setoid version.

[jamesmckinna]

Various nitpicks and bugfixes suggested, but otherwise: good to go!

[JacquesCarette]

I have no comments beyond James'.

[jamesmckinna]

Sorry to go back on my original approval, but I think the new proof structure is... better!?

[JacquesCarette]

Definitely agree that your proof of injective⇒existsPivot is much nicer.

Minor nit: f∘inject! instead of h? Then the 'narrative' of the proof would be easier to follow top-down, instead of being forced to reconstruct it by reading it bottom-up.

[jamesmckinna]

@JacquesCarette if @MatthewDaggitt goes ahead with my proposed changes, then I think your function name change makes sense, but perhaps at the cost of what you then choose to call what currently is h-injective...so I'll leave such last things up to him... ;-)

[jamesmckinna]

Definitely agree that your proof of injective⇒existsPivot is much nicer.

Minor nit: f∘inject! instead of h? Then the 'narrative' of the proof would be easier to follow top-down, instead of being forced to reconstruct it by reading it bottom-up.

lower∘f∘inject!? I'd almost be tempted to call it ↓f↑? Or... f′ for 'f modified'?

[JacquesCarette]

I think lower gets elided a lot, and that's fine with me. So f∘inject! seems to capture the important meaning.

[jamesmckinna]

All looks great.
Last round of nitpicks: CHANGELOG is the one that really needs fixing

[jamesmckinna]

🎉 Very nice work!