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[ refactor ] make n≢i : n ≢ toℕ i argument to lower₁ irrelevant #2783

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@jamesmckinna jamesmckinna commented Jul 25, 2025

PR #2748 made me rethink whether Data.Fin.Base.lower₁ is fit-for-purpose (as an inverse to inject₁), or could instead be deprecated in favour of the new Data.Fin.Base.lower...

This PR doesn't entirely solve that issue, but does prove the two definitions extensionally equal on their domains, as a consequence, perhaps more importantly, of weakening the type of lower₁ so that its precondition is made irrelevant.

Two (possibly more downstream) knock-on consequences:

NB. As observed/observable in README.Data.Fin.Relation.Unary.Top, we can actually avoid having any uses of lower₁ in the library, so deprecation seems possible/desirable #2786

UPDATED: no longer blocked on #2785 .

@jamesmckinna jamesmckinna added the status: blocked-by-issue Progress on this issue or PR is blocked by another issue. label Jul 26, 2025
@jamesmckinna jamesmckinna added this to the v2.4 milestone Jul 26, 2025
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Modulo my comment on whether we even need those extra 2 lemmas, I'm now happy with this.

@jamesmckinna jamesmckinna removed the status: blocked-by-issue Progress on this issue or PR is blocked by another issue. label Aug 2, 2025
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