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Simplify (and generalize) invElPropElimN #1102

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merged 4 commits into from
Feb 16, 2024

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MatthiasHu
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This PR slightly simplifies the proof of invElPropElimN in Cubical/Algebra/CommRing/Localisation/InvertingElements.agda and drops the unnecessary restriction to positive numbers (suc n).

This slightly simplifies two other things as well:

  • Replace suc n by n in the whole file Cubical/Algebra/CommRing/Localisation/Limit.agda.
  • Remove the separate treatment of the n = 0 case of isSheaf𝓞ᴮ in Cubical/Algebra/ZariskiLattice/StructureSheaf.agda.

Disclaimer: I did not read/understand all of the code in which I replaced (suc n) with n. :-) But it only makes all statements stronger as far as I can see.

[I found this potential for improvement while reviewing #1086, and that PR will also be slightly simplified by the changes proposed here.]

@felixwellen
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Nice - looks good to me. Maybe @mzeuner has something to say as well.

@mzeuner
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mzeuner commented Feb 16, 2024

Amazing, I don't know how I convinced myself that invElPropElimN would not work for n = 0.
I think this PR can be merged.

@MatthiasHu
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Ok, thanks. I hope it is ok if I merge this myself then.

@MatthiasHu MatthiasHu merged commit 0dc865a into agda:master Feb 16, 2024
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3 participants