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Add lemmas, reduce axiom usage, shorten proofs #4264

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merged 2 commits into from
Oct 5, 2024

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GinoGiotto
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This PR contains the following changes:

  • Add rspw -> use it in the proof of solin to avoid ax-12.

  • Add vtocl3g -> use it in the proof of vtocl3ga to avoid ax-10 , ax-11 , ax-12

  • Add ab0w -> use it in the proof of rabeq0w to shorten its proof and use it in the proofs of 0mpo0, fsetdmprc0 to avoid ax-10, ax-11, ax-12.

  • Shorten proof of 0nelopab and avoid ax-10, ax-11, ax-12.

  • Shorten proof of pocl and avoid ax-12 (ax-10 and ax-11 are automatically removed by editing vtocl3ga).

  • Avoid ax-10, ax-11, ax-12 in dffr2, but add ax-8. All theorems using dffr2 depend on ax-8 anyway, so this does not affect them. The original proof of dffr2 is kept as dffr2ALT.

  • Prove peano5 without ax-10, ax-12.


Results:
Drop ax-12 from 304 theorems.
Drop ax-11 from 135 theorems.
Drop ax-10 from 304 theorems.

Axiom usage here: d486acf

@benjub benjub merged commit dbb92ce into metamath:develop Oct 5, 2024
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@GinoGiotto GinoGiotto deleted the PR13 branch October 7, 2024 10:29
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3 participants