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Idempotent ring elements #2105

Merged
merged 6 commits into from
Oct 4, 2024
Merged

Idempotent ring elements #2105

merged 6 commits into from
Oct 4, 2024

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Alizter
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@Alizter Alizter commented Sep 30, 2024

Addresses first part of #2009. I can't recall any other identities to do with idempotent ring elements.

Signed-off-by: Ali Caglayan <[email protected]>

<!-- ps-id: d7fcadf7-90ae-4f92-8dd4-bb25a7aa8114 -->
theories/Algebra/Rings/Idempotent.v Outdated Show resolved Hide resolved
theories/Algebra/Rings/Idempotent.v Outdated Show resolved Hide resolved
Comment on lines +101 to +105
Proof.
snrapply Build_IsOrthogonal.
- exact (rng_idem_orth' (R:=R)).
- exact (rng_idem_orth (R:=R)).
Defined.
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Does it work to replace this proof with := isorthogonal_swap R e f r.?

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Not quite. I tried it again and it still doesn't work. I also thought something like this should work but I couldn't work it out.

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I wonder if it's because of the proofs of idempotency that are carried along? (Incidentally, they aren't used in any way, but I guess it makes sense to keep them.) In any case, this isn't worth worrying about.

theories/Algebra/Rings/Idempotent.v Outdated Show resolved Hide resolved
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theories/Algebra/Rings/Idempotent.v Outdated Show resolved Hide resolved
Comment on lines +101 to +105
Proof.
snrapply Build_IsOrthogonal.
- exact (rng_idem_orth' (R:=R)).
- exact (rng_idem_orth (R:=R)).
Defined.
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I wonder if it's because of the proofs of idempotency that are carried along? (Incidentally, they aren't used in any way, but I guess it makes sense to keep them.) In any case, this isn't worth worrying about.

@Alizter Alizter merged commit 6cdd74f into HoTT:master Oct 4, 2024
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@Alizter Alizter deleted the idem branch October 4, 2024 18:16
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Alizter commented Oct 4, 2024

Forgot to merge this the other day.

@Alizter Alizter mentioned this pull request Oct 5, 2024
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2 participants