Finiteness of UpWords given finite alphabet #4533
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tirix
reviewed
Jan 5, 2025
| paysd.1 $e |- ( ph -> A e. Fin ) $. | ||
| paysd.2 $e |- ( ph -> B : A --> RR ) $. | ||
| paysd.3 $e |- ( ph -> sum_ k e. A ( B ` k ) = 0 ) $. | ||
| paysd.4 $e |- ( ph -> C = (/) ) $. |
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I assume this is the initial step of a proof by induction?
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That's a comment with some proof... I'm actually not sure if I want to prove the fact that |A| transfers are sufficient by induction or by explicit construction of C.
tirix
approved these changes
Jan 5, 2025
avekens
reviewed
Jan 5, 2025
| tworepnotupword.1 $e |- A e. _V $. | ||
| $( Word of two matching characters is never an increasing sequence. | ||
| (Contributed by Ender Ting, 22-Nov-2024.) $) | ||
| tworepnotupword $p |- -. ( <" A "> ++ <" A "> ) e. UpWord S $= |
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Why not -. <" A A "> e. UpWord S ? Then label could be s2repnupword.
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There was such a word constructor? 😮
avekens
reviewed
Jan 5, 2025
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| ${ | ||
| $d S a $. $d T a $. | ||
| $( There is a finite number of strictly increasing sequences over finite |
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"strictly increasing sequences of fixed length"
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Ah yes, I see how this can become misleading (given that total number of strictly increasing sequences will be finite as well).
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Hopefully I found the right place to put
rabss3dafter promotion.