Pet #4531
Merged
Pet #4531
Conversation
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
WIP
jkingdon
approved these changes
Jan 4, 2025
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
Add this suggestion to a batch that can be applied as a single commit.
This suggestion is invalid because no changes were made to the code.
Suggestions cannot be applied while the pull request is closed.
Suggestions cannot be applied while viewing a subset of changes.
Only one suggestion per line can be applied in a batch.
Add this suggestion to a batch that can be applied as a single commit.
Applying suggestions on deleted lines is not supported.
You must change the existing code in this line in order to create a valid suggestion.
Outdated suggestions cannot be applied.
This suggestion has been applied or marked resolved.
Suggestions cannot be applied from pending reviews.
Suggestions cannot be applied on multi-line comments.
Suggestions cannot be applied while the pull request is queued to merge.
Suggestion cannot be applied right now. Please check back later.
Mathbox only. (I used some theorems from other people's Mathboxes with TEMP ending: I'll put them in the main in my next PR). Maybe more appropriate for the weekend, since this is a big PR. The commits are more or less separate.
Partition and its relation to equivalence is the main topic. The main results are
MPET, the Member Partition-Equivalence Theorem in its shortest possible form: it shows, not too surprisingly, that member partitions and comember equivalence relations are literally the same. mpets $p |- MembParts = CoMembErs
PET, the Partition-Equivalence Theorem, which, while not general by itself (e.g. MPET is not a special case of it), works with general R in biconditional form, which is sufficient for my use case. pet $p |- ( ( R |X. (
' _E |A ) ) Part A <-> ,~ ( R |X. (' _E |A ) ) ErALTV A )Thank you for your time and effort.