Add equivalence between is-set and is-0-type - #185
Open
marco-david wants to merge 1 commit into
Open
Conversation
| #def is-property-is-set uses (funext) | ||
| ( A : U) | ||
| : is-prop (is-set A) | ||
| -- This proof was written by ChatGPT 5.6 Sol. |
Collaborator
There was a problem hiding this comment.
I'm not sure we want to intersperse comments like this, nor if we want to have AI generated proofs in the library.
@fizruk @emilyriehl @jonweinb
| Next, we explicitly construct the equivalence between sets and 0-types. | ||
|
|
||
| ```rzk | ||
| #def is-set-to-is-0-type |
Collaborator
There was a problem hiding this comment.
Suggested change
| #def is-set-to-is-0-type | |
| #def is-0-type-is-set |
| : is-set A → is-0-type A | ||
| := \ s x y → is-prop-all-elements-equal (x = y) (s x y) | ||
|
|
||
| #def is-0-type-to-is-set |
Collaborator
There was a problem hiding this comment.
Suggested change
| #def is-0-type-to-is-set | |
| #def is-set-is-0-type |
| : is-0-type A → is-set A | ||
| := \ t x y → all-elements-equal-is-prop (x = y) (t x y) | ||
|
|
||
| #def is-set-is-0-type uses (weakfunext funext) |
Collaborator
There was a problem hiding this comment.
Suggested change
| #def is-set-is-0-type uses (weakfunext funext) | |
| #def equiv-is-set-is-0-type uses (weakfunext funext) |
Collaborator
|
Hey @marco-david! I've spoken with the TAs about this now and we've decided we will leave these goals open for someone to formalize as an exercise in HoTT and to familiarize themselves with the library for now. It's not critical to have this merged, but if no one else does it we might merge your contribution later. |
This file contains hidden or 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
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
2 participants
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.
In response to issue #175