Witness | Monitor file system events using Swift

Looking at the documentation, it does not seem that the decision procedure for lia handles existential quantifiers, so you have to instantiate the existential by yourself, e.g.

Let's analyze

In the two links you mention, the problem is the segregation enforced by Coq between propositions (those types of type Prop) and other types (those with type Set or Type), with the idea being that proofs should not be needed for programs to run. However, in your case both set M and subset M are propositions, so this separation is not a problem: as you saw when defining fn0, Coq is perfectly happy to use the first component of your existential type to build the function you are looking for. This is a good point of constructive mathematics: modulo the separation between Prop and Type, choice is simply true!

Rather, the problem comes from the second part of the proof, i.e. the proof of equality of functions. It is a subtle issue of Coq that equality of functions is not extensional, that is the following axiom cannot, in general, be proven

I have realised the understanding that I was missing and it is rather simple. The proof in this case is not verifying that a * a is equal to b but instead it is simply a proof that I have run the computation.

For example the following generates a proof that I have run this program with a = 337 and b = 113569 and the return value is true.

The short answer is that you can't.

When git merge runs, it reads three commits into Git's index. These three commits are:

• the merge base (in slot 1);
• the --ours commit (in slot 2); and
• the --theirs commit (in slot 3).

These are stored in the usual index format: a path name including slashes, a mode (100644 or 100755 for regular files, 120000 for symbolic links, and 160000 for gitlinks), and a hash ID.

The first part of the merge then compares the modes to make sure those are suitable (if not, this is a merge conflict). Assuming normal files and suitable modes here, it goes on to compare the hash IDs:

• all three equal? file is successfully merged, drop to slot 0, erase slots 1-3
• two equal? take the third one: drop to slot 0, erase slots 1-3
• all three unequal? leave for later, for the real merge code.

There are a few more special cases (e.g., file exists in merge base and theirs/ours, but deleted in ours/theirs) that are also handled directly in the index, I think, but your particular case—file modified in theirs, but identical in ours and base—hits the middle "two equal? take third" case: the file is the same in your commit and the merge base, so Git just assumes that their updated file is the correct result.

When Git does this in the early pass, it never runs your merge driver at all. The file goes to staging slot zero—"ready to be committed"—rather than conflicted and you never get a chance to do anything. Your pre-merge-commit will get invoked, but the copy of the file in the index will be the one from the theirs commit.

We now get into the seriously dark magic part: "the index" assumes that there's a single index (.git/index) that is always used. This isn't really the case: it's mostly true, but:

• $GIT_INDEX_FILE overrides the name;
• added work-trees (from git worktree add) have their own index; and
• various Git commands read the index into memory and then work with that.

In this case, it looks like git merge has the index in-memory and just uses it as is to make the new commit. Your git add replaces the stage-zero copy in the .git/index file, but git merge does not notice this, and goes on to produce the new merge commit using the incoming copy that was there before it even ran your pre-merge-commit hook.

Assuming this is all true—and it may change from one Git version to another, depending on when and whether Git does any re-reading of the index—this would answer your question #1, and render the answer to #2 "no" and the answer to #3 be "you're trying to do something outside the range of what Git handles".

What you want to do is not inherently unreasonable, but Git just doesn't support it.

Have you considered writing the Good Chosen string directly to firestore?

Instead of / additionally to your print statements, you could write

At least, code below doesn't make much sense. Please don't set state value as a component. Also, try to name state variable different from components, since it will confuse you at some ppint.

According to this document you need to add freesolo