proof | Secure Authentication for Single Page Applications | Authentication library

Easy to see the difference

Worst case is when the input has only unique numbers. In that case, the equivalent is:

You can't do this from command level. But I guess you could write container_commands script to rename your docker-compose file from docker-compose.dev.yml to docker-compose.yml:

You can use the container_commands key to execute commands that affect your application source code. Container commands run after the application and web server have been set up and the application version archive has been extracted, but before the application version is deployed.

UPDATE 12 Jun 2021

I tried to replicate the issue using simplified setup with just docker-compose.prod.yml and Docker running on 64bit Amazon Linux 2 3.4.1 EB platform.

docker-compose.prod.yml

We could specify the j with the column names of the data created i.e. startsWith returns a logical vector from the column names based on the names that starts with 'b', use the logical vector to extract the column names with [ (nm1).

aws cloudformation deregister-type --arn

https://docs.aws.amazon.com/cli/latest/reference/cloudformation/deregister-type.html

https://github.com/aws-cloudformation/cloudformation-cli/issues/401

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 believe that the lemma you are trying to prove does not appropriately consider the case of infinite sets.

In Isabelle/HOL, infinite cardinalities are represented by zero. As we can see by the following lemma.

If what you meant to ask is whether the .length property is calculated from scratch by counting the array elements every time, that is definitely NOT how it works. It is an internal property of the Array object that is maintained as the array is modified. Accessing the .length property, just retrieves that internal property value. If that's what you meant by cached, then yes it is cached.

There also may be specific circumstances where the optimizing compiler can be sure that your array is not being modified (such as a for loop iterating the array with only local code that does not modify the array) where the compiler itself may cache the .length property outside of the array (but apparently that is not what you meant to ask about).

I don't understand why it worked at all initially, but the solution was to fix the crate_type option so that I'm producing both C ABI libraries and native Rust libraries.