lean | Lean Theorem Prover | Interpreter library

I have a simple interface setter:

I am trying to increment the number in MongoDB using mongoose. But I start failing right at the query stage. When I // @ts-ignore it flows silently with no error but the value doesn't update.

The error it throws out is: Type 'number' is not assignable to type 'undefined'

My Schema:

I have a pretty basic construction of loops in mind for lean. I construct a class for magmata, a class for quasigroups (cancellative magmata), and a class for unital magmata. From there a loop is just something that is both a quasigroup and a unital magma.

In Haskell this would look like

The lidR package has a neat way to work with huge (pointcloud) datasets: The catalog function (doc here) avoids loading the dataset to memory and can treat mosaics [datasets that are spread across multiple (non-overlapping) tiles] as single dataset. It loads required tiles on-the-fly during computations in an intelligent way. It is great to avoid working with huge files (multiple GBs) and keep memory requirements lean if only working with small parts of the dataset.

Is there a similar convenient/memory-efficient/"lidR-catalog-way" to process large raster mosaics in R? Or more put in a more general way: Is there a way to work with mosaic raster datasets in R without merging them first?

I am aware of the mosaic (doc) and merge functions, which allow me to merge my tiled raster mosaic into a single raster dataset. I also found that gdal will do so a lot faster and memory efficient. Here is a R-snippet for this:

I've noticed React Router DOM (v6) is now using functions in their help guides in regards to pages instead of using classes.

Previously used classes like so:

Symbolic calculations performed manually or by a computer algebra system may be faulty or hold only subject to certain assumptions. A classical example is sqrt(x^2) == x which is not true in general but it does hold if x is real and non-negative.

Are there examples where proof assistants/checkers such as Coq, Isabelle, HOL, Metamath, or others are used to certify correctness of symbolic calculations? In particular, I am interested in calculus and linear algebra examples such as solving definite or indefinite integrals, differential equations, and matrix equations.

Update: To be more concrete, it would be interesting to know whether there are examples of undergraduate assignments in calculus and linear algebra that could be formally solved (possibly with the help of a proof assistant) such that the solution can be automatically verified by a proof checker. A very simple example assignment for Lean is here.

Since around 2 weeks ago, my console filter starts to filter out even matching text. Tried restarting, is currently on the latest chrome version, also tried to restore settings, nothing. Searched on the web too didn't really find anything similar... I am banging my head against the wall right now if anyone has a lead, please... (Apparently one of my coworkers also starts to have this issue recently... )

Edit1: So played with a couple versions of chrome more. I am current on 95.0.4638.69. Tried beta version 96.x, same issue. Tried chromium 94.x, it works all fine! Haven't got a chance to try chrome 94.x as I dont' want to uninstall my chrome yet. But yeah I am leaning towards that the 95.x updates may break it, though I haven't seen any official info regarding it.

In lean, there exists a notation for the summation sign (Σ, large Sigma) to write sums with many terms. Sadly, neither the mathlib documentation nor the reference manual seem to provide much information about how it can be used.

What imports are required in order to use it, and how do you write sums with it?

For example, how would you write the theorem that the first n natural numbers add up to n * (n + 1) / 2, using the summation sign?

When using the cases-tactic on an inductive data type, lean produces multiple cases, but does not create a hypothesis stating the assumption of the current case. For example: