# Getting Lean running on your computer

Here’s an example of a simple logic proof in Lean.
It’s a proof that that if `P`

and `Q`

are propositions
(that is, true/false statements), and if `P`

is true and `P ⇒ Q`

is true, then `Q`

is true.

```
example (P Q : Prop) (h1 : P) (h2 : P → Q) : Q :=
begin
apply h2,
exact h1
end
```

The first line of the code states the theorem. Hypothesis
`h1`

is that `P`

is true, and hypothesis `h2`

is
that `P`

implies `Q`

(note that Lean uses a regular
arrow for implication rather than the more common `⇒`

sign). The conclusion, after the colon,
is that `Q`

is true. The proof is between the `begin`

and the `end`

and it’s clear that it somehow uses
both hypothesis `h1`

and hypothesis `h2`

. But
just reading the proof, it’s hard to see exactly what
is going on. We can’t learn Lean this way.

The whole point of using a theorem prover is that it makes
proofs like this *interactive*. So, before we get going,
we need to get this and other proofs running on your computer somehow.
There are several ways to do it.

## The best way: install Lean on your computer

The main advantage of this method is that, once you
have it all working, Lean will be *quick*. It will
start up instantly and it will run fast.

You will need to install Lean 3, and the Lean community tools. Instructions on how to get these things installed on your computer are here (right click and open in new tab if you don’t want to lose your place).

Once you have them, you can install the
Lean repository `formalising-mathematics-2022`

associated with this
course. Fire up your command line, navigate to the place where you want
to install the repository, and type

```
leanproject get ImperialCollegeLondon/formalising-mathematics-2022
```

Then use VS Code’s “open folder” open and open the `formalising-mathematics-2022`

directory.

## An alternative: Gitpod

You will need to set up an account in some way, but it is possible to access the course repository using Gitpod.

Right click here and “open link in new tab” to access the repository using Gitpod.

It takes longer to fire up, and I’ve had problems with some browsers, but I’ve got it working with Chrome. The disadvantages of this method: you are not able to save your work, you are not able to create your own projects, and I believe there is some time limit for the amount that you can use gitpod for free. However if you are just dabbling then this might be the solution for you.