README: refactor description of running the demo

README.md

@@ -63,10 +63,9 @@ When you have Nix installed on your system, you can get access to all necessary
 ```shell
 nix-shell
 ```
-Alternatively, the demo can be compiled and run directly using
+Alternatively, the demo can be compiled locally to [./result/bin](./result/bin):
 ```shell
 nix-build
-./result/bin/Vatras
 ```
 
 #### Alternative 2: Setup via Docker
@@ -90,11 +89,6 @@ docker images
 ```
 and checking that an image called `vatras` is listed.
 
-You can then run the demo by running the image:
-
-```shell
-docker run -t vatras
-```
 
 #### Alternative 3: Manual Setup
 
@@ -133,6 +127,10 @@ Following the [Agda book's installation instructions], we recommend using [GHCup
 In case of confusion or trouble, we recommend to check the [official installation instructions](https://agda.readthedocs.io/en/v2.6.4.3/getting-started/installation.html), or follow the Getting-Started guide in the [Programming Language Foundations in Agda][plfa] book, or use the Nix setup.
 
 ### Compiling the Library and Running the Demo
+> The following three alternatives depend on the setup you have chosen above. Please make sure to use the instructions meant for your setup. 
+
+#### Running the demo in a `nix-shell` or after a `manual setup`. 
+If you set up the environment using `nix-shell` or a `manually`, you can compile and run the demo using `make`. 
 
 To test whether your setup is correct, and to run the demo you may use our makefile (except for the docker setup which requires to run the image as explained above).
 Make sure your terminal is in full-screen because the demo assumes to have at least 100 characters of horizontal space in the terminal for pretty-printing.
@@ -142,10 +140,21 @@ Then run
 make
 ```
 which will compile the library and run its small demo.
-Alternatively, you may use `nix-build` as explained above.
 The demo will then print a range of translations of variational expressions to the terminal.
 The expected output is explained in detail in the Step-by-Step guide below.
 
+#### Running the demo after `nix-build`
+If you already build the library locally with `nix-build`, you should run the demo's binary directly instead of using `make`.
+```shell
+./result/bin/Vatras
+```
+
+#### Running the demo with Docker
+You can then run the demo by running the Docker image that you created during the setup:
+```shell
+docker run -t vatras
+```
+
 ## Step-by-Step Guide
 
 The "Kick-The-Tires" section above basically explains all necessary steps to get the library up and running.