README.md: add a short tutorial

README.md

@@ -10,6 +10,37 @@ This is a work in progress, this library barely works at the moment.
 Once I go over the most pressing [TODO] items,
 I will remove this notice and release it on PyPI.
 
+The usual drill in unit testing involves making assertions
+about specific input-output cases of functions, such as:
+
+```py
+assertEqual(sorted([4,2,1,3]), [1,2,3,4])
+```
+
+There are no arguments to the unit test.
+
+In property-based testing (with LeanCheck)
+one writes more general properties that should be true
+for a given set of arguments.
+
+For example:
+given __any__ list, sorting it twice is the same as sorting it once.
+We can encode this as a function returning a boolean value:
+
+```py
+def prop_sorted_twice(xs: list[int]) -> bool:
+    return sorted(sorted(xs)) == sorted(xs)
+```
+
+For whatever list we provide this function,
+it should return `True`.
+Now one can use LeanCheck to verify this automatically:
+
+```
+>>> check(prop_sorted_twice)
++++ OK, passed 360 tests: prop_sorted_twice
+```
+
 Quick Example
 -------------