Assertions allows you to configure the assertion checking levels for your project. This means that any assertion type marked True in the Assertions table will be checked at runtime. So, in the example screen shown below, only preconditions (denoted in the table by Require) will be checked at runtime. All other assertion types will not be checked at runtime.
Each assertion setting can be configured independently of the others.
Supplier Precondition is a special case. When you develop new software, your software reuses libraries of existing software from other sources, such as the Eiffel Libraries. This library software is often well-established and highly reliable. Setting Supplier Precondition to True is a convenient way of setting only precondition checking on libraries, while allowing your own software to be checked to whatever degree you've determined by adjusting the other assertion level settings.