Definition: part object

Any object that is a whole branch (e. g. a sub-list object, main-Fib-object or sub-root-object) of a branch element is part of a part object. Furthermore, to the part object belong all root-elements, in which it is contained or which it uses for external objects. Even Fib elements, which define variables that are used in the part object, belong to it. The union of two part objects is again a part object. The complete Fib object itself is also a part object. A part object can always be evaluated to a multimedia object.

A genuine part object is a part object, that is not the (complete) Fib object itself.

A simple part object is a genuine part object, that contains only one leaf with one point object.

A coherent part object is a genuine part object that contains the whole object of one branch (subobject), of just one branch element (e. g. list element or root-element) and the required elements above it. In particular, every simple object is a coherent subobject.

To create a coherent part object, one branch element (for example list element or root-element) from the complete Fib object can be deleted and replaced by one of the subobjects contained in it. The resulting subobject must of course be correct, to be a coherent part object. (For example, if the main-Fib-object of a root-element is deleted, the result isn't a coherent part object. Also if a sub-root-element is deleted, and the next above main-Fib-object is replaced by its main-Fib-object, the domains of the replace root-element should be adapted by the next root-element.)

With figure 6 this definition is illustrated with an example of a Fib object. In the following, some examples of different types of part objects in Figure 6 are being given, for the Fib elements their numbers (from the Fib element order respectively figure 6) are given. Furthermore, it is establish that the point element with the number $10$ does not use the variable that is defined by the area element with the number $2$. All other variables are needed in the points, which are below the respective variable definitions.

Figure 6: Example object for part objects

Part objects:

• 1; 2; 4; 5
• 1; 2; 6; 7
• 1; 2; 3 (just subobjects $1$ and $2$); 4; 5; 6; 7
• 1; 9; 10
• 1; 2; 8; 9; 10; 11; 12
• 1; 2; 3 (just subobjects $1$ and $3$); 4; 5; 8; 9; 10; 11; 12
• 1; 2; 3 (just subobjects $1$ and $3$); 4; 5; 11; 12
• (all Fib elements) 1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12

Genuine part objects:

• 1; 2; 4; 5
• 1; 2; 6; 7
• 1; 2; 3 (just subobjects $1$ and $2$); 4; 5; 6; 7
• 1; 9; 10
• 1; 2; 8; 9; 10; 11; 12
• 1; 2; 3 (just subobjects $1$ and $3$); 4; 5; 8; 9; 10; 11; 12
• 1; 2; 3 (just subobjects $1$ and $3$); 4; 5; 11; 12

Simple part objects:

• 1; 2; 4; 5
• 1; 2; 6; 7
• 1; 9; 10
• 1; 2; 11; 12

Coherent part objects:

• 1; 2; 4; 5
• 1; 2; 6; 7
• 1; 9; 10
• 1; 2; 11; 12
• 1; 2; 8; 9; 10; 11; 12