Lambda the Ultimate

I'm student thesis, and i'm interested in proofs of the following :
Show tha the functor F presrves pullback ????

F = Ox(1+_) : Set to Set
Where :
O is an arbitrairy Set
Set : category of set.

Thank you very much in advance

I'm a bit nervous to be posting here, but I am interested in feedback from the many bright minds that visit here regarding an idea I've been considering for a while:
Here is my official blog posting on the subject

The essence is this:
"Under Condition Propagation missing information is explicitly noted and antecedently avoided. Rather than extend logic systems or stop execution at run time, the compiler in-effect ensures that expressions are never evaluated that do not satisfy the conditions. The logical implications of this are significant. Unlike null-like solutions, operators, and thus truth-tables, remain logically unaffected by the missing information. For example, the AND truth table remains in it's traditional, four entry, form. Each primitive operator may publish compiler meta-data regarding the conditions under which the operator is able to operate. With this information the compiler ensures that any conditions are resolved prior to evaluation. The compiler also propagates the condition meta-data to allow the developer to choose at what point prior to evaluation to resolve the condition. Logic, arithmetic, relational and other operations can all be defined in their true logical form, unaware of missing information because they will never be requested to deal with it."