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This non-implication, Form 114 \( \not \Rightarrow \) Form 200, whose code is 6, is constructed around a proven non-implication as follows:

• This non-implication was constructed without the use of this first code 2/1 implication.
• A proven non-implication whose code is 5. In this case, it's Code 3: 282, Form 114 \( \not \Rightarrow \) Form 200 whose summary information is:
  

  Hypothesis	Statement
  Form 114	<p> Every A-bounded \(T_2\) topological space is weakly Loeb. (<em>\(A\)-bounded</em> means amorphous subsets are relatively compact. <em>Weakly Loeb</em> means the set of non-empty closed subsets has a multiple choice function.) </p>

  
  

  Conclusion	Statement
  Form 200	<p> For all infinite \(x\), \(|2^{x}| = |x!|\). </p>

  
  
• This non-implication was constructed without the use of this last code 2/1 implication

The conclusion Form 114 \( \not \Rightarrow \) Form 200 then follows.

Finally, the
List of models where hypothesis is true and the conclusion is false:

Name	Statement
\(\cal N1\) The Basic Fraenkel Model	The set of atoms, \(A\) is denumerable; \(\cal G\) is the group of all permutations on \(A\); and \(S\) isthe set of all finite subsets of \(A\)