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Aug 18th, 2017
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  1. \begin{center}
  2. \begin{sideways}
  3. \small\infertrue
  4. $
  5. %logical consequence
  6. \La{{{
  7. \CA F {\WHILE\ a \neq b \ \DO\ \ASS a{a+1}; \ASS b{b-1}\ \OD\ }{G}}}}
  8. %LC-Unterm Strich
  9. {F \Rightarrow {\INV\ }}
  10. %LC-Übern Strich 1. Ausdruck
  11. {\WHt{{
  12. \CA\INV{\WHILE\ a \neq b \ \DO\ \ASS a{a+1}; \ASS b{b-1}\ \OD\ }
  13. {\INV\land\lnot e}}}
  14. %Wht-Unterm Strich
  15. {\SC
  16. {\CA
  17. {\INV\land a \neq b \land t = t_0}%CA - 1.
  18. {\ASS a{a+1}; \ASS b{b-1}\ }%CA - 2.
  19. {\INV\land 0 \leq t \leq t_0}}%CA - 3.
  20. %Sequence-unterm Strich
  21. {\La{\CA{\INV\land a \neq b \land t = t_0}{\ASS a{a+1};\ }{B}}{{\INV\land a \neq b \land t = t_0} => C}{\CA{C}{\ASS a{a+1}}{B}}
  22. }
  23. %Sequence-überm Strich 1. Ausdruck
  24. {\CA{B}{\ASS b{b-1}\ }{\INV\land 0 \leq t \leq t_0}}}
  25. %Sequence-überm Strich 2. Ausdruck
  26. %Wht-Übern Strich 1. Ausdruck
  27. {}
  28. %Wht-Übern Strich 2. Ausdruck (Wird nciht gebraucht da wir wht'' verwenden)
  29. }%LC-Übern Strich 2. Ausdruck
  30. {\INV\land \neg e \Rightarrow G
  31. }
  32. %LC-Übern Strich 3. Ausdruck
  33. $
  34. \end{sideways}
  35. \end{center}
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