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CS's system S

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aarne
2005-12-20 14:20:42 +00:00
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examples/systemS/ex2eng.txt Normal file
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Suppose A -> B. We will show that ~ B -> ~ A.
It is enough to assume A -> B, ~ B and show ~ A.
Thus, by rewriting ~ A we may assume A -> B, ~ B and show A -> _|_.
It is enough to assume A, A -> B, ~ B and show _|_.
Then, by Modus ponens, we get A, A -> B, B, ~ B to prove _|_.
In particular we get B, ~ B to prove _|_.
Hence we get _|_ as desired.