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Diffstat (limited to 'examples/systemS/ex2eng.txt')
| -rw-r--r-- | examples/systemS/ex2eng.txt | 7 |
1 files changed, 7 insertions, 0 deletions
diff --git a/examples/systemS/ex2eng.txt b/examples/systemS/ex2eng.txt new file mode 100644 index 000000000..f1ef836ae --- /dev/null +++ b/examples/systemS/ex2eng.txt @@ -0,0 +1,7 @@ +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. |