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Diffstat (limited to 'old-examples/systemS/ex4eng.txt')
| -rw-r--r-- | old-examples/systemS/ex4eng.txt | 8 |
1 files changed, 8 insertions, 0 deletions
diff --git a/old-examples/systemS/ex4eng.txt b/old-examples/systemS/ex4eng.txt new file mode 100644 index 000000000..3ad4f3549 --- /dev/null +++ b/old-examples/systemS/ex4eng.txt @@ -0,0 +1,8 @@ +We will show that (A -> B) v (B -> A). +To that end, we will assume ~ ((A -> B) v (B -> A)) and show _|_. +So let us assume that ~ ((A -> B) v (B -> A)). +Then, by the first de Morgan's law, we get ~ (A -> B) & ~ (B -> A) to prove _|_. +So by splitting we get ~ (A -> B), ~ (B -> A) to prove _|_. +By implication negation, we get A, ~ (B -> A) to prove _|_. +By implication negation, we get A, ~ A to prove _|_. +Hence we get _|_ as desired. |