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Indirect Proof

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In order to show that a premise $ V$ implies an assertion $ B$ ( $ V \Longrightarrow B$), one can deduce a contradiction by assuming that $ V$ is true while $ B$ is false, which then implies a false statement $ F$, particularly with $ F = \lnot V$ or $ F=B$:

$\displaystyle V\land(\lnot B)\,\Longrightarrow\,F \,, $

In particular, we note that the equivalences

$\displaystyle B = (\lnot B \Longrightarrow F) \,=\,(\lnot B\Rightarrow B) $

hold if no premises are made.
(Authors: Höllig/Knesch/Apprich/Abele)

Example:

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  automatically generated 9/18/2007