NEGATED QUANTIFIER DECOMPOSITION RULES
As an example, let’s determine the validity of the sequent:
Notice that here we applied the -∣ v rule to line 2 first, since this is a non-branching rule.
So is
but had we applied that before Ξ (which branches), then we would not have been able to apply
without either breaking the restriction on it that we cannot have used the same name previously on the same path, or using a different name, which would havegot us nowhere. The economy of the Truth Tree method can be seen by comparing the succinct 8 line tree-proof above with a rule-of-inference proof of the same sequent:1
23.1.4
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