4.4 Demonstration of the Equivalence

Concerning the demonstrating method for p iff q (p <=> q), p implies q is demonstrated first, then q implies p is demonstrated. The system automatically interprets p iff q as p implies q & q implies p. Therefore, if we state that p implies q, the first half is considered to be demonstrated. The rest is the other half's demonstration. As a result, with assume q, it becomes thus p and it is judged that p iff q is said.


     p iff q
        proof
          assume p;
          ···
          thus q;　p => q could be said
          assume q;
          ···
          thus p;　q => p can be said and p <=> q
        end: