Given :(adsbygoogle = window.adsbygoogle || []).push({});

a)

1) c is a constant

2) P and K are one place operation symbols

3) G and H are a two place predicate symbols

b)

The following hypothesis

1)for all A { G(A,A) }

2) for all A,B { H(A,c) =>( G[P(A),B] <=> ( G[K(B),A] and H(B,c)))}

Then prove :

1) for all A { H(A,c) => G[K(P(A),A] }

2) for all A { H(A,c) => H( P(A),c) }

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# Proof in predicate calculus

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