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## Main Question or Discussion Point

Let:

1)P be one place operation

2)K be one place operation

3) c be a constant

let :

1) G be a two place predicate

2) H be a two place predicate

Let :

The following axioms or assumptions)

1)for all A { H(A,c)v H(c,A)v G(A,c)}

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

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

4)for all A {G[K(A),c] => G(A,c)}.

5)for all A,B,C { [G(A,B) and G(A,C)]=> G(B,C)}

Then formally prove :

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

1)P be one place operation

2)K be one place operation

3) c be a constant

let :

1) G be a two place predicate

2) H be a two place predicate

Let :

The following axioms or assumptions)

1)for all A { H(A,c)v H(c,A)v G(A,c)}

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

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

4)for all A {G[K(A),c] => G(A,c)}.

5)for all A,B,C { [G(A,B) and G(A,C)]=> G(B,C)}

Then formally prove :

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