Proof in predicate calculus 2

  • Thread starter solakis
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  • #1
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Let:

1) P be one place operation

2) H be two place operation

3) G be two place predicate

4) k, m be two constants


Let :

The following assumptions :

1) [itex]\forall x [\neg G(x,k)\Longrightarrow G[H(P(x),x),m]][/itex]



2)[itex]\forall x\forall y\forall z[G(x,y)\Longrightarrow G[H(z,x),H(z,y)]][/itex]

3)[itex]\forall x\forall y\forall z [G(x,y)\wedge G(y,z)\Longrightarrow G(x,z)][/itex]

4)[itex]\forall x\forall y [G(x,y)\Longrightarrow G(y,x)][/itex]

5)[itex]\forall x\forall y [G[H(x,y),H(y,x)]][/itex]

6)[itex]\forall x[ G[H(x,m),m]][/itex]

Then formally prove that:

Then formally prove : [itex]\forall x\forall y\forall z[\neg G(x,k)\Longrightarrow(G[H(x,y),H(x,z)]\Longrightarrow G(y,z))][/itex]
 

Answers and Replies

  • #2
CompuChip
Science Advisor
Homework Helper
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That's the same one as here, luckily you've formatted it a bit better this time (Y).

Any progress on the answer?
 
  • #3
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That's the same one as here, luckily you've formatted it a bit better this time (Y).

Any progress on the answer?
That is a completely different problem.

No, no any answer yet.
 

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