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Proof in predicate calculus 2

  1. Nov 2, 2011 #1

    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]
  2. jcsd
  3. Nov 2, 2011 #2


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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?
  4. Nov 2, 2011 #3
    That is a completely different problem.

    No, no any answer yet.
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