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Thread: Induction to prove WFF

  1. #1
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    Induction to prove WFF

    Let A and B be formula and p be a variable, prove with induction that A[p:=B] is a well-formed formula

    i'm struggling with this question, i'm not sure about how to use the proper syntax in the proof I was hoping someone could point me in the right direction on where to start
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  2. #2
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    Re: Induction to prove WFF

    Since you are trying to prove that something is a "WFF", start with the definition of "well formed formula". What definition are you using?
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  3. #3
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    Re: Induction to prove WFF

    A word A is well-formed if and only if it is the last word of a formula calculation. Am I allowed to assume that A and B in the question are WFF themselves?
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  4. #4
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    Re: Induction to prove WFF

    If A is well-formed and I replaced every variable "p" in A with B, and B is well-formed, then it would make sense the new formula is well-formed but I have no idea how to write that out as an induction proof, i've only done those with numbers
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