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Math Help - How to prove this (Ev1)(v1=v1)

  1. #1
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    How to prove this (Ev1)(v1=v1)

    I know i can represent that as ~(Av1)~(v1=v1)

    A = for all
    E= there exist.

    Is this on the right track?

    : A(v1) initial sequent note the A is a formula
    : (Av1)(A(v1))
    : ??
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  2. #2
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    Re: How to prove this (Ev1)(v1=v1)

    Could you say what proof system you are using? See this sticky thread. Is it sequent calculus?
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  3. #3
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    Re: How to prove this (Ev1)(v1=v1)

    As emakrov said, this depends on what proof system you're using.

    In one system, such a proof is simple:

    1. Ax x=x ... axiom of identity theory
    2. x=x ... universal instantiation
    3. Ex x=x ... existential generalization
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  4. #4
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    Re: How to prove this (Ev1)(v1=v1)

    sorry, i wasn't aware of that. yeah i think its sequent type using rules of inference from peanos first order arithmetic.
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  5. #5
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    Re: How to prove this (Ev1)(v1=v1)

    I am not sure what sequent type is. PA does not specify the rules of inference; it is a set of axioms. In any case, this is something very trivial and similar to post #3.
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  6. #6
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    Re: How to prove this (Ev1)(v1=v1)

    its propositional calculus where you start with an initial sequent and then use rules of inference such as introduction, elimination etc to deduce theorems. I have no idea what post 3 is
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  7. #7
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    Re: How to prove this (Ev1)(v1=v1)

    First, it's not propositional, but first-order calculus since your formulas include an existential quantifier and a binary equality predicate.

    Post numbers are locates in the Bali Hai-colored bar above each post. Post #3 is located here.

    Of various deductive system that I know, introduction and elimination occur in natural deduction. Usually ND is formulated so that derivations consist of formulas; however, there is also a sequent presentation where all open assumptions are collected in the left-hand side of sequents. In any case, MoeBlee's outline is pretty close.

    To have a precise derivation, please provide the rules of universal elimination, existential introduction and describe how equality is incorporated into the system.
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  8. #8
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    Re: How to prove this (Ev1)(v1=v1)

    Quote Originally Posted by emakarov View Post
    Post numbers are locates in the Bali Hai-colored bar above each post.
    Now THAT'S specific (and color self-referential too!)! Nicely done, emakarov... Bali Hai and talley-ho!
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