Object

at.logic.gapt.proofs.lk

ExistsRightBlock

Related Doc: package lk

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object ExistsRightBlock

Source
macroRules.scala
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  1. final def !=(arg0: Any): Boolean

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  2. final def ##(): Int

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  3. final def ==(arg0: Any): Boolean

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  4. def apply(subProof: LKProof, main: HOLFormula, terms: Seq[LambdaExpression]): LKProof

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    Applies the ExistsRight-rule n times.

    Applies the ExistsRight-rule n times. This method expects a formula main with a quantifier block, and a proof s1 which has a fully instantiated version of main on the right side of its bottommost sequent.

    The rule:

                   (π)
     Γ :- Δ, A[x1\term1,...,xN\termN]
    ---------------------------------- (∀_l x n)
          Γ :- Δ, ∃ x1,..,xN.A
    

    subProof

    The top proof with (Γ :- Δ, A[x1\term1,...,xN\termN]) as the bottommost sequent.

    main

    A formula of the form (∃ x1,...,xN.A).

    terms

    The list of terms with which to instantiate main. The caller of this method has to ensure the correctness of these terms, and, specifically, that A[x1\term1,...,xN\termN] indeed occurs at the bottom of the proof π.

  5. final def asInstanceOf[T0]: T0

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  6. def clone(): AnyRef

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  7. final def eq(arg0: AnyRef): Boolean

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  8. def equals(arg0: Any): Boolean

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  9. def finalize(): Unit

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  10. final def getClass(): Class[_]

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  11. def hashCode(): Int

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  12. final def isInstanceOf[T0]: Boolean

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  13. final def ne(arg0: AnyRef): Boolean

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  14. final def notify(): Unit

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  15. final def notifyAll(): Unit

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  16. final def synchronized[T0](arg0: ⇒ T0): T0

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  17. def toString(): String

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  18. final def wait(): Unit

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  19. final def wait(arg0: Long, arg1: Int): Unit

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  20. final def wait(arg0: Long): Unit

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  21. def withOccConnector(subProof: LKProof, main: HOLFormula, terms: Seq[LambdaExpression]): (LKProof, OccConnector[HOLFormula])

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    Applies the ExistsRight-rule n times.

    Applies the ExistsRight-rule n times. This method expects a formula main with a quantifier block, and a proof s1 which has a fully instantiated version of main on the right side of its bottommost sequent.

    The rule:

                   (π)
     Γ :- Δ, A[x1\term1,...,xN\termN]
    ---------------------------------- (∀_l x n)
          Γ :- Δ, ∃ x1,..,xN.A
    

    subProof

    The top proof with (Γ :- Δ, A[x1\term1,...,xN\termN]) as the bottommost sequent.

    main

    A formula of the form (∃ x1,...,xN.A).

    terms

    The list of terms with which to instantiate main. The caller of this method has to ensure the correctness of these terms, and, specifically, that A[x1\term1,...,xN\termN] indeed occurs at the bottom of the proof π.

    returns

    A pair consisting of an LKProof and an OccConnector.

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