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gapt.proofs.lk.rules.macros

ForallLeftBlock

object ForallLeftBlock

Source
ForallLeftBlock.scala
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  1. final def !=(arg0: Any): Boolean
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  2. final def ##: Int
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  4. def apply(subProof: LKProof, main: Formula, terms: Seq[Expr]): LKProof

    Applies the ForallLeft-rule n times.

    Applies the ForallLeft-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 left side of its bottommost sequent.

    The rule:

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

    subProof

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

    main

    A formula of the form (Forall 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.

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  19. final def wait(): Unit
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  20. def withSequentConnector(subProof: LKProof, main: Formula, terms: Seq[Expr]): (LKProof, SequentConnector)

    Applies the ForallLeft-rule n times.

    Applies the ForallLeft-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 left side of its bottommost sequent.

    The rule:

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

    subProof

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

    main

    A formula of the form (Forall 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 SequentConnector.

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