Object

at.logic.gapt.proofs.lk

ForallRightRule

Related Doc: package lk

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object ForallRightRule extends StrongRuleHelper

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  1. ForallRightRule
  2. StrongRuleHelper
  3. QuantifierRuleHelper
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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(s1: OccSequent, term1oc: FormulaOccurrence, main: HOLFormula, eigen_var: Var): Sequent[FormulaOccurrence]

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    Constructs a proof ending with a ForallRight rule.
    This function merely returns the resulting sequent, not a proof.
    
    The rule:
      (rest of s1)
     sL |- sR, A[y/x]
    -------------------- (ForallRight)
    sL |- sR, Forall x.A
    

    Constructs a proof ending with a ForallRight rule.
    This function merely returns the resulting sequent, not a proof.
    
    The rule:
      (rest of s1)
     sL |- sR, A[y/x]
    -------------------- (ForallRight)
    sL |- sR, Forall x.A
    

    s1

    The sequent (sL |- sR, A[y/x]).

    term1oc

    The formula A[y/x], in which a free variable y is to be all-quantified.

    main

    The resulting (Forall x.A), with some (not necessarily all) instances of the free variable eigen_var replaced by a newly introduced variable.

    eigen_var

    The eigenvariable to be all-quantified & whose substitution into the main formula yields the auxiliary formula.

    returns

    The sequent (sL |- sR, Forall x.A).

  5. def apply(s1: LKProof, aux: HOLFormula, quantifiedVar: Var, eigenVar: Var): LKProof

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  6. def apply(s1: LKProof, term1oc: FormulaOccurrence, main: HOLFormula, eigen_var: Var): LKProof

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    Constructs a proof ending with a ForallRight rule.
    
    The rule:
      (rest of s1)
     sL |- sR, A[y/x]
    -------------------- (ForallRight)
    sL |- sR, Forall x.A
    

    Constructs a proof ending with a ForallRight rule.
    
    The rule:
      (rest of s1)
     sL |- sR, A[y/x]
    -------------------- (ForallRight)
    sL |- sR, Forall x.A
    

    s1

    The top proof with (sL |- sR, A[y/x]) as the bottommost sequent.

    term1oc

    The occurrence of the formula A[y/x], in which a free variable y is to be all-quantified.

    main

    The resulting (Forall x.A), with some (not necessarily all) instances of the free variable eigen_var replaced by a newly introduced variable.

    eigen_var

    The eigenvariable to be all-quantified & whose substitution into the main formula yields the auxiliary formula.

    returns

    An LK Proof ending with the new inference.

  7. def apply(s1: LKProof, aux: HOLFormula, main: HOLFormula, eigen_var: Var): LKProof

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    Constructs a proof ending with a ForallRight rule.
    
    The rule:
      (rest of s1)
     sL |- sR, A[y/x]
    -------------------- (ForallRight)
    sL |- sR, Forall x.A
    

    Constructs a proof ending with a ForallRight rule.
    
    The rule:
      (rest of s1)
     sL |- sR, A[y/x]
    -------------------- (ForallRight)
    sL |- sR, Forall x.A
    

    s1

    The top proof with (sL |- sR, A[y/x]) as the bottommost sequent.

    aux

    The formula A[y/x], in which a free variable y is to be all-quantified.

    main

    The resulting (Forall x.A), with some (not necessarily all) instances of the free variable eigen_var replaced by a newly introduced variable.

    eigen_var

    The eigenvariable to be all-quantified & whose substitution into the main formula yields the auxiliary formula.

    returns

    An LK Proof ending with the new inference.

  8. final def asInstanceOf[T0]: T0

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  9. def clone(): AnyRef

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

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  11. def equals(arg0: Any): Boolean

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  12. def finalize(): Unit

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

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  14. def hashCode(): Int

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  15. final def isInstanceOf[T0]: Boolean

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

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  17. final def notify(): Unit

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  18. final def notifyAll(): Unit

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

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  20. def toString(): String

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  21. def unapply(proof: LKProof): Option[(LKProof, OccSequent, FormulaOccurrence, FormulaOccurrence, Var)]

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  22. final def wait(): Unit

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

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

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Inherited from StrongRuleHelper

Inherited from QuantifierRuleHelper

Inherited from AnyRef

Inherited from Any

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