Package

at.logic.gapt.proofs

lksk

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package lksk

Source
package.scala
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Type Members

  1. case class AllLeft(subProof: LKskProof, aux: Ant, mainFormula: HOLFormula, substitutionTerm: LambdaExpression) extends UnaryRule with SameLabel with Product with Serializable

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  2. case class AllRight(subProof: LKskProof, aux: Suc, mainFormula: HOLFormula, eigenVar: Var) extends UnaryRule with SameLabel with Product with Serializable

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  3. case class AllSkLeft(subProof: LKskProof, aux: Ant, mainFormula: HOLFormula, substitutionTerm: LambdaExpression) extends UnaryRule with Product with Serializable

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  4. case class AllSkRight(subProof: LKskProof, aux: Suc, mainFormula: HOLFormula, skolemSymbol: LambdaExpression, skolemDef: LambdaExpression) extends UnaryRule with SameLabel with Product with Serializable

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  5. case class AndLeft(subProof: LKskProof, aux1: Ant, aux2: Ant) extends UnaryRule with SameLabel with Product with Serializable

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  6. case class AndRight(subProof1: LKskProof, aux1: Suc, subProof2: LKskProof, aux2: Suc) extends BinaryRule with SameLabel with Product with Serializable

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  7. case class Axiom(antLabel: Label, sucLabel: Label, atom: HOLFormula) extends InitialSequent with Product with Serializable

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  8. trait BinaryRule extends LKskProof

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  9. case class BottomLeft(label: Label) extends InitialSequent with Product with Serializable

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  10. case class ContractionLeft(subProof: LKskProof, aux1: Ant, aux2: Ant) extends UnaryRule with Product with Serializable

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  11. case class ContractionRight(subProof: LKskProof, aux1: Suc, aux2: Suc) extends UnaryRule with Product with Serializable

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  12. case class Cut(subProof1: LKskProof, aux1: Suc, subProof2: LKskProof, aux2: Ant) extends BinaryRule with Product with Serializable

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  13. case class Equality(subProof: LKskProof, eq: Ant, aux: SequentIndex, leftToRight: Boolean, con: Abs) extends UnaryRule with SameLabel with Product with Serializable

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  14. case class ExLeft(subProof: LKskProof, aux: Ant, mainFormula: HOLFormula, eigenVar: Var) extends UnaryRule with SameLabel with Product with Serializable

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  15. case class ExRight(subProof: LKskProof, aux: Suc, mainFormula: HOLFormula, substitutionTerm: LambdaExpression) extends UnaryRule with SameLabel with Product with Serializable

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  16. case class ExSkLeft(subProof: LKskProof, aux: Ant, mainFormula: HOLFormula, skolemSymbol: LambdaExpression, skolemDef: LambdaExpression) extends UnaryRule with SameLabel with Product with Serializable

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  17. case class ExSkRight(subProof: LKskProof, aux: Suc, mainFormula: HOLFormula, substitutionTerm: LambdaExpression) extends UnaryRule with Product with Serializable

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  18. case class ImpLeft(subProof1: LKskProof, aux1: Suc, subProof2: LKskProof, aux2: Ant) extends BinaryRule with SameLabel with Product with Serializable

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  19. case class ImpRight(subProof: LKskProof, aux1: Ant, aux2: Suc) extends UnaryRule with SameLabel with Product with Serializable

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  20. trait InitialSequent extends LKskProof

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  21. trait LKskProof extends SequentProof[LabelledFormula, LKskProof] with ContextRule[LabelledFormula, LKskProof]

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  22. case class NegLeft(subProof: LKskProof, aux: Suc) extends UnaryRule with SameLabel with Product with Serializable

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  23. case class NegRight(subProof: LKskProof, aux: Ant) extends UnaryRule with SameLabel with Product with Serializable

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  24. case class OrLeft(subProof1: LKskProof, aux1: Ant, subProof2: LKskProof, aux2: Ant) extends BinaryRule with SameLabel with Product with Serializable

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  25. case class OrRight(subProof: LKskProof, aux1: Suc, aux2: Suc) extends UnaryRule with SameLabel with Product with Serializable

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  26. case class Reflexivity(label: Label, term: LambdaExpression) extends InitialSequent with Product with Serializable

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  27. trait SameLabel extends LKskProof

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  28. case class TopRight(label: Label) extends InitialSequent with Product with Serializable

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  29. trait UnaryRule extends LKskProof

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  30. case class WeakeningLeft(subProof: LKskProof, weakLabelledFormula: LabelledFormula) extends UnaryRule with Product with Serializable

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  31. case class WeakeningRight(subProof: LKskProof, weakLabelledFormula: LabelledFormula) extends UnaryRule with Product with Serializable

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Value Members

  1. object LKskProof

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  2. object LKskToExpansionProof

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  3. object applySubstitution

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  4. implicit val lkskClosedUnderSubst: ClosedUnderSub[LKskProof]

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