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gapt.examples.sequence

UniformAssociativity3ExampleProof

object UniformAssociativity3ExampleProof extends ProofSequence

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  1. UniformAssociativity3ExampleProof
  2. ProofSequence
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Value Members

  1. final def !=(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  2. final def ##(): Int
    Definition Classes
    AnyRef → Any
  3. final def ==(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  4. val Ax1: FOLFormula
  5. val Cs: FOLFormula
  6. val Symm: FOLFormula
  7. val Trans: FOLFormula
  8. def addAllAxioms(proof: LKProof): LKProof
  9. def apply(n: Int): LKProof
  10. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  11. def ax2_ax(x: FOLTerm, y: FOLTerm): FOLFormula
  12. def ax2_ax(x: FOLTerm): FOLFormula
  13. def ax2_ax(): FOLFormula
  14. def clone(): AnyRef
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.CloneNotSupportedException]) @native()
  15. val cp: AllQuantifiedConditionalAxiomHelper
  16. def cs_ax(x: FOLTerm, y: FOLTerm): FOLFormula
  17. def cs_ax(x: FOLTerm): FOLFormula
  18. def cs_ax(): FOLFormula
  19. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  20. def equals(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef → Any
  21. def f1(sym: String, arg: FOLTerm): FOLTerm
  22. def f2(arg1: FOLTerm, sym: String, arg2: FOLTerm): FOLTerm
  23. def f2(sym: String, arg1: FOLTerm, arg2: FOLTerm): FOLTerm
  24. def finalize(): Unit
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.Throwable])
  25. def gen_proof_step(i: Int, n: Int): LKProof

    * Returns proof Pi (currently including line above and below Pi), with numerals n, i, i+1: (n + n) + i+1 = n + (n + i+1), Ax |- ...

    * Returns proof Pi (currently including line above and below Pi), with numerals n, i, i+1: (n + n) + i+1 = n + (n + i+1), Ax |- ... Pi (n + n) + i = n + (n + i), Ax |- ...

  26. final def getClass(): Class[_ <: AnyRef]
    Definition Classes
    AnyRef → Any
    Annotations
    @native()
  27. def hashCode(): Int
    Definition Classes
    AnyRef → Any
    Annotations
    @native()
  28. def induction_start(n: Int, p0: LKProof): LKProof

    Close off proof ending in (n + n) + 0 = n + (n + 0) |- ...

  29. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  30. def name: String
    Definition Classes
    ProofSequence
  31. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  32. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native()
  33. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native()
  34. val p: String
  35. def refl_ax(x: FOLTerm, y: FOLTerm): FOLFormula
  36. def refl_ax(x: FOLTerm): FOLFormula
  37. def refl_ax(): FOLFormula
  38. def reflect(x: FOLTerm, y: FOLTerm, p: LKProof): LKProof

    Takes a proof s2 with end-sequent of the form (x=y), ...

    Takes a proof s2 with end-sequent of the form (x=y), ... |- ... and return one with end-sequent of the form (y=x), ... |- ...

  39. val s: String
  40. def show_by_ax2(x: FOLTerm, y: FOLTerm, p: LKProof): LKProof
  41. def show_by_cs(x: FOLTerm, y: FOLTerm, p: LKProof): LKProof
  42. final def synchronized[T0](arg0: => T0): T0
    Definition Classes
    AnyRef
  43. def toString(): String
    Definition Classes
    AnyRef → Any
  44. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException])
  45. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException])
  46. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException]) @native()
  47. val x: FOLVar
  48. val x1: FOLVar
  49. val x2: FOLVar
  50. val y: FOLVar
  51. val y1: FOLVar
  52. val y2: FOLVar
  53. val z: FOLVar

Inherited from ProofSequence

Inherited from AnyRef

Inherited from Any

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