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at.logic.gapt.examples

UniformAssociativity3ExampleProof

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object UniformAssociativity3ExampleProof extends ProofSequence

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  1. UniformAssociativity3ExampleProof
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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. val Ax1: FOLFormula

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  5. val Cs: FOLFormula

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  6. val Symm: FOLFormula

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  7. val Trans: FOLFormula

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  8. def addAllAxioms(proof: LKProof): LKProof

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  9. def apply(n: Int): LKProof

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  10. def apply_conditional_equality(equalities: List[FOLFormula], result: FOLFormula, p: LKProof): LKProof

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  11. final def asInstanceOf[T0]: T0

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  12. def ax2_ax(x: FOLTerm, y: FOLTerm): FOLFormula

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  13. def ax2_ax(x: FOLTerm): FOLFormula

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  14. def ax2_ax(): FOLFormula

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  15. def clone(): AnyRef

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    protected[java.lang]
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    @throws( ... )
  16. val cp: AllQuantifiedConditionalAxiomHelper

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  17. def cs_ax(x: FOLTerm, y: FOLTerm): FOLFormula

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  18. def cs_ax(x: FOLTerm): FOLFormula

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  19. def cs_ax(): FOLFormula

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

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  21. def equals(arg0: Any): Boolean

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  22. def f1(sym: String, arg: FOLTerm): FOLTerm

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  23. def f2(arg1: FOLTerm, sym: String, arg2: FOLTerm): FOLTerm

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  24. def f2(sym: String, arg1: FOLTerm, arg2: FOLTerm): FOLTerm

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  25. def finalize(): Unit

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    @throws( classOf[java.lang.Throwable] )
  26. def gen_proof_step(i: Int, n: Int): LKProof

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    * 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 |- ...

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

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  28. def hashCode(): Int

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  29. def induction_start(n: Int, p0: LKProof): LKProof

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

  30. final def isInstanceOf[T0]: Boolean

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  31. def name: String

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    ProofSequence
  32. final def ne(arg0: AnyRef): Boolean

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  33. final def notify(): Unit

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  34. final def notifyAll(): Unit

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  35. val p: String

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  36. def refl_ax(x: FOLTerm, y: FOLTerm): FOLFormula

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  37. def refl_ax(x: FOLTerm): FOLFormula

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  38. def refl_ax(): FOLFormula

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  39. def reflect(x: FOLTerm, y: FOLTerm, p: LKProof): LKProof

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    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), ... |- ...

  40. val s: String

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  41. def show_by_ax2(x: FOLTerm, y: FOLTerm, p: LKProof): LKProof

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  42. def show_by_cs(x: FOLTerm, y: FOLTerm, p: LKProof): LKProof

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

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  44. def toString(): String

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  45. final def wait(): Unit

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    @throws( ... )
  46. final def wait(arg0: Long, arg1: Int): Unit

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    @throws( ... )
  47. final def wait(arg0: Long): Unit

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  48. val x: FOLVar

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  49. val x1: FOLVar

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  50. val x2: FOLVar

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  51. val y: FOLVar

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  52. val y1: FOLVar

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  53. val y2: FOLVar

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  54. val z: FOLVar

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Inherited from ProofSequence

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