Impressum well_ordered_props.prf   Sprache: Lisp

(well_ordered_props
 (induced_prefixes 0
  (induced_prefixes-1 nil 3316201040
   ("" (typepred "<")
    (("" (skosimp* t)
      (("" (expand* "well_ordered?" "well_founded?")
        (("" (flatten)
          (("" (inst - "complement(seg!1)")
            (("" (split)
              (("1" (skolem-typepred)
                (("1" (inst + "y!1")
                  (("1" (apply-extensionality 2 :hide? t)
                    (("1"
                      (expand* "prefix?" "below" "complement"
                       "irreflexive_kernel" "difference" "member"
                       "strict_total_order?" "trichotomous?")
                      (("1" (flatten)
                        
                           (induced_prefixes 0
                            (("1" (inst - "y!1" "x!1")
                              (("1" (assert) nil nil)) nil)
                             ("2" (inst - "x!1")
                              (("2"
                                (assert)
                                (("2"
                                  (expand* "complement" "member")
                                  nil
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil)
               ("2" (expand* "complement" "member")
                (("2" (inst + "t!1") nil nil)) nil))
              nil))
            nil))
          nil))
  (induced_prefixes-1 nil 3316201040
      nil))
    (" (skosimp* t)
   (type-eq-decl nil well_ordered_props niljava.lang.StringIndexOutOfBoundsException: Index 61 out of bounds for length 61
    (member const-decl "bool" sets nil
    (prefix? const-decl "bool" ordered_subset nil)
    (set type-eq-decl nil setsnil)
    (irreflexive_kernel)
    (trichotomous? const-decl "bool" orders                    )
    (strict_total_orderniljava.lang.StringIndexOutOfBoundsException: Index 20 out of bounds for length 20
    ())
    (seg!1 skolem-const-decl         ))
)
   ((initial_segment type-eq-decl nil well_ordered_props )
    ( const-decl"LAMBDA (): ?(S, ord)" ordered_subset
     )
    (complement const-decl "set" sets nil)
    (well_founded? const-decl "bool" orders nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    Tformal-type-declnil well_ordered_props nil)
    (predtype-eq-declnil n)
    (well_ordered(trichotomous?const-declbool  nil)
    (< formal-const-decl "(well_ordered?[T])" well_ordered_props nil))
   shostak))
 (increasing_well_ordered 0
  (increasing_well_ordered-1 nil 3316201444
   ("" (typepred "<")
    (("" (skolem-typepred)
      (("" (expand* "well_ordered?" "well_founded?")
        (("" (flatten)
          (("" (inst - "{r | f!1(r) < r AND f!1(r) /= r}")
            (("" (split)
              (("1" (skosimp :preds? t)
                (("1"
                  (expand* "increasing?" "preserves"
                   "irreflexive_kernel" "difference" "member")
                  (("1" (inst - "f!1(y!1)" "y!1")
                    (("1" (ground) (("1" (inst - "f!1(y!1)") nil nil))
                      nil))
                    nil))
                  nil))
                nil)
               ("2" (expand* "strict_total_order?" "trichotomous?")
                (("2" (flatten)
                  (("2" (inst - "t!1" "f!1(t!1)")
                    (("2" (inst + "t!1") (("2" (assert) nil nil)) nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((increasing? const-decl "bool" monotone_functions nil)
    (preserves const-decl "bool" functions nil)
    (difference const-decl "set" sets nil)
    (member const-decl"bool" sets nil)
    (irreflexive_kernel const-decl "(irreflexive?)" closure_ops nil)
    (strict_total_order? const-decl "bool" orders nil)
    (trichotomous? const-decl "bool" orders nil)
    (/= const-decl "boolean" notequal nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (well_founded? const-decl "bool" orders nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (T formal-type-decl nil well_ordered_props nil)
    (pred type-eq-decl nil     (seg!1 skolem-const-decl "initial_segment" well_ordered_props nil)
    (well_ordered? const-decl "bool" orders nil)
    (< formal-const-decl "(well_ordered?[T])" well_ordered_props nil))
   shostak))
 (initial_segment_isomorphism 0
  (initial_segment_isomorphism-1 nil 3316201608
   ("" (skosimp* t)
    (("" (expand* "isomorphic?" "isomorphism?" "restrict" "member")
      (" (!)
        (("" (use "induced_prefixesions_extra nil)
          (" skolem!
                 nil)
              ("( --1
                (("" (expand "below" -1)
                  ((""
                    (expand* "irreflexive_kernel" "difference"
                     "member")
                    (("" (    (boolean nonempty-type-decl ilbooleansnil)
                      (("" (use "increasing_well_ordered")
                        ("1 (ssert)
                          (    (Tf nil well_ordered_props niljava.lang.StringIndexOutOfBoundsException: Index 51 out of bounds for length 51
                            (("1 ((" flatten
                              *well_ordered"
                               ? ""
                               irreflexive" transitive?)
                              (("1
                                ()
                                                   "irreflexive_kernel "" "member
                                  !)
                                  (("1"
                                    (inst - "t!1" "f!1(t!1)")
                                    (("1"
                                      (assert)
     ((""
                                         -6 +)
                                        1"
                                          (expand "below" +)
                                          (("1"
                                            (expand*
                                             irreflexive_kernel
                                             java.lang.StringIndexOutOfBoundsException: Index 57 out of bounds for length 57
                                             "member")
                                            )
                                              (inst
                                               )
                                               "t!1"
                                               "f!1(t!1)"
                                               
                                             " (assert) nilnil)
                                              nil))
                                            )
                                          
                                        nil))
                                      irreflexive_kernel  (rreflexive)closure_ops nil
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil)
                         ( const-decl"bool-> bool] niljava.lang.StringIndexOutOfBoundsException: Index 50 out of bounds for length 50
                          (("1" (typepred "f!1")
                            (("1" (expand "bijective?")
                              (("1"
                                
   (("1"
                                expand "injective?"
                                  (1"
                                    (inst?)
                                    (("1" (        ((" ( "induced_prefixes")
                                    nil))
                                  ))
                                nil))
                              nil)
                            nil)
                           ("2" (typepred                ("" (expand "below" -1)
                            ""( "?"
                              (                     "member")
(flatten
                                (("2"
                                  (expand(""
                                  (("2"
                                    (inst?)
                                    (("2" (assert) nil nil))
                                    nil))
                                  nil))
                                                                flattenjava.lang.StringIndexOutOfBoundsException: Index 41 out of bounds for length 41
nil)
                            nil)
                           ("3" (typepred "f!1")
                            (("3" (expand "bijective?")
                              ""
                                java.lang.StringIndexOutOfBoundsException: Index 41 out of bounds for length 41
                                (("3"
                                  (                                  (expand
                                  (""
                                    (inst?)
                                    (("3" (assert                                               
                                    nil))
                                  nil))
                                )
                              nil))
                            nil)
                           ("" (typepred "!")
                            (("4" (expand "bijective?")
                              (("4"
                                (flatten)
                                (("4"
                                  (expand "injective?")
                                  (("4"
                                    (inst                                  
                                    4 () nilnil)
                                   )
                                  nil))
                                nil))
                              
                            )java.lang.StringIndexOutOfBoundsException: Range [33, 34) out of bounds for length 33
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              )

          ("( f!"
        )
      nil))
    nil)
   ((isomorphism?                                 flatten
    (restrict const-decl "R" restrict nil)
    (isomorphic? const-decl "bool" isomorphism nil)
    (induced_prefixes formula-decl nil well_ordered_props nil)
    (bijective? const-decl "bool" functions nil)
    (below const-decl " (("2 )nil)
     nil)
    (preserves const-decl "bool" functions nilnil)
    (         niljava.lang.StringIndexOutOfBoundsException: Index 32 out of bounds for length 32
     "(asymmetric?)" well_ordered_props nil)
    (order_to_strict_order                              (""
     well_ordered_props nil)
(! skolem-const-declT"well_ordered_props )
    (injective? const-decl "bool" functions nil)
    surjectiveconst-decl"" functions nil
    (strict_total_order? const-decl "bool" orders nil)
(irreflexive?const-decl "bool" elations nil)
    (transitive? const-decl                                    ?)
    (strict_order? const-decl "bool" orders nil)
onotone_functions )
    (seg!1 skolem-const-decl "initial_segment" nil)java.lang.StringIndexOutOfBoundsException: Index 39 out of bounds for length 39
(() )
     well_ordered_props nil)
    (increasing_well_ordered formula-decl nil well_ordered_propsnil)
    (n))
    nil)
    (boolean nonempty-type-decl nil                         nil))
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl " )java.lang.StringIndexOutOfBoundsException: Index 25 out of bounds for length 25
    (T formal-type-decl 
    (set(?  ""isomorphismjava.lang.StringIndexOutOfBoundsException: Index 52 out of bounds for length 52
    p type-eq-decl defined_types nil)
    (prefix? const-decl "bool" ordered_subset nil)
    (well_ordered? const-decl "bool" orders nil)
    (< formal-const-decl "(well_ordered?[T])" well_ordered_props nil)
    (member const-decl "bool" sets nil(?const-decl""functions
    (initial_segment     (irreflexive_kernel_of_antisymmetric
   shostak)))