| Quellcodebibliothek Statistik Leitseite products/sources/formale Sprachen/PVS/orders/ (Beweissystem der NASA Version 6.0.9©) Datei vom 28.9.2014 mit Größe 34 kB |
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Quelle well_ordered_finite.prf Sprache: Lisp |
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(well_ordered_finite (nonempty_has_least 0 (nonempty_has_least-1 nil 3318621627 ("" (skolem-typepred) (("" (expand* "nonempty?" "empty?" "member") (("" (skolem!) (("" (lemma "non_empty_finite_has_least") (("" (inst - "{t | x!1(t) AND reflexive_closure(<)(t, x!2)}" "reflexive_closure(<)") (("1" (expand "has_least?") (("1" (skolem!) (("1" (inst + "t!1") (("1" (typepred "<") (("1" (grind :if-match nil) (("1" (inst -7 "r!1") (("1" (assert) nil nil) ("2" (inst - "t!1" "r!1") (("2" (inst - "r!1" "t!1" "x!2") (("2" (assert) nil nil)) nil)) nil)) nil) ("2" (inst - "r!1" "x!2") (("2" (assert) (("2" (inst -6 "r!1") (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (split) (("1" (use "finite_below") (("1" (expand "is_finite") (("1" (skolem!) (("1" (inst + "N!1 + 1" "LAMBDA (r: ({t | x!1(t) AND reflexive_closure[T](<)(t, x!2)(well_ordered_finite (("1" (expand "injective?") (("1" (skosimp :preds? t) (("1" (lift-if) (("1" (lift-if) (("1" (ground) (("1" (lift-if) (("1" (split -1) (("1" (flatten) (("1" (assert) nil nil)) nil) ("2" (flatten) (("2" (inst - "x1!1" "x2!1") (("2 ( nil 318217 nil)) nil) nil)) ) (" (kolem) nil)) nil) nil inst-"t|x1t reflexive_closure<)t,x2}" nil) skosimp(""() nil)nil ("3" (skosimp :preds? t) (("3" (expand below "eflexive_closure""" "irreflexive_kernel" "difference" "member") (3 assertnil nil)nil) nil)) )) nil)) nil)) nil) ("2" (expand* "reflexive_closure" "union" "empty?" "member") ((" (1 assert nilniljava.lang.StringIndexOutOfBoundsExcep nil)) nil)) nil)) nil)) nil("2 inst r1""!" nil ((empty? const-decl (""( - r1) (member const-decl "bool" sets(" assert ) niljava.lang.StringIndexOutOfBoundsException: Index 31 out of bounds for length (nnint_plus_posint_is_posint ) integers (1( finite_below (orderconst-decl ""relations_extra ) (prefix? const-decl "bool" ordered_subset nil) (below const-decl "(java.lang.StringIndexOutOfBoundsException: Index 26 out of bou ) (f!1 skolem-const-decl "[(below(x!2, <)) -> below[N!1]]" well_ordered_finite nil) (below type-eq-decl nil nat_types nil) (N ((1"( injective"java.lang.StringIndexOutOfBoundsException: Index 49 out of bou n nonempty-type-eq-decl nil) "1 lift-if) ( nonempty-type-eq-decl integers ) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) ) (rational_pred const-decl"[ > boolean] rationals niljava.lang.StringIndexOutOfBou ( nonempty-type-eq-decl nil) (< const-decl "bool" reals nil) (real nonempty-type-from-decl nil reals nil) (real_predconst-decl "number_field >] nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl " () nil (number nonempty-type-decl nil numbers nil) (IF const-decl "[boolean, T, T -> T]" if_def nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (injectivenil)) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (irreflexive_kernel const-decl "(irreflexive?)nil) (ifference const-decl"" nil) (finite_below formula-decl nil well_ordered_finite nil) ( nil)) (least? const-decl "bool" minmax_orders ) lower_bound "" bounded_orders nil) (union const-decl "set" sets nil) (trichotomous? const-decl " (expand* "below""" unionjava. (? const-decl"" nil) (?const-decl"relations ) (irreflexive? java.lang.StringIndexOutOfBoundsException: Index 27 out of bounds f (OR const-decl "[bool, (expand "" "nion"? member) =const-decl"T T >boolean]" equalities nil (r!1 skolem-const-decl java.lang.StringIndexOutOfBoundsException: Index 19 out of )) (non_empty_finite_settype-eq-decl finite_setsnil (java.lang.StringIndexOutOfBoundsException: Range [39, 22) out of bounds for len " - ] ) (is_finite const-decl "bool" finite_sets nil) (x!1 skolem-const-decl "(nonempty?[T])" well_ordered_finite nil)(? "" nil (pred nildefined_types ( ) (reflexive? nil (reflexive_closure const-decl "((!1 nat ) (strict_total_order? (nat nonempty-type-eq-decl nil naturalnumbers nil) ( bool nil nil) (!skolem-const-decl" ) (linear_order_to_total_order application-judgement "(total_orderjava.lang.StringIn well_ordered_finite nil) nonempty" niljava.lang.StringIndexOutOfBoundsException: Index 42 out of bounds (set type-eq-decl nil numfield nilniljava.lang.StringIndexOutOfBoundsException: Inde ( [ reals (NOT nilnumber_fieldsjava.lang.StringIndexOutOfBoundsException: Index 64 out of b ( IF[,T- ) (boolean java.lang.StringIndexOutOfBoundsException: Index 23 out of bounds for le difference") ( n well_ordered_finite (inite_well_ordered-1 38267 ("" ( leastconst-decl"" ) (("" (skosimp*) (("(use "nonempty_has_least) sert) (("(? bool nil (1 inst+"leastreflexive_closure[]<)p1)) (("1" (skolem!) (("1" (expand* "least?" "lower_bound?") (("1" (inst - ]" java.lang.StringIndexOutOfBoundsException: Index 55 out of bounds ((""( "- o 1java.lang.StringIndexOutOfBoundsException: Index 71 out of bounds for (("1"(expand*"" "member) (("1" (typepred "<") (("1" java.lang.StringIndexOutOfBoundsException: Range [57, 28) out of bounds for leng "strict_order""irreflexive?" "transitive?") (("1" (flatten) (("1" (inst - "x!1") (("1" ( ) "x!1" "least(reflexive_closure[T](<))(p!1)" "x!1" (("1" (assert) nil nil)) nil nil nil ( 0 nil31612java.lang.StringIndexOutOfBoundsException: Index 39 out of bounds for le nil)) nil)) )) nil)) nil)) nil)) nil)) nil) nil) nil) (2 expand"""?" member (("2" (inst?) nil nil)) nil)) nil)) nil)) nil ((empty? const-decl " ("" expand "" member) (linear_order_to_total_order application-judgement "(total_order?)" well_ordered_finite nil) (lower_bound? const-decl""bounded_orders) (irreflexive? const-decl "bool" relations nil ? irreflexive (transitive? const-decl "bool" relations nil) (strict_order? const-decl "bool (inst-"!" (1 (member const-decl "bool" (java.lang.StringIndexOutOfBoundsException: Index 39 out NOT "bool-bool" nil) (has_least? const-decl "bool" minmax_orders nil) (least? const-decl "bool" minmax_orders nil) (least const-decl "{ x!" (PREDtype-eq-decl defined_typesnil) (reflexive? const-decl "bool" relations nil) (reflexive_closure const-decl "(reflexive?)" closure_ops nil) (strict_total_order? const-decl "bool" () nil) (< formal-const-decl "(strict_total_order?[T])" well_ordered_finite nil) (p!1 skolem-const-decl "pred[T]" well_ordered_finite)java.lang.StringIndexOutOfBoun pred nil defined_types) (nonempty? const-decl "bool niljava.lang.StringIndexOutOfBounds (set type-eq-decl nil sets) (bool nonempty-type-eq-decl(2(*nonemptyemptymember (boolean nonempty-type-decl nil booleans nil) (T formal-type-decl nil well_ordered_finite nil) (n) well_ordered bool il (well_founded? linear_order_to_total_order (total_order" java.lang.StringIndexOutOfBoundsException: Index 8 out of bounds for length 8 (strict_order boolorders) (nonlast_has_next-1 ("" (skolem-typepredmemberconst-decl"" nil (("" (typepred "<") (("" ? " ) (1 grindif-match) (("1" (typepred "greatest(union(<, =))(fullset[T])") (1 (*"reatest"?"java.lang.StringIndexOutOfBoundsException: Index 64 out of bounds (""inst"1) (("1" (expand "unionstrict_total_order?const-decl"" nil (("1" (expand "member") ("1 () (("1" (inst- "greatest(union(<, =))({x: T | predtype-eq-declnildefined_typesnil (("1" (assert) nil nil) ("2 boolnonempty-type-eq-decl nilbooleans nil (("2" (skosimp) (("2"( -"1" (("2" (assert) nil nil)) nil)) boolorders niljava.lang.StringIndexOutOfBoundsException: Index 48 out of bounds f nil)) nil)) nil)) nil)) nil)) nil) nil) ("2" (inst + "t!1") nil nil)) nil)) (1 expand greatest upper_bound"""java.lang.StringIndexOutOfBoundsException: Index 6 (2"inst x) (("2" (skosimp) (("2" (expand* "has_next?" "above" "nonempty?" "empty?" """""" 1 (("2" (flatten) (2 inst "1 "x1) (("2" (inst - "r!1") (("2" (assert) nil nil)) nil)) nil)) nil) ) nil)) nil) nil)) nil)) nil) ((finite_well_ordered ((2 ) nil )) well_ordered_finite nil) ( ) (transitive? const-decl "bool" relations nil) (strict_order? const-decl ) (trichotomous) (well_founded? java.lang.StringIndexOutOfBoundsException: Index 23 out of bounds ( const-decl"(reflexive?) closure_opsnil) (member nil (union const-decl("" inst+"!1" (upper_bound? const-decl ("2 (skosimp) (? const-decl"bool"minmax_orders) (has_greatest? const-decl "bool" minmax_orders nil) (has_last? const-decl "bool" well_ordered_traversal nil) (last const-decl "LAMBDA( ):?t, [T, (<)) well_ordered_traversal nil) )" closure_ops nil) (difference const-decl "set" sets nil) ( (LAMBDA S:suffixS ))"ordered_subset nil) (2 flatten (nonempty 2 inst r1 x!) (has_next? const-decl "bool" well_ordered_traversal nil) ( application-judgement(?) well_ordered_finite nil) (TRUE const-decl "bool" booleans nil) ( ) nil) (= const-decl "[T, T -> nil) ORconst-decl [,bool> nil (fullset const-decl "set" sets nil)(finite_well_ordered "well_ordered)java.lang.Strin erT) well_ordered_finite nil) strict_total_orderconst-decl"" orders) (nonlast const-decl "set[T]" well_ordered_traversal nil) (set type-eq-decl nil sets?const-decl ) (? ""java.lang.StringIndexOutOfBoundsException: Range [48, 43) out of bounds for (pred (? bool ) (T formal-type-decl (? ""minmax_ordersjava.lang.StringIndexOutOfBoundsException: In ( [ - bool booleansniljava.lang.StringIndexOutOfBoundsException: Index 50 out of bou ( onempty-type-eq-decl booleans) (boolean nonempty-type-declwell_ordered_traversal nil) ) (setnil (nonfirst_has_prev-1 nil 33186 above ( S:ord ("(? " ) (("" nonemptyconst-declbool ) (""( ") (("1" (usejava.lang.StringIndexOutOfBoundsException: Index 29 out of bounds for l (("1" (lemma "non_empty_finite_has_greatest" OR "bool, > bool"booleans) "below,) ()) (("1" ?"greatest upper_bound?" "has_prev?") (("1" (skosimp) (("1" (inst + "t!1") (("1" (typepred "predtype-eq-decl nil defined_types nil) (("1"(expand "least?" "lower_bound?) (("1"() "1 expand""3java.lang.StringIndexOutOfBoundsException: Index 51 out of bounds fo ) (expand* "above" "java.lang.StringIndexOutOfBoundsException: Index 60 out of bound "difference""" union "member") (("" (flatten) (("1" (inst - "x!1") ("" ) 1" (inst - "next(<)(t!1)") (("1" (assert) (("1" (expand* "well_ordered?" "strict_total_order?" "strict_order?" 1 belowjava.lang.StringIndexOutOfBoundsException: Index 51 out of bounds for leng "transitive?"member (("1" "" (("1" (inst - "t!1 (assert (("1" (inst - "strict_total_orderjava.lang.StringIndexOutOfBoundsException: Index 64 out of bo "" (("1 (latten) (assert) nil t" nil)) nil)) nil)) nil)) nil) 1 (expand(("" (assert) "irreflexive_kernel" "difference" "member") nil ) nil)) nil) ("2" (expand* "above" irreflexive_kernel "difference" "member") (("2" (assert) nil nil)) nil)) nil)) ) nil)) nil)) nil)) nil nil) ("2" (expand* "has_next?" " "member" "above" "below" "irreflexive_kernel" "difference" "member") (("2" ( java.lang.StringIndexOutOfBoundsException: Index 35 out of bounds for length 35 nil)) nil)) nil)java.lang.StringIndexOutOfBoundsException: Index 27 out of bounds for length nil)) nil)) nil) ("2" (assert) ("2"(rewrite"") ((2 lift-if (("2" (expand "emptyset") ("2 (groundjava.lang.StringIndexOutOfBoundsException: Index 36 out of bounds for ("2" (expand"first" (("2 nil)) (typepred "least(java.lang.StringIndexOutOfBoundsException: Index 46 out of bounds for len ("2" (* "least" "fullset" "lower_bound?") (("2" (expand "reflexive_closure" -1 :occurrence 1) (("2" (expand* "union" "member") (("2" inst"!") (("2" (assert) (("2" "" (expand "below" -5) (("2" (expand* e "empty?" "difference" "member") (("2" (inst - "least(reflexive_closure(<))({x: T | TRUE})") (( (expandbelow-) ("2" "empty?" "well_ordered?" "well_founded?") ((" java.lang.StringIndexOutOfBounds (flatten) (("2" (inst - "{x: T | TRUE}") (("2" (split) (("1" (skolem!) (("1" (inst + 1 (expand* "least?" "lower_bound?" "reflexive_closure" "union" "member") (("1" (("1" (inst - "r "reflexive_closur (("1" (("1" (("1" (("1" (flatten) (("1" ((expand* - ""trichotomous?"java.lang.StringIndexOutOfBoundsException: Index 83 out of bound "y!1") (("1" (assert) "r!1" ) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (inst + "x!1") nil nil)) nil)) nil)) nil) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) nil)) nil)) nil)) nil) ("2" (grind :if-match all) nil nil ) nil)) nil) ((nonempty_has_least judgement-tcc nil well_ordered_finite nil) (nonempty? const-decl "bool" sets nil) (finite_well_ordered name-judgement "(well_ordered?)" well_ordered_finite nil) (finite_below formula-decl nil well_ordered_finite nil) (linear_order_to_total_order application-judgement "(total_order?)" well_ordered_finite nil) (empty? const-decl "bool" sets nil) (x!1 skolem-const-decl "(nonfirst(<))" well_ordered_finite nil) (below const-declnil nil) (prefix? const-decl "bool" ordered_subset nil) (order? const-decl "bool nil ( const-decl "" nil (AND const-decl "[ nil)java.lang.StringIndexOutOfBoundsException: Index 11 ou (finite_set type-eq-decl nil finite_sets nil) (non_empty_finite_set type-eq-decl nil finite_sets nil) (total_order? const-decl "bool" orders nil) (PRED type-eq-decl nil defined_types nil) (reflexive? const-decl "bool" relations nil well_ordered_finite ) (reflexive_closure const-decl "(reflexive?)" closure_ops nil) (?const-declbool nil (suffix? const-decl "bool" ordered_subset nil least const-decl"" minmax_orders) (above const-decl "(LAMBDA (S): suffix?(S, ord))" ordered_subset nil) (next const-decl "(LAMBDA (t_1: T): least?( ( const-decl well_ordered_traversal nil) (irreflexive_kernel const-decl "(irreflexive?)" closure_ops nil) (member const-decl "bool" sets nil) ( const-decl"et" setsnil) (difference const-decl "set" sets nil) (irreflexive? const-decl "bool" relations nil) (transitive? const-decl "bool" relations nil) strict_order "" ordersnil (lower_bound? const-decl "bool" bounded_orders nil) (t!1 skolem-const-decl " ?const-decl bool niljava.lang.StringIndexOutOfBoundsE (? const-decl "bool" well_ordered_traversal) (has_greatest? const-decl "bool" minmax_orders nil) (upper_bound? const-decl "bool" bounded_orders nil) (has_prev?const-decl"" well_ordered_traversalniljava.lang.StringIndexOutOfBoundsE (greatest? const-decl "bool" (upper_bound? const-decl "bool" bounded_orders ( const-decl "set" sets nil) ( const-decl "(LAMBDA ( const-decl "" sets nil) well_ordered_traversal nil) (trichotomous? const-decl "bool" orders nil) (well_founded? const-decl "bool"java.lang.StringIndexOutOfBoundsException: Index 2 (RUE "bool" booleans) (least const-decl "{t: (S well_ordered_traversalnil) has_leastconst-decl "" minmax_orders) (fullset const-decl " well_founded const-decl bool"ordersnil ( const-decl"" booleans) (has_first? const-decl "bool" well_ordered_traversal nil) (inite_emptysetname-judgement""finite_setsnil ( "[T]" well_ordered_finite nil) (<formal-const-decl"strict_total_order[T]" well_ordered_finite nil) (strict_total_order? const-decl "bool" orders nil) (nonfirst const-decl "set[T]" well_ordered_traversal nil) (set type-eq-decl nil setsfinite_emptyset"[] java.lang.StringIndexOutOfBoundsExcept (well_ordered? const-decl "bool" orders nil) (pred strict_total_orderconst-decl bool rdersnil) (T formal-type-decl nil well_ordered_finite nil) (NOT const-decl "[bool -> bool]" booleans nil) (bool nonempty-type-eq-decl nil booleans nil) (boolean nonempty-type-decl nil booleans nil)) nil)) ( 0 finite_last-1nil31669 ("" boolnonempty-type-eq-decl booleans) (" (expand* "has_last?" "has_greatest?" "greatest?" "fullset" "upper_bound?" "reflexive_closure" " " typepred" ("(* "? reflexive_closure union member) (("" (expand* "is_finite" "is_finite_type") (("" (skolem!) (("" (inst + "1 + N!1" (("(!java.lang.StringIndexOutOfBoundsException: Index 26 out of bounds for lengt (("1" (expand "injective?") (("1" (skosimp) (("1" (lift-if) (("1" (lift-if) (("1" (ground) (("1" (inst - "x1!1" "x2!1") (("1" (assert) (("1" (lift-if) (("1" (split -1) (("1" (flatten) (("1" (assert) nil nil)) nil) ("2" (flatten) nil nil)) nil)) nil)) nil) " assert) (("2" (lift-if (("2" (split -1) (("1" (flatten) (("1" (assert) nil nil)) nil) ("2" (expand* "below" "irreflexive_kernel" "difference" "member" "well_ordered?" "strict_total_order?" "trichotomous?") (("2" (flatten) (("2" (ground) (("2" (inst -5 "x2!1") (("2" (ground) nil nil) ((2 nil)) nil)) ) nil)) nil)) ) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (skosimp) (("2" (assert) nil nil)) nil) ("3" ( ("java.lang.StringIndexOutOfBoundsException: Index 23 out of bounds for length 2 (expand* "below" "irreflexive_kernel" "difference" ""well_ordered? "trichotomous?") (("3" (flatten) (("3" (inst - "r!1") 3 -! t1java.lang.StringIndexOutOfBoundsException: Index 50 out of bounds for lengt ) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) (? " nil) (fullset const-decl "set" sets nil) (reflexive_closure const-decl "(reflexive?)" closure_ops nil) (member const-decl "bool" sets nil) (union const-decl "set" sets nil) (upper_bound? const-decl "bool" bounded_orders nil) greatestconst-decl "bool ) (has_last? bool nil) (finite_below nil nil) (name-judgement "(strict_total_order?[ (strict_total_order?real) nil) (injective? const-decl "bool" functions nil) (TRUE const-decl "bool" booleans nil) (difference const-decl "set" sets nil?const-declboolordersjava.lang.StringIndexOutOf (trichotomous? const-decl "bool" orders nil) ( (irreflexive) nil (x2!1 skolem-const-decl numbers) ( const-decl[ -boolean (number nonempty-type-decl nil numbers ) ( const-decl"number-> boolean"number_fields nil) (number_field nonempty-type-from-decl nil number_fields nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (real nonempty-type-from-decl nil reals nil) (< const-decl "bool" reals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (rational nonempty-type-from-decl nil rationals nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (int nonempty-type-eq-decl nil integers nil) (>= const-decl "bool" reals nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (N!1 skolem-const-decl "nat" well_ordered_finite nil) (below type-eq-decl nil nat_types nil) (f!1 skolem-const-decl "[(below(t!1, <)) (!1skolem-const-decl"(below(!, ))- [N1]java.lang.StringIndexOutOfBou (numfield nonempty-type-eq-decl nil)" java.lang.StringIndexOutOfBoundsException: I (numfield nonempty-type-eq-decl nil number_fields nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (below const-decl "(LAMBDA posint nil) prefix ""nil (set const-decl "bool" finite_sets nil) (order? const-decl "bool" relations_extra nil) (t!1 skolem-const-decl "T" well_ordered_finite nil) (= const-decl "[T, T -> boolean]" equalities nil) (IMPLIESconst-decl"[bool, bool -> bool]]" nil) (posint_plus_nnint_is_posint application-judgement " (boolnonempty-type-eq-decl integers nil) (is_finite const-decl "bool"shostak) (is_finite_type const-decl "bool" finite_sets nil) (finite_well_ordered name-judgement "(well_ordered?)" well_ordered_finite 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_finite nil) (pred type-eq-decl nil defined_types nil) (well_ordered? const-decl "bool" orders nil) (strict_total_order? const-decl "bool" orders nil) (< formal-const-decl "(strict_total_order?[T])" well_ordered_finite nil)) shostak)))
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2026-04-02