Quelle polylist.prf
Sprache: Lisp
(polylistnil 3601220513 ("" (subtype-tcc) nil nil )"listn[rat](0)" polylist nil )nil booleans nil )nil booleans nil )NOT const-decl "[bool -> bool]" booleans nil )nil numbers nil )nil defined_types nil )nil list_adt nil )"boolean" list_adt nil )AND const-decl "[bool, bool -> bool]" booleans nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[number_field -> boolean]" reals nil )nil reals nil )"[real -> boolean]" rationals nil )nil rationals nil )"[list -> boolean]" list_adt nil )nil polylist nil )"bool" reals nil )nil rationals nil )"[rational -> boolean]" integers nil )nil integers nil )nil number_fields nil )"[numfield, numfield -> numfield]" number_fields nil )nil naturalnumbers nil )"nat" list_props nil )nil integers nil )"odd_int" integers nil )"(total_order?[real])" nil )"boolean" notequal nil )"int" integers nil )"int" integers nil ))nil ))nil 3601220513 ("" (subtype-tcc) nil nil )"listn[rat](0)" polylist nil )nil booleans nil )nil booleans nil )NOT const-decl "[bool -> bool]" booleans nil )nil numbers nil )nil defined_types nil )nil list_adt nil )"boolean" list_adt nil )AND const-decl "[bool, bool -> bool]" booleans nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[number_field -> boolean]" reals nil )nil reals nil )"[real -> boolean]" rationals nil )nil rationals nil )"[list -> boolean]" list_adt nil )nil polylist nil )"bool" reals nil )nil rationals nil )"[rational -> boolean]" integers nil )nil integers nil )nil number_fields nil )"[numfield, numfield -> numfield]" number_fields nil )nil naturalnumbers nil )"nat" list_props nil )nil integers nil )"(total_order?[real])" nil )"int" integers nil )"int" integers nil ))nil ))nil 3601220513 ("" (termination-tcc) nil nil )"listn[rat](0)" polylist nil )nil booleans nil )nil booleans nil )NOT const-decl "[bool -> bool]" booleans nil )nil numbers nil )nil defined_types nil )nil list_adt nil )"boolean" list_adt nil )AND const-decl "[bool, bool -> bool]" booleans nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[number_field -> boolean]" reals nil )nil reals nil )"[real -> boolean]" rationals nil )nil rationals nil )"[list -> boolean]" list_adt nil )nil polylist nil )"bool" reals nil )nil rationals nil )"[rational -> boolean]" integers nil )nil integers nil )nil number_fields nil )"[numfield, numfield -> numfield]" number_fields nil )nil naturalnumbers nil )nil integers nil )"int" integers nil )"int" integers nil )"(total_order?[real])" nil )"posint" nil )"posint" nil )"nat" list_props nil ))nil ))nil 3601220513 ("" (subtype-tcc) nil nil )"listn[rat](0)" polylist nil )nil booleans nil )nil booleans nil )NOT const-decl "[bool -> bool]" booleans nil )nil numbers nil )nil defined_types nil )nil list_adt nil )"boolean" list_adt nil )AND const-decl "[bool, bool -> bool]" booleans nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[number_field -> boolean]" reals nil )nil reals nil )"[real -> boolean]" rationals nil )nil rationals nil )"[list -> boolean]" list_adt nil )nil polylist nil )"bool" reals nil )nil rationals nil )"[rational -> boolean]" integers nil )nil integers nil )nil number_fields nil )"[numfield, numfield -> numfield]" number_fields nil )nil naturalnumbers nil )"nat" list_props nil )nil integers nil )"odd_int" integers nil )"(total_order?[real])" nil )"boolean" notequal nil )"int" integers nil )"int" integers nil ))nil ))nil 3601224651 ("" (termination-tcc) nil nil )"listn[rat](0)" polylist nil )nil booleans nil )nil booleans nil )NOT const-decl "[bool -> bool]" booleans nil )nil numbers nil )nil defined_types nil )nil list_adt nil )"boolean" list_adt nil )AND const-decl "[bool, bool -> bool]" booleans nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[number_field -> boolean]" reals nil )nil reals nil )"[real -> boolean]" rationals nil )nil rationals nil )"[list -> boolean]" list_adt nil )nil polylist nil )"bool" reals nil )nil rationals nil )"[rational -> boolean]" integers nil )nil integers nil )nil number_fields nil )"[numfield, numfield -> numfield]" number_fields nil )nil naturalnumbers nil )nil integers nil )"int" integers nil )"(total_order?[real])" nil )"posint" nil )"(strict_total_order?[real])" real_props nil )"posint" nil )"nat" list_props nil ))nil ))nil 3601231397"" (subtype-tcc) nil nil ) nil nil ))nil 3601231397"" (subtype-tcc) nil nil ) nil nil ))nil 3601231398"" (induct "pl" )"1" (grind) nil nil ) ("2" (ground) nil nil )"3" (ground)"3" (skeep)"3" (skeep)"3" (assert )"3" (expand "eval_polylist" +)"3" (lift-if)"3" (split +)"1" (grind) nil nil )"2" (flatten)"2" (assert )"2" (inst?)"1" (assert )"1" (lemma "expt_plus" )"1" "(deg - length(cons(cons1_var, cons2_var)))" "1" "x" )"1" expand "^" -1 3)"1" expand "expt" -1)"1" expand "expt" -1)"1" (assert ) nil nil ))nil ))nil ))nil )"2" "2" "2" assert )"2" expand "^" 2)"2" expand "expt" 2)"2" (propax) nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" (assert )"2" (typepred "deg" )"2" (expand "length" -1)"2" (assert ) nil nil )) nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"int" integers nil )"int" integers nil )"(total_order?[real])" nil )"posint" nil )"real" reals nil )"real" exponentiation nil )"real" exponentiation nil )"nzreal" nil )"posint" nil )NOT const-decl "[bool -> bool]" booleans nil )"real" polylist nil )nil reals nil )"rat" rationals nil )"nat" exponentiation nil )nil exponentiation nil )"[numfield, numfield -> numfield]" number_fields nil )OR const-decl "[bool, bool -> bool]" booleans nil )"boolean" notequal nil )"upfrom(length(cons(cons1_var, cons2_var)))" nil )"list[rat]" polylist nil )"rat" polylist nil )"[[T, list] -> (cons?)]" list_adt nil )"listn[rat](0)" polylist nil )nil list_adt nil )nil numbers nil )nil booleans nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[number_field -> boolean]" reals nil )nil reals nil )"[real -> boolean]" rationals nil )nil rationals nil )"real" polylist nil )"[numfield, numfield -> numfield]" number_fields nil )nil polylist nil )"[numfield, numfield -> numfield]" number_fields nil )nil number_fields nil )"[T, T -> boolean]" equalities nil )nil integers nil )"nat" list_props nil )nil naturalnumbers nil )"bool" reals nil )nil integers nil )"[rational -> boolean]" integers nil )nil rationals nil )"[list -> boolean]" list_adt nil )"[bool, bool -> bool]" booleans nil )AND const-decl "[bool, bool -> bool]" booleans nil )"boolean" list_adt nil )nil defined_types nil )nil booleans nil )nil list_adt nil )"int" integers nil )"real" reals nil ))nil 3601307736"" (induct "pl" )"1" (grind) nil nil ) ("2" (assert ) nil nil )"3" (skeep)"3" (assert )"3" (skeep)"3" (expand "eval_polylist" +)"3" (lift-if)"3" (split +)"1" (flatten) (("1" (assert ) nil nil )) nil )"2" (flatten)"2" (assert )"2" (copy -1)"2" (inst?)"2" (replaces -1)"2" (invoke (name "AA" "%1" ) (! 2 1))"2" (replace -1)"2" "2" "2" replace -1)"2" expand "AA" )"2" (propax) nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"real" polylist nil )"[numfield, numfield -> numfield]" number_fields nil )OR const-decl "[bool, bool -> bool]" booleans nil )"boolean" notequal nil )"real" exponentiation nil )"[[T, list] -> (cons?)]" list_adt nil )"real" reals nil )"real" reals nil )"int" integers nil )"int" integers nil )"listn[rat](0)" polylist nil )nil list_adt nil )nil numbers nil )nil booleans nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[number_field -> boolean]" reals nil )nil reals nil )"[real -> boolean]" rationals nil )nil rationals nil )"[numfield, numfield -> numfield]" number_fields nil )"real" polylist nil )nil polylist nil )"[T, T -> boolean]" equalities nil )nil integers nil )"nat" list_props nil )nil naturalnumbers nil )"[numfield, numfield -> numfield]" number_fields nil )nil number_fields nil )"bool" reals nil )nil integers nil )"[rational -> boolean]" integers nil )nil rationals nil )"[list -> boolean]" list_adt nil )"[bool, bool -> bool]" booleans nil )AND const-decl "[bool, bool -> bool]" booleans nil )"boolean" list_adt nil )nil defined_types nil )nil booleans nil )nil list_adt nil ))nil 3601225669 ("" (grind) nil nil )"boolean" list_adt nil )"listn[rat](0)" polylist nil ))nil ))nil 3601225669 ("" (grind) nil nil )"(total_order?[real])" nil )"int" integers nil )"listn[rat](0)" polylist nil )"posint" nil )"nat" list_props nil ))nil ))nil 3601225669 ("" (subtype-tcc) nil nil )"boolean" notequal nil )) nil ))nil 3601728884 ("" (subtype-tcc) nil nil )"boolean" notequal nil )) nil ))nil 3601225671 ("" (grind) nil nil )"nat" list_props nil )"real" exponentiation nil )"real" exponentiation nil )"real" polylist nil )"real" reals nil )"real" reals nil ))nil 3601220513 ("" (subtype-tcc) nil nil ) nil nil ))nil 3601224651 ("" (grind) nil nil )"nat" list_props nil )"boolean" notequal nil ))nil ))nil 3601313859"" (skeep)"" (split)"1" (replaces -1) (("1" (grind) nil nil )) nil )"2" (replaces -1) (("2" (grind) nil nil )) nil ))nil ))nil )"Polylist" polylist nil )"nat" list_props nil )"odd_int" integers nil )"posint" nil )"posint" nil )"listn[rat](0)" polylist nil )"real" polylist nil )"real" polylist nil )"real" exponentiation nil )"real" exponentiation nil ))nil ))nil 3601313859 ("" (subtype-tcc) nil nil )nil booleans nil )nil booleans nil )NOT const-decl "[bool -> bool]" booleans nil )nil numbers nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[number_field -> boolean]" reals nil )nil reals nil )"bool" reals nil )"[real -> boolean]" rationals nil )nil rationals nil )"[rational -> boolean]" integers nil )nil integers nil )nil naturalnumbers nil )"int" integers nil )"(total_order?[real])" nil ))nil ))nil 3601313859 ("" (termination-tcc) nil nil ) nil nil ))nil 3601313859"" (skeep)"" (invoke (case "NOT %1" ) (! 2 1))"1" (hide 3)"1" (expand "length" +) (("1" (assert ) nil nil )) nil )) nil )"2" (assert )"2" (skeep)"2" (typepred "v(c,deg-1)" )"2" (inst - "x" )"2" (expand "^" )"2" (expand "expt" +)"2" (mult-by -4 "x" )"2" (replace -1 :dir rl)"2" (expand "polylist" +)"2" (expand "eval_polylist" + 1)"2" (expand "length" 2 1)"2" (rewrite "eval_polylist_times_x" )"2" (assert ) nil nil )) nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"3" (assert ) nil nil ))nil ))nil )"(total_order?[real])" nil )"(strict_total_order?[real])" real_props nil )"posint" nil )"int" integers nil )nil booleans nil )nil booleans nil )NOT const-decl "[bool -> bool]" booleans nil )nil numbers nil )"[T, T -> boolean]" equalities nil )nil list_adt nil )nil defined_types nil )"boolean" list_adt nil )AND const-decl "[bool, bool -> bool]" booleans nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[number_field -> boolean]" reals nil )nil reals nil )"[real -> boolean]" rationals nil )nil rationals nil )nil rationals nil )"[rational -> boolean]" integers nil )nil integers nil )"bool" reals nil )nil naturalnumbers nil )"nat" list_props nil )"[list -> boolean]" list_adt nil )"[[T, list] -> (cons?)]" list_adt nil )"bool" reals nil )nil polylist nil )nil number_fields nil )"[numfield, numfield -> numfield]" number_fields nil )"real" polylist nil )"[numfield, numfield -> numfield]" number_fields nil )OR const-decl "[bool, bool -> bool]" booleans nil )"boolean" notequal nil )"real" exponentiation nil )"[numfield, numfield -> numfield]" number_fields nil )"listn[rat](0)" polylist nil )"real" exponentiation nil )"real" polylist nil )nil integers nil )nil polylist nil )"real" reals nil )nil extra_real_props nil ))nil ))nil 3601220513"" (skeep*)"" (expand "polylist" + 2)"" (expand "length" +)"" (expand "length" +)"" (assert )"" (expand "eval_polylist" )"" (expand "length" +)"" (expand "length" +)"" (expand "^" +)"" (expand "expt" )"" (expand "polylist" +)"" (expand "length" + 1)"" (expand "eval_polylist" +)"" (lift-if)"" "" "" assert )"" "1" (grind) nil nil )"2" replace -5 :dir rl)"2" expand "length" + 3)"2" expand "length" + 3)"2" case "x^0=1" )"1" assert )"1" "1" rewrite "eval_polylist_remove_acc" "1" "AA" "%1" )"1" replace -1)"1" "1" rewrite "eval_polylist_remove_acc" "1" expand "AA" )"1" assert )"1" expand "length" "1" assert )nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" "2" (grind) 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 )"real" polylist nil )"real" polylist nil )"real" exponentiation nil )"int" integers nil )"posint" nil )"(total_order?[real])" nil )"rat" rationals nil )"bool" reals nil )"boolean" notequal nil )OR const-decl "[bool, bool -> bool]" booleans nil )nil booleans nil )nil integers nil )"[rational -> boolean]" integers nil )nil rationals nil )"[real -> boolean]" rationals nil )"[number_field -> boolean]" reals nil )nil number_fields nil )"[number -> boolean]" number_fieldsnil )nil reals nil )"[T, T -> boolean]" equalities nil )nil booleans nil )nil numbers nil )"real" polylist nil )"[(cons?) -> T]" list_adt nil )nil integers nil )nil naturalnumbers nil )"[numfield, numfield -> numfield]" number_fields nil )nil polylist nil )"[list -> boolean]" list_adt nil )AND const-decl "[bool, bool -> bool]" booleans nil )"boolean" list_adt nil )nil defined_types nil )nil list_adt nil )nil rationals nil )"[numfield, numfield -> numfield]" number_fields nil )"[numfield, numfield -> numfield]" number_fields nil )nil number_fields nil )nil polylist nil )"real" reals nil )"posint" nil )"real" exponentiation nil )"rat" rationals nil )"real" reals nil )"nat" list_props nil )"listn[rat](0)" polylist nil ))nil ))nil 3601315963"" (skeep*)"" (expand "polylist" + 3)"" (expand "length" +)"" (expand "length" +)"" (assert )"" (expand "eval_polylist" )"" (expand "length" +)"" (expand "length" +)"" (expand "^" +)"" (expand "expt" )"" (expand "polylist" +)"" (expand "length" + 1)"" (expand "eval_polylist" +)"" (assert )"" expand "length" + 3)"" expand "length" + 3)"" case "x^0=1" )"1" assert )"1" "1" rewrite "eval_polylist_remove_acc" "1" "AA" "%1" )"1" replace -1)"1" "1" rewrite "eval_polylist_remove_acc" "1" expand "AA" )"1" assert )"1" expand "length" "1" assert )nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" "2" (grind) nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"real" polylist nil )"real" polylist nil )"real" exponentiation nil )"int" integers nil )"real" reals nil )"(total_order?[real])" nil )nil polylist nil )nil number_fields nil )"[numfield, numfield -> numfield]" number_fields nil )"[numfield, numfield -> numfield]" number_fields nil )nil rationals nil )nil list_adt nil )nil defined_types nil )"boolean" list_adt nil )AND const-decl "[bool, bool -> bool]" booleans nil )"[list -> boolean]" list_adt nil )nil polylist nil )"[numfield, numfield -> numfield]" number_fields nil )nil naturalnumbers nil )nil integers nil )"rat" rationals nil )"[(cons?) -> list]" list_adt nil )"[(cons?) -> T]" list_adt nil )"real" polylist nil )nil numbers nil )nil booleans nil )"[T, T -> boolean]" equalities nil )nil reals nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[number_field -> boolean]" reals nil )"[real -> boolean]" rationals nil )nil rationals nil )"[rational -> boolean]" integers nil )nil integers nil )nil booleans nil )OR const-decl "[bool, bool -> bool]" booleans nil )"boolean" notequal nil )"bool" reals nil )"posint" nil )"real" exponentiation nil )"rat" rationals nil )"real" reals nil )"nat" list_props nil )"listn[rat](0)" polylist nil ))nil )nil 3601220513 ("" (termination-tcc) nil nil )nil list_adt nil )"[list -> boolean]" list_adt nil ))nil ))nil 3601225382 ("" (termination-tcc) nil nil )"listn[rat](0)" polylist nil )nil booleans nil )nil booleans nil )NOT const-decl "[bool -> bool]" booleans nil )nil numbers nil )nil defined_types nil )nil list_adt nil )"boolean" list_adt nil )AND const-decl "[bool, bool -> bool]" booleans nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[number_field -> boolean]" reals nil )nil reals nil )"[real -> boolean]" rationals nil )nil rationals nil )"[list -> boolean]" list_adt nil )nil polylist nil ))nil ))nil 3601315195 ("" (subtype-tcc) nil nil )"listn[rat](0)" polylist nil )nil booleans nil )nil booleans nil )NOT const-decl "[bool -> bool]" booleans nil )nil numbers nil )nil defined_types nil )nil list_adt nil )"boolean" list_adt nil )AND const-decl "[bool, bool -> bool]" booleans nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[number_field -> boolean]" reals nil )nil reals nil )"[real -> boolean]" rationals nil )nil rationals nil )"[list -> boolean]" list_adt nil )nil polylist nil ))nil ))nil 3601315195 ("" (termination-tcc) nil nil )"nat" list_props nil )"posint" nil ))nil ))nil 3601315195"" (skeep*)"" (expand "polylist" +)"" (expand "length" + 1)"" (expand "eval_polylist" +)"" (assert )"" (lift-if)"" (ground)"" (expand "length" + 3)"" (expand "length" + 3)"" (case "x^0=1" )"1" (replaces -1)"1" (assert )"1" (rewrite "eval_polylist_remove_acc" +)"1" (invoke (name "AA" "%1" ) (! 2 1))"1" "1" rewrite "eval_polylist_remove_acc" "1" "BB" "%1" ) (! 2 2 1))"1" "1" rewrite "eval_polylist_remove_acc" "1" expand "AA" )"1" expand "BB" )"1" assert )"1" "v(cdr[rat](pl), cdr[rat](ql))" )"1" "x" )"1" expand "polylist" "1" "eval_polylist_times_x" )"1" case "0 = 0*x" )"1" "1" rewrite "1" "AAA" "%1" )"1" "1" rewrite "1" "BBB" "%1" )"1" "1" rewrite "1" expand "AAA" )"1" expand "BBB" )"1" expand "length" "1" expand "length" "1" assert )nil nil ))nil ))nil ))nil ))nil )"2" expand "length" "2" assert )nil nil ))nil ))nil ))nil ))nil )"2" expand "length" "2" assert )nil nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" assert )nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" (hide-all-but 1) (("2" (grind) nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"real" polylist nil )"posint" nil )"real" polylist nil )"real" exponentiation nil )"bool" reals nil )"boolean" notequal nil )OR const-decl "[bool, bool -> bool]" booleans nil )nil booleans nil )nil integers nil )"[rational -> boolean]" integers nil )nil rationals nil )"[real -> boolean]" rationals nil )"[number_field -> boolean]" reals nil )nil number_fields nil )"[number -> boolean]" number_fieldsnil )nil reals nil )"[T, T -> boolean]" equalities nil )nil booleans nil )nil numbers nil )"rat" rationals nil )"real" polylist nil )nil polylist nil )"Polylist" polylist nil )"real" polylist nil )"real" polylist nil )"Polylist" polylist nil )"(total_order?[real])" nil )"[numfield, numfield -> numfield]" number_fields nil )NOT const-decl "[bool -> bool]" booleans nil )"real" polylist nil )nil integers nil )"[numfield, numfield -> numfield]" number_fields nil )"[(cons?) -> list]" list_adt nil )nil naturalnumbers nil )"bool" reals nil )nil polylist nil )"[(cons?) -> T]" list_adt nil )"[list -> boolean]" list_adt nil )nil rationals nil )AND const-decl "[bool, bool -> bool]" booleans nil )"boolean" list_adt nil )nil defined_types nil )nil list_adt nil )"[numfield, numfield -> numfield]" number_fields nil )nil number_fields nil )nil polylist nil )"real" exponentiation nil )"rat" rationals nil )"real" reals nil )"int" integers nil )"real" reals nil )"nat" list_props nil )"listn[rat](0)" polylist nil ))nil ))nil 3601227496 ("" (skeep) (("" (grind) nil nil )) nil )"nat" list_props nil )"real" exponentiation nil )"real" exponentiation nil )"real" polylist nil )"real" polylist nil )"rat" rationals nil )"posint" nil )"listn[rat](0)" polylist nil ))nil ))nil 3601747475 ("" (termination-tcc) nil nil )"listn[rat](0)" polylist nil )nil booleans nil )nil booleans nil )NOT const-decl "[bool -> bool]" booleans nil )nil numbers nil )nil defined_types nil )nil list_adt nil )"boolean" list_adt nil )AND const-decl "[bool, bool -> bool]" booleans nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[number_field -> boolean]" reals nil )nil reals nil )"[real -> boolean]" rationals nil )nil rationals nil )"[list -> boolean]" list_adt nil )nil polylist nil ))nil ))nil 3601747631 ("" (termination-tcc) nil nil )"nat" list_props nil )) nil ))nil 3601747631"" (skeep)"" (split)"1" (expand "length" + 1)"1" (assert )"1" (typepred "v(c,cdr[rat](pl))" )"1" (replace -3)"1" (expand "length" + 2) (("1" (propax) nil nil ))nil ))nil ))nil ))nil ))nil )"2" (skeep)"2" (expand "polylist" +)"2" (expand "length" + 1)"2" (typepred "v(c,cdr[rat](pl))" )"1" (expand "polylist" )"1" (expand "eval_polylist" +)"1" (lift-if)"1" (split)"1" (flatten) (("1" (grind) nil nil )) nil )"2" (flatten)"2" (assert )"2" (expand "length" + 3)"2" (case "x^0=1" )"1" "1" assert )"1" rewrite "eval_polylist_remove_acc" "1" "AA" "%1" ) (! 2 1))"1" replace -1)"1" rewrite "eval_polylist_remove_acc" "1" "1" expand "AA" )"1" assert )"1" "x" )"1" "x" )"1" rewrite "eval_polylist_times_x" )"1" "BBC" "eval_polylist(cdr[rat](pl), length(cdr[rat](pl)) - 1, 0)(x) * x" )"1" rewrite "eval_polylist_times_x" "1" expand "BBC" "1" "c" )"1" replace "1" assert )"1" expand "length" "1" assert )nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" "2" (grind) nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" (grind) nil nil ))nil ))nil ))nil ))nil ))nil ))nil )"posint" nil )nil booleans nil )nil booleans nil )NOT const-decl "[bool -> bool]" booleans nil )nil numbers nil )nil defined_types nil )nil list_adt nil )"boolean" list_adt nil )AND const-decl "[bool, bool -> bool]" booleans nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[number_field -> boolean]" reals nil )nil reals nil )"[real -> boolean]" rationals nil )nil rationals nil )"[list -> boolean]" list_adt nil )nil polylist nil )"bool" reals nil )nil rationals nil )"[rational -> boolean]" integers nil )nil integers nil )"bool" reals nil )nil naturalnumbers nil )"[T, T -> boolean]" equalities nil )"real" polylist nil )nil number_fields nil )"[numfield, numfield -> numfield]" number_fields nil )"[(cons?) -> list]" list_adt nil )"nat" list_props nil )"real" polylist nil )"rat" rationals nil )"int" integers nil )"real" reals nil )OR const-decl "[bool, bool -> bool]" booleans nil )"boolean" notequal nil )"real" exponentiation nil )"[numfield, numfield -> numfield]" number_fields nil )"real" polylist nil )"(total_order?[real])" nil )nil polylist nil )"real" polylist nil )nil extra_real_props nil )"real" reals nil )nil polylist nil )"[(cons?) -> T]" list_adt nil )"[numfield, numfield -> numfield]" number_fields nil )nil integers nil )"real" exponentiation nil )"listn[rat](0)" polylist nil ))nil ))nil 3601224651 ("" (grind) nil nil )"listn[rat](0)" polylist nil )nil booleans nil )nil booleans nil )NOT const-decl "[bool -> bool]" booleans nil )nil numbers nil )nil defined_types nil )nil list_adt nil )"boolean" list_adt nil )AND const-decl "[bool, bool -> bool]" booleans nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[number_field -> boolean]" reals nil )nil reals nil )"[real -> boolean]" rationals nil )nil rationals nil )"[list -> boolean]" list_adt nil )nil polylist nil )"(total_order?[real])" nil )"nat" list_props nil ))nil ))nil 3601806618"" (skeep)"" (skolem 1 "ii" )"" case "FORALL (a,b:[nat->rat],n,m:nat): rational_pred(polynomial_prod(a, ") "1" case "FORALL (pzl:Polylist): FORALL (x1: nat): rational_pred(list2array[rat](0)(pzl)(x1))" )"1" (inst? -2)"1" (grind) nil nil ) ("2" (grind) nil nil )) nil )"2" (hide-all-but 1) (("2" (grind) nil nil )) nil ))nil )"2" (hide 2)"2" (skeep)"2" (expand "polynomial_prod" )"2" case "FORALL (FF:[nat->rat],mm,nn:nat): rational_pred(sigma(mm,nn,FF))" )"1" (rewrite -1)"1" (assert ) nil nil )"2" (skosimp*) (("2" (assert ) nil nil )) nil ))nil )"2" (hide 2)"2" (induct "nn" )"1" (grind)"1" (expand "sigma" )"1" (expand "sigma" ) (("1" (propax) nil nil ))nil ))nil ))nil )"2" (skeep)"2" (skeep)"2" (inst - "FF" "mm" )"2" (expand "sigma" +)"2" (ground)"2" case "FORALL (r1,r2:rat): rational_pred(r1+r2)" )"1" (rewrite -1) nil nil )"2" "2" (grind) nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"posint" nil )"real" reals nil )"[numfield, numfield -> numfield]" number_fields nil )"rat" rationals nil )NOT const-decl "[bool -> bool]" booleans nil )"(strict_total_order?[real])" real_props nil )nil naturalnumbers nil )nil defined_types nil )"{s: rat | s >= q AND s >= r}" nil )"{k: int | i <= k AND j <= k}" nil )"rat" rationals nil )max const-decl "{p: real | p >= m AND p >= n}" real_defs nil )"[numfield, numfield -> numfield]" number_fields nil )IF const-decl "[boolean, T, T -> T]" if_def nil )"[bool, bool -> bool]" booleans nil )"nat" polylist nil )"nat" polylist nil )"(total_order?[real])" nil )OR const-decl "[bool, bool -> bool]" booleans nil )"bool" reals nil )nil sigma "reals/" )nil sigma "reals/" )"real" sigma "reals/" )"T" array2list "structures/" )nil polylist nil )"[list -> boolean]" list_adt nil )AND const-decl "[bool, bool -> bool]" booleans nil )"boolean" list_adt nil )nil defined_types nil )nil list_adt nil )"posint" nil )"Polylist" polylist nil )"Polylist" polylist nil )nil number_fields nil )"[numfield, numfield -> numfield]" number_fields nil )"nat" list_props nil )"int" integers nil )"(total_order?[real])" nil )nil numbers nil )nil booleans nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[number_field -> boolean]" reals nil )nil reals nil )"[real -> boolean]" rationals nil )nil rationals nil )"[rational -> boolean]" integers nil )nil integers nil )nil booleans nil )"bool" reals nil )nil naturalnumbers nil )nil rationals nil )nil sequences nil )"real" polynomials "reals/" )"listn[rat](0)" polylist nil ))nil )nil 3601376563 ("" (grind) nil nil )nil list_adt nil )"[list -> boolean]" list_adt nil ))nil ))nil 3601728884 ("" (grind) nil nil )"listn[rat](0)" polylist nil )nil booleans nil )nil booleans nil )NOT const-decl "[bool -> bool]" booleans nil )nil numbers nil )nil defined_types nil )nil list_adt nil )"boolean" list_adt nil )AND const-decl "[bool, bool -> bool]" booleans nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[number_field -> boolean]" reals nil )nil reals nil )"[real -> boolean]" rationals nil )nil rationals nil )"[list -> boolean]" list_adt nil )nil polylist nil )"(total_order?[real])" nil )"nat" list_props nil )"posint" nil ))nil ))nil 3601806454 ("" (grind) nil nil )"listn[rat](0)" polylist nil )nil booleans nil )NOT const-decl "[bool -> bool]" booleans nil )nil defined_types nil )nil list_adt nil )"boolean" list_adt nil )AND const-decl "[bool, bool -> bool]" booleans nil )"[list -> boolean]" list_adt nil )nil polylist nil )"(divides(n))" divides nil )"(divides(m))" divides nil )"{k: int | i <= k AND j <= k}" nil )"{s: rat | s >= q AND s >= r}" nil )"(strict_total_order?[real])" real_props nil )"rat" rationals nil )"(strict_total_order?[real])" real_props nil )"{l: listn(n - i) | FORALL (j: subrange(i, n - 1)): a(j) = nth(l, j - i)}" "structures/" )"real" polynomials "reals/" )"T" array2list "structures/" )max const-decl "{p: real | p >= m AND p >= n}" real_defs nil )"nat" list_props nil )nil rationals nil )"[real -> boolean]" rationals nil )nil reals nil )"[number_field -> boolean]" reals nil )nil number_fields nil )"[number -> boolean]" number_fieldsnil )nil booleans nil )nil numbers nil )"{l: listn(n) | FORALL (i: below(n)): a(i) = nth(l, i)}" "structures/" )"int" integers nil )"posint" nil ))nil ))nil 3601811247 ("" (subtype-tcc) nil nil )"listn[rat](0)" polylist nil )nil booleans nil )nil booleans nil )NOT const-decl "[bool -> bool]" booleans nil )nil numbers nil )nil defined_types nil )nil list_adt nil )"boolean" list_adt nil )AND const-decl "[bool, bool -> bool]" booleans nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[number_field -> boolean]" reals nil )nil reals nil )"[real -> boolean]" rationals nil )nil rationals nil )"[list -> boolean]" list_adt nil )nil polylist nil )"bool" reals nil )nil rationals nil )"[rational -> boolean]" integers nil )nil integers nil )"bool" reals nil )nil naturalnumbers nil )"nat" list_props nil )nil naturalnumbers nil ))nil ))nil 3601811247 ("" (grind) nil nil )"listn[rat](0)" polylist nil )nil booleans nil )nil booleans nil )NOT const-decl "[bool -> bool]" booleans nil )nil numbers nil )nil defined_types nil )nil list_adt nil )"boolean" list_adt nil )AND const-decl "[bool, bool -> bool]" booleans nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[number_field -> boolean]" reals nil )nil reals nil )"[real -> boolean]" rationals nil )nil rationals nil )"[list -> boolean]" list_adt nil )nil polylist nil )"posint" nil )"(strict_total_order?[real])" real_props nil )"nat" list_props nil ))nil ))nil 3601811247"" (skeep) (("" (grind) nil nil )) nil )nil booleans nil )nil booleans nil )NOT const-decl "[bool -> bool]" booleans nil )nil numbers nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[number_field -> boolean]" reals nil )nil reals nil )"bool" reals nil )"[real -> boolean]" rationals nil )nil rationals nil )"[rational -> boolean]" integers nil )nil integers nil )"bool" reals nil )nil naturalnumbers nil )nil list_adt nil )nil defined_types nil )"boolean" list_adt nil )AND const-decl "[bool, bool -> bool]" booleans nil )nil rationals nil )"nat" list_props nil )"[list -> boolean]" list_adt nil )nil polylist nil )nil naturalnumbers nil )"(strict_total_order?[real])" real_props nil )"posint" nil )"T" list_props nil )"listn[rat](0)" polylist nil ))nil ))nil 3601811247 ("" (grind) nil nil )"listn[rat](0)" polylist nil )nil booleans nil )nil booleans nil )NOT const-decl "[bool -> bool]" booleans nil )nil numbers nil )nil defined_types nil )nil list_adt nil )"boolean" list_adt nil )AND const-decl "[bool, bool -> bool]" booleans nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[number_field -> boolean]" reals nil )nil reals nil )"[real -> boolean]" rationals nil )nil rationals nil )"[list -> boolean]" list_adt nil )nil polylist nil )"(strict_total_order?[real])" real_props nil )"posint" nil )"nat" list_props nil ))nil ))nil 3601811247"" (skeep)"" (assert )"" (ground)"1" (inst - "0" )"1" (grind) nil nil ) ("2" (grind) nil nil )) nil )"2" (skeep)"2" (typepred "j" )"2" (case "NOT j = 1" )"1" (grind) nil nil )"2" (replaces -1) (("2" (grind) nil nil )) nil ))nil ))nil ))nil )"3" (grind) nil nil ))nil ))nil ))nil )"[T, T -> boolean]" equalities nil )"(strict_total_order?[real])" real_props nil )NOT const-decl "[bool -> bool]" booleans nil )"(strict_total_order?[real])" real_props nil )"Polylist" polylist nil )nil polylist nil )"[list -> boolean]" list_adt nil )"nat" list_props nil )nil naturalnumbers nil )"bool" reals nil )nil integers nil )"[rational -> boolean]" integers nil )nil rationals nil )nil rationals nil )"[real -> boolean]" rationals nil )AND const-decl "[bool, bool -> bool]" booleans nil )"boolean" list_adt nil )nil defined_types nil )nil list_adt nil ) (< const-decl "bool" reals nil )nil booleans nil )nil reals nil )"[number_field -> boolean]" reals nil )nil number_fields nil )"[number -> boolean]" number_fieldsnil )nil booleans nil )nil numbers nil )nil naturalnumbers nil )"T" list_props nil )"posint" nil )"listn[rat](0)" polylist nil ))nil ))nil 3601811247"" (skeep)"" (skeep)"" (skeep)"" (assert )"" (hide 2)"" (typepred "v(cdr(pl))" )"" (replace -5 :dir rl)"" (assert )"" (typepred "v(cdr(pl))`maxnon" )"" (expand "length" 4) (("" (assert ) nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"posint" nil )"(strict_total_order?[real])" real_props nil )"[(cons?) -> list]" list_adt nil )"boolean" notequal nil )"bool" reals nil )OR const-decl "[bool, bool -> bool]" booleans nil )"T" list_props nil )nil nat_types nil )"[T, T -> boolean]" equalities nil )"[bool, bool -> bool]" booleans nil )nil naturalnumbers nil )"nat" list_props nil )nil naturalnumbers nil )"bool" reals nil )nil integers nil )"[rational -> boolean]" integers nil )nil rationals nil )"bool" reals nil )nil polylist nil )"[list -> boolean]" list_adt nil )nil rationals nil )"[real -> boolean]" rationals nil )nil reals nil )"[number_field -> boolean]" reals nil )nil number_fields nil )"[number -> boolean]" number_fieldsnil )AND const-decl "[bool, bool -> bool]" booleans nil )"boolean" list_adt nil )nil defined_types nil )nil list_adt nil )nil numbers nil )"[bool, bool -> bool]" booleans nil )NOT const-decl "[bool -> bool]" booleans nil )nil booleans nil )nil booleans nil )"listn[rat](0)" polylist nil ))nil ))nil 3601811247"" (skeep)"" (skeep)"" (skeep)"" (assert )"" (hide 2)"" (split)"1" (typepred "v(cdr(pl))" )"1" (replace -6 :dir rl)"1" (assert )"1" (hide -1)"1" (inst -3 "upans`maxnon+1" )"1" (expand "nth" -3)"1" (lift-if) (("1" (ground) nil nil ))nil ))nil )"2" (typepred "v(cdr(pl))`maxnon" )"2" (expand "length" 1)"2" (assert ) nil nil )) nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" (skeep)"2" (typepred "v(cdr(pl))" )"2" (assert )"2" (hide -1)"2" (inst - "j-1" )"1" (assert )"1" (expand "nth" 2)"1" (propax) nil nil )) nil ))nil )"2" (typepred "j" )"2" (expand "length" -1)"2" (assert ) nil nil )) nil ))nil ))nil ))nil ))nil ))nil ))nil )"3" (flatten)"3" (typepred "v(cdr(pl))" )"3" (assert )"3" (hide (-1 -2))"3" (expand "nth" -2) (("3" (assert ) nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"posint" nil )nil number_fields nil )"[numfield, numfield -> numfield]" number_fields nil )"Polylist" polylist nil )"{degans: [# allzero: bool, maxnon: below(length(cdr(pl))) #] | AND OR AND (degans`allzero OR nth(cdr(pl), degans`maxnon) /= 0)}" nil )"posint" nil )"(strict_total_order?[real])" real_props nil )nil booleans nil )nil booleans nil )NOT const-decl "[bool -> bool]" booleans nil )"[bool, bool -> bool]" booleans nil )nil numbers nil )nil list_adt nil )nil defined_types nil )"boolean" list_adt nil )AND const-decl "[bool, bool -> bool]" booleans nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[number_field -> boolean]" reals nil )nil reals nil )"[real -> boolean]" rationals nil )nil rationals nil )"[list -> boolean]" list_adt nil )nil polylist nil )"bool" reals nil )nil rationals nil )"[rational -> boolean]" integers nil )nil integers nil )"bool" reals nil )nil naturalnumbers nil )"nat" list_props nil )nil naturalnumbers nil )"[bool, bool -> bool]" booleans nil )"[T, T -> boolean]" equalities nil )nil nat_types nil )"T" list_props nil )OR const-decl "[bool, bool -> bool]" booleans nil )"bool" reals nil )"boolean" notequal nil )"[(cons?) -> list]" list_adt nil )"below(length(pl))" polylist nil )"[numfield, numfield -> numfield]" number_fields nil )"int" integers nil )"(total_order?[real])" nil )"(strict_total_order?[real])" real_props nil )"listn[rat](0)" polylist nil ))nil ))nil 3601811247"" (skeep)"" (skeep)"" (skeep) (("" (hide 2) (("" (grind) nil nil )) nil )) nil ))nil ))nil )"nat" list_props nil )"posint" nil )"(strict_total_order?[real])" real_props nil )"listn[rat](0)" polylist nil ))nil ))nil 3601811247"" (skeep)"" (skeep)"" (skeep)"" (assert )"" (hide 2)"" (skeep)"" (case "j = 0" )"1" (expand "nth" 3) (("1" (assert ) nil nil )) nil )"2" (expand "nth" +)"2" (assert )"2" (typepred "v(cdr(pl))" )"2" (replace -5 :dir rl)"2" (assert )"2" (hide -3)"2" (hide -2)"2" (inst - "j-1" ) nil nil )) nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"[(cons?) -> list]" list_adt nil )"boolean" notequal nil )"bool" reals nil )OR const-decl "[bool, bool -> bool]" booleans nil )nil nat_types nil )"[bool, bool -> bool]" booleans nil )"[bool, bool -> bool]" booleans nil )NOT const-decl "[bool -> bool]" booleans nil )nil number_fields nil )"[numfield, numfield -> numfield]" number_fields nil )"(total_order?[real])" nil )"int" integers nil )"T" list_props nil )nil numbers nil )nil booleans nil )"[T, T -> boolean]" equalities nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[number_field -> boolean]" reals nil )nil reals nil )"[real -> boolean]" rationals nil )nil rationals nil )"[rational -> boolean]" integers nil )nil integers nil )nil booleans nil )"bool" reals nil )nil naturalnumbers nil )"bool" reals nil ) (list type-decl nil list_adt nil )nil defined_types nil )"boolean" list_adt nil )AND const-decl "[bool, bool -> bool]" booleans nil )nil rationals nil )"nat" list_props nil )"[list -> boolean]" list_adt nil )nil polylist nil )nil naturalnumbers nil )"listn[rat](0)" polylist nil ))nil ))nil 3601811247"" (skeep)"" (skeep)"" (skeep)"" (assert ) (("" (hide 2) (("" (grind) nil nil )) nil )) nil ))nil ))nil ))nil )"(strict_total_order?[real])" real_props nil )"nat" list_props nil )"posint" nil )"listn[rat](0)" polylist nil ))nil ))nil 3601811247"" (skeep)"" (skeep)"" (skeep)"" (assert )"" (hide 2)"" (split)"1" (inst - "0" )"1" (grind) nil nil ) ("2" (grind) nil nil )) nil )"2" (skeep)"2" (typepred "v(cdr(pl))" )"2" (replace -6 :dir rl)"2" (assert )"2" (inst -1 "j-1" )"1" (expand "nth" 1) (("1" (propax) nil nil ))nil )"2" (assert )"2" (typepred "j" )"2" (expand "length" -1)"2" (assert ) nil nil )) nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"3" (flatten) (("3" (grind) nil nil )) nil ))nil ))nil ))nil ))nil ))nil ))nil )"posint" nil )"T" list_props nil )nil naturalnumbers nil )nil numbers nil )nil booleans nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[number_field -> boolean]" reals nil )nil reals nil )nil booleans nil )"bool" reals nil ) (list type-decl nil list_adt nil )nil defined_types nil )"boolean" list_adt nil )AND const-decl "[bool, bool -> bool]" booleans nil )"[real -> boolean]" rationals nil )nil rationals nil )nil rationals nil )"[rational -> boolean]" integers nil )nil integers nil )"bool" reals nil )nil naturalnumbers nil )"nat" list_props nil )"[list -> boolean]" list_adt nil )nil polylist nil )"Polylist" polylist nil )"(strict_total_order?[real])" real_props nil )"[(cons?) -> list]" list_adt nil )"boolean" notequal nil )"bool" reals nil )OR const-decl "[bool, bool -> bool]" booleans nil )nil nat_types nil )"[T, T -> boolean]" equalities nil )"[bool, bool -> bool]" booleans nil )"[bool, bool -> bool]" booleans nil )NOT const-decl "[bool -> bool]" booleans nil )"(strict_total_order?[real])" real_props nil )"posint" nil )"below(length(pl))" polylist nil )"[numfield, numfield -> numfield]" number_fields nil )nil number_fields nil )"int" integers nil )"(total_order?[real])" nil )"listn[rat](0)" polylist nil ))nil ))nil 3601814826"" (skeep)"" (assert )"" (typepred "drec" )"" (assert )"" (split +)"1" (skeep) (("1" (inst - "j" ) nil nil )) nil )"2" (hide -) (("2" (grind) nil nil )) nil ))nil ))nil ))nil ))nil ))nil )"(strict_total_order?[real])" real_props nil )"(strict_total_order?[real])" real_props nil )"posint" nil )nil booleans nil )nil booleans nil )NOT const-decl "[bool -> bool]" booleans nil )"[bool, bool -> bool]" booleans nil )nil naturalnumbers nil )nil numbers nil )nil list_adt nil )nil defined_types nil )"boolean" list_adt nil )AND const-decl "[bool, bool -> bool]" booleans nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[number_field -> boolean]" reals nil )nil reals nil )"[real -> boolean]" rationals nil )nil rationals nil )nil rationals nil )"[rational -> boolean]" integers nil )nil integers nil )"bool" reals nil )nil naturalnumbers nil )"nat" list_props nil )"[list -> boolean]" list_adt nil )nil polylist nil )"[bool, bool -> bool]" booleans nil )"bool" reals nil )"[T, T -> boolean]" equalities nil )nil nat_types nil )"T" list_props nil )OR const-decl "[bool, bool -> bool]" booleans nil )"bool" reals nil )"boolean" notequal nil )"listn[rat](0)" polylist nil ))nil ))nil 3601814826"" (skeep)"" (assert )"" (typepred "drec" )"" (assert )"" (hide -1)"" (split)"1" (flatten)"1" (assert )"1" (inst + "drec`maxnon" ) (("1" (assert ) nil nil ))nil ))nil ))nil )"2" (flatten)"2" (assert )"2" (skeep -1)"2" (inst - "j" ) (("2" (assert ) nil nil )) nil ))nil ))nil ))nil )"3" (flatten) nil nil ))nil ))nil ))nil ))nil ))nil ))nil )"(strict_total_order?[real])" real_props nil )nil booleans nil )nil booleans nil )NOT const-decl "[bool -> bool]" booleans nil )"[bool, bool -> bool]" booleans nil )nil naturalnumbers nil )nil numbers nil )nil list_adt nil )nil defined_types nil )"boolean" list_adt nil )AND const-decl "[bool, bool -> bool]" booleans nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[number_field -> boolean]" reals nil )nil reals nil )"[real -> boolean]" rationals nil )nil rationals nil )nil rationals nil )"[rational -> boolean]" integers nil )nil integers nil )"bool" reals nil )nil naturalnumbers nil )"nat" list_props nil )"[list -> boolean]" list_adt nil )nil polylist nil )"[bool, bool -> bool]" booleans nil )"bool" reals nil )"[T, T -> boolean]" equalities nil )nil nat_types nil )"T" list_props nil )OR const-decl "[bool, bool -> bool]" booleans nil )"bool" reals nil )"boolean" notequal nil )"listn[rat](0)" polylist nil ))nil ))nil 3601229241"" (expand "polylist" )"" case "FORALL (pl: Polylist, x,acc: real): ") "1" (skeep)"1" (inst - "pl" "x" "0" ) (("1" (assert ) nil nil )) nil )) nil )"2" (hide 2)"2" (induct "pl" )"1" (grind) nil nil ) ("2" (ground) nil nil )"3" (skeep)"3" (skeep)"3" (assert )"3" (expand "length" +)"3" (assert )"3" (expand "eval_polylist" +)"3" (lift-if)"3" (split +)"1" (flatten)"1" (expand "length" +)"1" assert )"1" expand "length" +)"1" assert )"1" expand "list2array" +)"1" assert )"1" expand "list2array" +)"1" "1" (grind) nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" (flatten)"2" (expand "length" + 3)"2" assert )"2" "x" "cons1_var*x^0+acc" )"2" expand "^" )"2" expand "expt" )"2" assert )"2" "polynomial_eq_a0_plus" )"2" "list2array(0)(cons(cons1_var, cons2_var))" "length(cons2_var)" "x" )"2" assert )"2" "1" "1" expand "list2array" "1" case "NOT (LAMBDA (i: nat): ") "1" "1" expand "list2array" "1" nil nil ))nil ))nil )"2" "2" assert )"2" rewrite "eval_polylist_remove_acc" "2" rewrite "eval_polylist_remove_acc" "2" "eval_polylist_times_x" )"2" assert )"2" "0" "cons2_var" "x" "length[rat](cons2_var)" )"2" assert )"2" replace "2" rewrite "eval_polylist_remove_acc" "2" rewrite "eval_polylist_remove_acc" "2" assert )nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" "2" nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"4" (hide 2) (("4" (grind) nil nil )) nil ))nil ))nil )"3" (hide 2) (("3" (grind) nil nil )) nil ))nil ))nil )"T" array2list "structures/" )"[real -> real]" polynomials "reals/" )nil sequences nil )"[numfield, numfield -> numfield]" number_fields nil )"real" polylist nil )nil integers nil )"nat" list_props nil )nil naturalnumbers nil )"[numfield, numfield -> numfield]" number_fields nil )nil number_fields nil )"bool" reals nil )nil integers nil )"[rational -> boolean]" integers nil )nil rationals nil )"[T, T -> boolean]" equalities nil )nil polylist nil )"[list -> boolean]" list_adt nil )nil rationals nil )"[real -> boolean]" rationals nil )nil reals nil )"[number_field -> boolean]" reals nil )nil number_fields nil )"[number -> boolean]" number_fieldsnil )AND const-decl "[bool, bool -> bool]" booleans nil )"boolean" list_adt nil )nil defined_types nil )nil booleans nil )nil booleans nil )nil list_adt nil )nil numbers nil )"int" integers nil )"real" reals nil )"listn[rat](0)" polylist nil )"[bool, bool -> bool]" booleans nil )nil list_adt nil )"posint" nil )"real" exponentiation nil )"real" exponentiation nil )"real" sigma "reals/" )"rat" rationals nil )"(strict_total_order?[real])" real_props nil )"(total_order?[real])" nil )"real" reals nil )"boolean" notequal nil )OR const-decl "[bool, bool -> bool]" booleans nil )"[numfield, numfield -> numfield]" number_fields nil )nil polynomials "reals/" )"posint" nil )NOT const-decl "[bool -> bool]" booleans nil )nil polylist nil )nil polylist nil )"[[T, list] -> (cons?)]" list_adt nil )"real" polylist nil ))nil 3601815971"" case "FORALL (pl: Polylist, x: real,k:nat): ") "1" (skeep)"1" (inst - "pl" "x" "length(pl)-1-deg(pl)" )"1" (assert ) nil nil ) ("2" (assert ) nil nil )) nil ))nil )"2" (hide 2)"2" (induct "k" )"1" (skeep) (("1" (assert ) nil nil )) nil )"2" (skolem 1 "k" )"2" (flatten)"2" (assert )"2" (skeep)"2" (inst - "pl" "x" )"2" (assert )"2" (rewrite "polynomial_rec" 1)"2" case " list2array[rat](0)(pl)(1 + deg(pl) + k) = 0" )"1" (assert ) nil nil )"2" (hide-all-but (-2 1))"2" (rewrite "list2array_sound" )"2" (lift-if)"2" "2" "deg(pl)" )"2" assert )"2" "1+deg(pl)+k" )"2" (assert ) nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"posint" nil )nil polynomials "reals/" )"odd_int" integersnil )"real" reals nil )"real" reals nil )NOT const-decl "[bool -> bool]" booleans nil )"(strict_total_order?[real])" real_props nil )nil array2list "structures/" )nil naturalnumbers nil )nil defined_types nil )"listn[rat](0)" polylist nil )"(strict_total_order?[real])" real_props nil )"Polylist" polylist nil )"[numfield, numfield -> numfield]" number_fields nil )"int" integers nil )"(total_order?[real])" nil )"nonneg_int" nil )nil numbers nil )nil list_adt nil )nil booleans nil )nil booleans nil )nil defined_types nil )"boolean" list_adt nil )AND const-decl "[bool, bool -> bool]" booleans nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[number_field -> boolean]" reals nil )nil reals nil )"[real -> boolean]" rationals nil )nil rationals nil )"[list -> boolean]" list_adt nil )nil polylist nil )nil rationals nil )"[rational -> boolean]" integers nil )nil integers nil )"bool" reals nil )nil naturalnumbers nil )"[bool, bool -> bool]" booleans nil )"bool" reals nil ) (< const-decl "bool" reals nil )"nat" list_props nil )nil naturalnumbers nil )"[bool, bool -> bool]" booleans nil )"boolean" notequal nil )nil nat_types nil )"T" list_props nil )"[T, T -> boolean]" equalities nil )"{d: below(length(pl)) | AND nth(pl, j) /= 0))AND AND (d > 0 IMPLIES nth(pl, d) /= 0)}" polylist nil) nil sequences nil )"[real -> real]" polynomials "reals/" )"T" array2list "structures/" )nil number_fields nil )"[numfield, numfield -> numfield]" number_fieldsnil ))nil 3601309766 ("" (grind) nil nil )"Polylist" polylist nil )"nat" list_props nil )"real" exponentiation nil )"real" exponentiation nil )"real" polylist nil )"real" polylist nil ))nil 3601220513 ("" (subtype-tcc) nil nil )"boolean" notequal nil )) nil ))nil 3601309814"" (skeep)"" (typepred "pmonom(c,n)" ) (("" (inst - "x" ) nil nil )) nil ))nil )"{pl: Polylist | AND " polylist nil )"real" exponentiation nil )"boolean" notequal nil )OR const-decl "[bool, bool -> bool]" booleans nil )"[numfield, numfield -> numfield]" number_fields nil )"real" polylist nil )"[numfield, numfield -> numfield]" number_fields nil )nil number_fields nil )"nat" list_props nil )"[T, T -> boolean]" equalities nil )nil polylist nil )"[list -> boolean]" list_adt nil )nil naturalnumbers nil )"bool" reals nil )nil integers nil )"[rational -> boolean]" integers nil )nil rationals nil )nil rationals nil )"[real -> boolean]" rationals nil )nil reals nil )"[number_field -> boolean]" reals nil )nil number_fields nil )"[number -> boolean]" number_fieldsnil )AND const-decl "[bool, bool -> bool]" booleans nil )"boolean" list_adt nil )nil list_adt nil )nil defined_types nil )nil numbers nil )NOT const-decl "[bool -> bool]" booleans nil )nil booleans nil )nil booleans nil ))nil 3601373214"" case "FORALL (pl, ql: Polylist, x: real): ") "1" (skeep) (("1" (inst?) (("1" (assert ) nil nil )) nil )) nil )"2" (hide 2)"2" (skeep)"2" (expand "pprod" 1)"2" (rewrite "polylist_eval" )"2" (rewrite "polylist_eval" )"2" (rewrite "polylist_eval" )"1" "plp" "polynomial_prod(list2array(0)(pl), ") "1" (replace -1)"1" case "plp = list2array(0)(array2list(length(pl) + length(ql)-1)(plp))" )"1" (replace -1 :dir rl)"1" (assert )"1" "array2list(length(pl) + length(ql)-1)(plp)" )"1" (replace -2)"1" rewrite "polynomial_prod_def" )"1" replace -5)"1" (assert ) nil nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" (hide 2)"2" (decompose-equality)"2" (rewrite "array2list_inv" )"2" (invoke (case "NOT %1 = 0" ) (! 2 2))"1" "array2list(length(pl) + length(ql)-1)(plp)" )"1" rewrite "list2array_sound" )nil nil ))nil )"2" "2" "2" expand "plp" )"2" expand "polynomial_prod" )"2" expand "max" )"2" "2" (grind) nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" (hide 2) (("2" (grind) nil nil )) nil )"3" (hide 2) (("3" (grind) nil nil )) nil ))nil )"2" (hide 2) (("2" (grind) nil nil )) nil )"3" (hide 2) (("3" (grind) nil nil )) nil )"4" (hide 2) (("4" (grind) nil nil )) nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"nonneg_int" nil )"int" integers nil )nil polynomials "reals/" )NOT const-decl "[bool -> bool]" booleans nil )nil array2list "structures/" )"posint" nil )"rat" rationals nil )"posint" nil )"(strict_total_order?[real])" real_props nil )"real" sigma "reals/" )max const-decl "{p: real | p >= m AND p >= n}" real_defs nil )"[nat -> real]" polylist nil )nil array2list "structures/" )"(strict_total_order?[real])" real_props nil )"T" array2list "structures/" )"real" polynomials "reals/" )nil sequences nil )"[numfield, numfield -> numfield]" number_fields nil )"[numfield, numfield -> numfield]" number_fields nil )"{l: listn(n) | FORALL (i: below(n)): a(i) = nth(l, i)}" "structures/" )"T" list_props nil )nil nat_types nil )nil naturalnumbers nil )"bool" reals nil )nil listn "structures/" )"nat" list_props nil )nil naturalnumbers nil )"bool" reals nil )nil integers nil )"[rational -> boolean]" integers nil )nil rationals nil )"(total_order?[real])" nil )"int" integers nil )nil polylist nil )"listn[rat](0)" polylist nil )"real" reals nil )nil numbers nil )nil list_adt nil )nil booleans nil )nil booleans nil )nil defined_types nil )"boolean" list_adt nil )AND const-decl "[bool, bool -> bool]" booleans nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[number_field -> boolean]" reals nil )nil reals nil )"[real -> boolean]" rationals nil )nil rationals nil )"[list -> boolean]" list_adt nil )nil polylist nil )"[T, T -> boolean]" equalities nil )nil number_fields nil )"[numfield, numfield -> numfield]" number_fields nil )"real" polylist nil )"Polylist" polylist nil ))nil 3601744687"" (skeep)"" (typepred "pscal(c,pl)" ) (("" (inst - "x" ) nil nil )) nil ))nil )"{pql: Polylist | AND " nil )"[numfield, numfield -> numfield]" number_fields nil )nil number_fields nil )"real" polylist nil )"nat" list_props nil )nil naturalnumbers nil )"bool" reals nil )nil integers nil )"[rational -> boolean]" integers nil )nil rationals nil )"[T, T -> boolean]" equalities nil )nil polylist nil )"[list -> boolean]" list_adt nil )nil rationals nil )"[real -> boolean]" rationals nil )nil reals nil )"[number_field -> boolean]" reals nil )nil number_fields nil )"[number -> boolean]" number_fieldsnil )AND const-decl "[bool, bool -> bool]" booleans nil )"boolean" list_adt nil )nil list_adt nil )nil defined_types nil )nil numbers nil )NOT const-decl "[bool -> bool]" booleans nil )nil booleans nil )nil booleans nil )"listn[rat](0)" polylist nil ))nil 3601314376"" (skeep)"" (typepred "psum(pl,ql)" ) (("" (inst - "x" ) nil nil )) nil ))nil )"{pql: Polylist | " nil )"[numfield, numfield -> numfield]" number_fields nil )nil number_fields nil )"real" polylist nil )"[T, T -> boolean]" equalities nil )nil polylist nil )"[list -> boolean]" list_adt nil )nil rationals nil )"[real -> boolean]" rationals nil )nil reals nil )"[number_field -> boolean]" reals nil )nil number_fields nil )"[number -> boolean]" number_fieldsnil )AND const-decl "[bool, bool -> bool]" booleans nil )"boolean" list_adt nil )nil list_adt nil )nil defined_types nil )nil numbers nil )NOT const-decl "[bool -> bool]" booleans nil )nil booleans nil )nil booleans nil )"listn[rat](0)" polylist nil ))nil 3601748130"" (skeep)"" (expand "pminus" )"" (rewrite "polylist_sum" )"" (rewrite "polylist_scal" ) (("" (assert ) nil nil )) nil ))nil ))nil ))nil )"odd_int" integers nil )"Polylist" polylist nil )nil polylist nil )"real" reals nil )"real" reals nil )"real" reals nil )"[numfield -> numfield]" number_fields nil )"{pql: Polylist | AND " nil )"[numfield, numfield -> numfield]" number_fields nil )nil number_fields nil )"real" polylist nil )"nat" list_props nil )nil naturalnumbers nil )"bool" reals nil )nil integers nil )"[rational -> boolean]" integers nil )nil rationals nil )"[T, T -> boolean]" equalities nil )nil polylist nil )"[list -> boolean]" list_adt nil )nil rationals nil )"[real -> boolean]" rationals nil )nil reals nil )"[number_field -> boolean]" reals nil )nil number_fields nil )"[number -> boolean]" number_fieldsnil )AND const-decl "[bool, bool -> bool]" booleans nil )"boolean" list_adt nil )nil defined_types nil )nil booleans nil )nil booleans nil )nil list_adt nil )nil numbers nil )nil polylist nil )"listn[rat](0)" polylist nil ))nil 3601377289 ("" (subtype-tcc) nil nil )"real" polylist nil )) nil ))nil 3601740624"" (induct "n" )"1" (grind) nil nil )"2" (skeep)"2" (skeep)"2" (inst - "pl" "x" )"2" (expand "^" )"2" (expand "expt" +)"2" (replaces -1)"2" (replaces -1 :dir rl)"2" (rewrite "polylist_prod" :dir rl)"2" (expand "ppow" + 1)"2" (lift-if)"2" (ground)"2" (replaces -1)"2" (expand "ppow" +)"2" case "pprod(pl,pconst(1)) = pl" )"1" (assert ) nil nil )"2" "2" expand "pprod" )"2" expand "length" + 1)"2" assert )"2" expand "pconst" 1)"2" expand "length" + 1)"2" expand "deg" )"2" expand "length" + 3)"2" expand "length" + 3)"2" case "NOT polynomial_prod(list2array[rat](0)(pl), length[rat](pl) - 1, ") "1" "1" "1" expand "polynomial_prod" )"1" expand "max" )"1" "sigma_eq_one_arg" )"1" "1" "x!1" )"1" assert )"1" "1" "1" expand "list2array" "1" nil nil ))nil ))nil )"2" assert )"2" expand "sigma" )"2" case "FORALL (kk:nat,plz:list[rat]): kk>length[rat](plz)-1 IMPLIES 0=list2array[rat](0)(plz)(kk)" )"1" "1" assert )nil nil ))nil )"2" "2" "plz" )"1" nil nil )"2" "2" "2" expand "length" "2" "kk-1" )"1" assert )"1" expand "list2array" "1" nil nil ))nil ))nil )"2" assert )nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"3" "3" nil nil ))nil ))nil ))nil ))nil )"2" "2" assert )nil nil ))nil ))nil ))nil ))nil ))nil )"2" "pl" )"2" nil nil ))nil ))nil ))nil )"2" "2" case "FORALL (plz:list[rat]): array2list[rat](length[rat](plz))(list2array[rat](0)(plz)) = plz" )"1" nil nil )"2" "2" "2" rewrite "list2array_inv_ext" )nil nil ))nil ))nil ))nil ))nil )"3" "3" 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 ))nil ))nil )NOT const-decl "[bool -> bool]" booleans nil )nil sequences nil )"real" polynomials "reals/" )"T" array2list "structures/" )nil number_fields nil )"[numfield, numfield -> numfield]" number_fields nil )"[[T, list] -> (cons?)]" list_adt nil )"[list -> boolean]" list_adt nil )"(null?)" list_adt nil )"(total_order?[real])" nil )"Polylist" polylist nil )max const-decl "{p: real | p >= m AND p >= n}" real_defs nil )"rat" rationals nil )"[bool, bool -> bool]" booleans nil )"bool" reals nil )"nat" polylist nil )nil sigma "reals/" )nil sigma "reals/" )"[numfield, numfield -> numfield]" number_fields nil )IF const-decl "[boolean, T, T -> T]" if_def nil )"(total_order?[real])" nil )"bool" reals nil )"(strict_total_order?[real])" real_props nil )nil list_adt nil )"nat" polylist nil )"real" sigma "reals/" )nil sigma "reals/" )"posint" nil )nil listn "structures/" )"bool" reals nil )nil naturalnumbers nil )nil nat_types nil )"T" list_props nil )"{l: listn(n) | FORALL (i: below(n)): a(i) = nth(l, i)}" "structures/" )nil array2list "structures/" )"nonneg_int" nil )"Polylist" polylist nil )nil polylist nil )"listn[rat](0)" polylist nil )"posint" nil )"int" integers nil )"Polylist" polylist nil )"nat" list_props nil )"real" exponentiation nil )"real" polylist nil )nil naturalnumbers nil )"real" exponentiation nil )"boolean" notequal nil )OR const-decl "[bool, bool -> bool]" booleans nil )"Polylist" polylist nil )"real" polylist nil )"[T, T -> boolean]" equalities nil )nil polylist nil )"[list -> boolean]" list_adt nil )nil rationals nil )AND const-decl "[bool, bool -> bool]" booleans nil )"boolean" list_adt nil )nil defined_types nil )nil list_adt nil )nil defined_types nil )nil naturalnumbers nil )"bool" reals nil )nil booleans nil )nil integers nil )"[rational -> boolean]" integers nil )nil rationals nil )"[real -> boolean]" rationals nil )nil reals nil )"[number_field -> boolean]" reals nil )nil number_fields nil )"[number -> boolean]" number_fieldsnil )nil booleans nil )nil numbers nil ))nil )nil 3601740585"" (induct "n" )"1" (grind) nil )"2" (skeep)"2" (skeep)"2" (inst - "pl" "x" )"2" (expand "^" )"2" (expand "expt" +)"2" (replaces -1)"2" (rewrite "polylist_prod" )"2" (expand "ppow" + 2)"2" (lift-if)"2" (ground)"2" (replaces -1)"2" (expand "ppow" )"2" (case "pprod(pl,pconst(1)) = pl" )"1" (assert ) nil )"2" "2" expand "pprod" )"2" expand "length" + 1)"2" assert )"2" expand "pconst" 1)"2" expand "length" + 1)"2" expand "deg" )"2" expand "length" + 3)"2" expand "length" + 3)"2" case "NOT polynomial_prod(list2array(0)(pl), length(pl) - 1, ") "1" "1" "1" expand "polynomial_prod" )"1" expand "max" )"1" "sigma_eq_one_arg" )"1" "1" "x!1" )"1" assert )"1" "1" "1" expand "list2array" "1" nil )))))"2" assert )"2" expand "sigma" )"2" case "FORALL (kk:nat,plz:list[real]): kk>length(plz)-1 IMPLIES 0=list2array(0)(plz)(kk)" )"1" "1" assert )nil )))"2" "2" "plz" )"1" nil )"2" "2" "2" expand "length" "2" "kk-1" )"1" assert )"1" expand "list2array" "1" nil )))))"2" assert )nil )))))))))))))))))))"3" "3" nil )))))))))"2" "2" assert )nil )))))))))))"2" "pl" )"2" nil )))))))"2" "2" case "FORALL (plz:list[real]): array2list[rat](length[rat](plz))(list2array[rat](0)(plz)) = plz" )"1" nil )"2" "2" "2" rewrite "list2array_inv_ext" )nil )))))))))"3" "3" nil ))))))))))))))))))))))))))))))))))))))))))))))))))nil )nil nil )nil 3601377290"" (induct "n" )"1" (grind) nil nil )"2" (skeep)"2" (skeep)"2" (inst - "pl" "x" )"2" (expand "^" )"2" (expand "expt" +)"2" (replaces -1)"2" (rewrite "polylist_prod" )"2" (expand "ppow" + 2)"2" (lift-if)"2" (ground)"2" (replaces -1)"2" (expand "ppow" )"2" (case "pprod(pl,pconst(1)) = pl" )"1" (assert ) nil nil )"2" "2" expand "pprod" )"2" expand "length" + 1)"2" assert )"2" expand "pconst" 1)"2" expand "length" + 1)"2" expand "deg" )"2" expand "length" + 3)"2" expand "length" + 3)"2" case "NOT polynomial_prod(list2array(0)(pl), length(pl) - 1, ") "1" "1" "1" expand "polynomial_prod" )"1" expand "max" )"1" "sigma_eq_one_arg" )"1" "1" "x!1" )"1" assert )"1" "1" "1" expand "list2array" "1" nil nil ))nil ))nil )"2" assert )"2" expand "sigma" )"2" case "FORALL (kk:nat,plz:list[real]): kk>length(plz)-1 IMPLIES 0=list2array(0)(plz)(kk)" )"1" "1" assert )nil nil ))nil )"2" "2" "plz" )"1" nil nil )"2" "2" "2" expand "length" "2" "kk-1" )"1" assert )"1" expand "list2array" "1" nil nil ))nil ))nil )"2" assert )nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"3" "3" nil nil ))nil ))nil ))nil ))nil )"2" "2" assert )nil nil ))nil ))nil ))nil ))nil ))nil )"2" "pl" )"2" nil nil ))nil ))nil ))nil )"2" "2" case "FORALL (plz:list[real]): array2list[real](length[real](plz))(list2array[real](0)(plz)) = plz" )"1" nil nil )"2" "2" "2" rewrite "list2array_inv_ext" )nil nil ))nil ))nil ))nil ))nil )"3" "3" 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 ))nil )"real" polynomials "reals/" )"T" array2list "structures/" )"[[T, list] -> (cons?)]" list_adt nil )"[list -> boolean]" list_adt nil )"(null?)" list_adt nil )nil sigma "reals/" )nil sigma "reals/" )nil list_adt nil )"real" sigma "reals/" )nil sigma "reals/" )nil listn "structures/" )"{l: listn(n) | FORALL (i: below(n)): a(i) = nth(l, i)}" "structures/" )nil array2list "structures/" )"[list -> boolean]" list_adt nil )nil list_adt nil ))nil 3601744560"" (skeep)"" (expand "pneg" )"" (rewrite "polylist_scal" ) (("" (assert ) nil nil )) nil ))nil ))nil )"odd_int" integers nil )"Polylist" polylist nil )"real" reals nil )"real" reals nil )nil polylist nil )"[list -> boolean]" list_adt nil )AND const-decl "[bool, bool -> bool]" booleans nil )"boolean" list_adt nil )nil defined_types nil )nil booleans nil )nil list_adt nil )"[numfield -> numfield]" number_fields nil )nil number_fields nil )nil rationals nil )"[real -> boolean]" rationals nil )nil reals nil )"[number_field -> boolean]" reals nil )nil number_fields nil )"[number -> boolean]" number_fieldsnil )nil booleans nil )nil numbers nil )nil polylist nil )"listn[rat](0)" polylist nil ))nil 3601748272"" (skeep)"" (expand "pdiv" )"" (rewrite "polylist_scal" ) (("" (assert ) nil nil )) nil ))nil ))nil )"nzrat" rationalsnil )"Polylist" polylist nil )"real" reals nil )"real" reals nil )nil polylist nil )"[list -> boolean]" list_adt nil )AND const-decl "[bool, bool -> bool]" booleans nil )"boolean" list_adt nil )nil defined_types nil )nil booleans nil )nil list_adt nil )nil rationals nil )nil rationals nil )"[numfield, nznum -> numfield]" number_fields nil )nil number_fields nil )"boolean" notequal nil )nil number_fields nil )nil rationals nil )"[real -> boolean]" rationals nil )nil reals nil )"[number_field -> boolean]" reals nil )nil number_fields nil )"[number -> boolean]" number_fieldsnil )nil booleans nil )nil numbers nil )nil polylist nil )"listn[rat](0)" polylist nil ))nil 3601748553"" (skeep)"" (expand "psq" )"" (expand "sq" ) (("" (rewrite "polylist_prod" ) nil nil )) nil ))nil ))nil )"Polylist" polylist nil )nil polylist nil )nil numbers nil )nil list_adt nil )nil booleans nil )nil booleans nil )nil defined_types nil )"boolean" list_adt nil )AND const-decl "[bool, bool -> bool]" booleans nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[number_field -> boolean]" reals nil )nil reals nil )"[real -> boolean]" rationals nil )nil rationals nil )"[list -> boolean]" list_adt nil )nil polylist nil )"nonneg_real" sq "reals/" )"listn[rat](0)" polylist nil ))
Messung V0.5 in Prozent C=100 H=100 G=100
¤ Dauer der Verarbeitung: 0.130 Sekunden
(vorverarbeitet am 2026-04-30)
¤ *© Formatika GbR, Deutschland
2026-05-26
