| Quellcodebibliothek Statistik Leitseite products/Sources/formale Sprachen/PVS/Sturm/ (Beweissystem der NASA Version 6.0.9©) Datei vom 28.9.2014 mit Größe 158 kB |
|
Quelle clear_denominators.prfSprache: Lisp |
|||||||||||||||
|
(clear_denominators (posratpair_plus 0 (posratpair_plus-1 nil 3599588076 ("" (grind) nil nil) ((posrat_div_posrat_is_posrat application-judgement "posrat" rationals nil) (posint_times_posint_is_posint application-judgement "posint" integers nil) (mult_divides1 application-judgement "(divides(n))" divides nil) (mult_divides2 application-judgement "(divides(m))" divides nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (+ const-decl "PosRatPair" clear_denominators nil) (posratpair_convert const-decl "posrat" clear_denominators nil)) shostak)) (posratpair_div 0 (posratpair_div-1 nil 3599588176 ("" (grind) nil nil) ((posrat_div_posrat_is_posrat application-judgement "posrat" rationals nil) (posint_times_posint_is_posint application-judgement "posint" integers nil) (mult_divides1 application-judgement "(divides(n))" divides nil) (mult_divides2 application-judgement "(divides(m))" divides nil) (/ const-decl "PosRatPair" clear_denominators nil) (posratpair_convert const-decl "posrat" clear_denominators nil)) shostak)) (PosRatSet_nonempty 0 (PosRatSet_nonempty-1 nil 3599814580 ("" (skeep) (("" (typepred "x") (("" (lemma "rational_pred_ax2") (("" (inst - "x") (("" (skeep -1) (("" (case "i<=0") (("1" (mult-by -1 "1/p") (("1" (assert) nil nil)) nil) ("2" (expand "nonempty?") (("2" (expand "empty?") (("2" (inst - "i+p") (("1" (expand "member") (("1" (expand "PosRatSet") (("1" (inst + "i" "p") (("1" (assert) nil nil)) nil)) nil)) nil) ("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((posrat nonempty-type-eq-decl nil rationals nil) (> const-decl "bool" reals nil) (nonneg_rat nonempty-type-eq-decl nil rationals nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (>= const-decl "bool" reals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (number nonempty-type-decl nil numbers nil) (NOT const-decl "[bool -> bool]" booleans nil) (bool nonempty-type-eq-decl nil booleans nil) (boolean nonempty-type-decl nil booleans nil) (rat nonempty-type-eq-decl nil rationals nil) (<= const-decl "bool" reals nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (int nonempty-type-eq-decl nil integers nil) (rat_div_nzrat_is_rat application-judgement "rat" rationals nil) (nnrat_times_nnrat_is_nnrat application-judgement "nonneg_rat" rationals nil) (rat_times_rat_is_rat application-judgement "rat" rationals nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (posnat nonempty-type-eq-decl nil integers nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (/ const-decl "[numfield, nznum -> numfield]" number_fields nil) (nznum nonempty-type-eq-decl nil number_fields nil) (/= const-decl "boolean" notequal nil) (numfield nonempty-type-eq-decl nil number_fields nil) (nonneg_real nonempty-type-eq-decl nil real_types nil) (both_sides_times_pos_le1_imp formula-decl nil extra_real_props nil) (posrat_div_posrat_is_posrat application-judgement "posrat" rationals nil) (empty? const-decl "bool" sets nil) (member const-decl "bool" sets nil) (PosRatSet const-decl "set[posnat]" clear_denominators nil) (p skolem-const-decl "posnat" clear_denominators nil) (i skolem-const-decl "int" clear_denominators nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (AND const-decl "[bool, bool -> bool]" booleans nil) (int_plus_int_is_int application-judgement "int" integers nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (nonempty? const-decl "bool" sets nil) (rational_pred_ax2 formula-decl nil rational_props nil)) shostak)) (PosRatSet_glb_posnat_TCC1 0 (PosRatSet_glb_posnat_TCC1-1 nil 3599840373 ("" (skeep) (("" (split) (("1" (lemma "PosRatSet_nonempty") (("1" (inst - "x") (("1" (expand "nonempty?") (("1" (expand "empty?") (("1" (skosimp*) (("1" (inst - "x!1") (("1" (grind) nil nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (expand "bounded_below?") (("2" (inst + "-1") (("2" (grind) nil nil)) nil)) nil)) nil)) nil) ((number nonempty-type-decl nil numbers nil) (boolean nonempty-type-decl nil booleans nil) (number_field_pred 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) (rational_pred const-decl "[real -> boolean]" rationals nil) (rational nonempty-type-from-decl nil rationals nil) (bool nonempty-type-eq-decl nil booleans nil) (>= const-decl "bool" reals nil) (nonneg_rat nonempty-type-eq-decl nil rationals nil) (> const-decl "bool" reals nil) (posrat nonempty-type-eq-decl nil rationals nil) (empty? const-decl "bool" sets nil) (posnat nonempty-type-eq-decl nil integers nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (extend const-decl "R" extend nil) (member const-decl "bool" sets nil) (PosRatSet const-decl "set[posnat]" clear_denominators nil) (nonempty? const-decl "bool" sets nil) (PosRatSet_nonempty formula-decl nil clear_denominators nil) (minus_odd_is_odd application-judgement "odd_int" integers nil) (numfield nonempty-type-eq-decl nil number_fields nil) (- const-decl "[numfield -> numfield]" number_fields nil) (NOT const-decl "[bool -> bool]" booleans nil) (FALSE const-decl "bool" booleans nil) (set type-eq-decl nil sets nil) (posrat_div_posrat_is_posrat application-judgement "posrat" rationals nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (lower_bound? const-decl "bool" bounded_real_defs nil) (bounded_below? const-decl "bool" bounded_real_defs nil)) nil)) (PosRatSet_glb_posnat 0 (PosRatSet_glb_posnat-1 nil 3599840375 ("" (skeep) (("" (lemma "glb_nat") (("" (inst?) (("1" (assert) (("1" (skosimp*) (("1" (inst + "n!1") (("1" (assert) (("1" (invoke (name "A" "%1") (! 1 2)) (("1" (replace -1) (("1" (case "n!1 > A") (("1" (typepred "A") (("1" (expand "greatest_lower_bound?" -1) (("1" (flatten) (("1" (inst - "n!1") (("1" (assert) (("1" (hide (-1 -2 -3)) (("1" (hide 2) (("1" (expand "greatest_lower_bound?") (("1" (flatten) (("1" (hide -2) (("1" (expand "lower_bound?") (("1" (skosimp*) (("1" (inst - "s!1") (("1" (expand "extend") (("1" (typepred "s!1") (("1" (expand "extend") (("1" (ground) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (case "NOT n!1 < A") (("1" (assert) nil nil) ("2" (hide +) (("2" (expand "greatest_lower_bound?") (("2" (flatten) (("2" (inst - "A") (("2" (assert) (("2" (hide -) (("2" (typepred "A") (("2" (expand "greatest_lower_bound?") (("2" (flatten) (("2" (hide -2) (("2" (expand "lower_bound?") (("2" (skosimp*) (("2" (inst - "s!1") (("2" (hide 2) (("2" (typepred "s!1") (("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) ("2" (hide 2) (("2" (split) (("1" (grind) nil nil) ("2" (lemma "PosRatSet_nonempty") (("2" (inst?) (("2" (assert) (("2" (expand "nonempty?") (("2" (expand "empty?") (("2" (skosimp*) (("2" (inst - "x!1") (("2" (assert) (("2" (expand "member") (("2" (propax) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((glb_nat formula-decl nil integer_props nil) (PosRatSet_nonempty formula-decl nil clear_denominators nil) (empty? const-decl "bool" sets nil) (member const-decl "bool" sets nil) (= const-decl "[T, T -> boolean]" equalities nil) (bounded_below? const-decl "bool" bounded_real_defs nil) (greatest_lower_bound? const-decl "bool" bounded_real_defs nil) (glb const-decl "{x | greatest_lower_bound?(x, SB)}" bounded_real_defs nil) (FALSE const-decl "bool" booleans nil) (extend const-decl "R" extend nil) (s!1 skolem-const-decl "(extend[real, posnat, bool, FALSE](PosRatSet(x)))" clear_denominators nil) (lower_bound? const-decl "bool" bounded_real_defs nil) (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (NOT const-decl "[bool -> bool]" booleans nil) (s!1 skolem-const-decl "(extend[real, nat, bool, FALSE](PosRatSet(x)))" clear_denominators nil) (posrat_div_posrat_is_posrat application-judgement "posrat" rationals nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (< const-decl "bool" reals nil) (boolean nonempty-type-decl nil booleans nil) (bool nonempty-type-eq-decl nil booleans nil) (AND const-decl "[bool, bool -> bool]" booleans nil) (number nonempty-type-decl nil numbers nil) (number_field_pred 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) (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) (nonneg_int nonempty-type-eq-decl nil integers nil) (IMPLIES const-decl "[bool, bool -> bool]" booleans nil) (nonneg_rat nonempty-type-eq-decl nil rationals nil) (> const-decl "bool" reals nil) (posrat nonempty-type-eq-decl nil rationals nil) (posnat nonempty-type-eq-decl nil integers nil) (set type-eq-decl nil sets nil) (PosRatSet const-decl "set[posnat]" clear_denominators nil) (x skolem-const-decl "posrat" clear_denominators nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (nonempty? const-decl "bool" sets nil)) shostak)) (PosRatMeas_TCC1 0 (PosRatMeas_TCC1-1 nil 3599814898 ("" (assert) (("" (skeep) (("" (lemma "PosRatSet_nonempty") (("" (inst - "x") (("" (split +) (("1" (expand "nonempty?") (("1" (expand "empty?") (("1" (skeep) (("1" (inst - "x_1") (("1" (expand "extend") (("1" (expand "member") (("1" (propax) nil nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (expand "bounded_below?") (("2" (inst + "0") (("2" (expand "lower_bound?") (("2" (skosimp*) (("2" (typepred "s!1") (("2" (expand "extend") (("2" (grind) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((number nonempty-type-decl nil numbers nil) (boolean nonempty-type-decl nil booleans nil) (number_field_pred 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) (rational_pred const-decl "[real -> boolean]" rationals nil) (rational nonempty-type-from-decl nil rationals nil) (bool nonempty-type-eq-decl nil booleans nil) (>= const-decl "bool" reals nil) (nonneg_rat nonempty-type-eq-decl nil rationals nil) (> const-decl "bool" reals nil) (posrat nonempty-type-eq-decl nil rationals nil) (bounded_below? const-decl "bool" bounded_real_defs nil) (lower_bound? const-decl "bool" bounded_real_defs nil) (PosRatSet const-decl "set[posnat]" clear_denominators nil) (set type-eq-decl nil sets nil) (FALSE const-decl "bool" booleans nil) (NOT const-decl "[bool -> bool]" booleans nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (nonempty? const-decl "bool" sets nil) (extend const-decl "R" extend nil) (member const-decl "bool" sets nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (int nonempty-type-eq-decl nil integers nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (posnat nonempty-type-eq-decl nil integers nil) (empty? const-decl "bool" sets nil) (PosRatSet_nonempty formula-decl nil clear_denominators nil)) nil)) (PosRatMeas_TCC2 0 (PosRatMeas_TCC2-1 nil 3599814898 ("" (assert) (("" (skeep) (("" (invoke (name "mmp" "%1") (! 1 2 2 1 1)) (("1" (lemma "glb_nat") (("1" (inst - "extend[real, posnat, bool, FALSE](PosRatSet(x))") (("1" (skosimp*) (("1" (case "mmp = n!1") (("1" (assert) (("1" (typepred "mmp") (("1" (expand "greatest_lower_bound?" -1) (("1" (flatten) (("1" (inst - "1/2") (("1" (assert) (("1" (hide 2) (("1" (expand "lower_bound?" 1) (("1" (skosimp*) (("1" (typepred "s!1") (("1" (expand "extend" -1) (("1" (ground) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide 2) (("2" (typepred "mmp") (("2" (lemma "glb_lem") (("2" (inst - "extend[real, posnat, bool, FALSE](PosRatSet(x))" "n!1") (("2" (assert) (("2" (hide (-1 -3 -4 2)) (("2" (expand "greatest_lower_bound?") (("2" (flatten) (("2" (assert) (("2" (split +) (("1" (hide -2) (("1" (expand "lower_bound?") (("1" (skosimp*) (("1" (inst - "s!1") (("1" (expand "extend") (("1" (expand "restrict") (("1" (typepred "s!1") (("1" (expand "PosRatSet") (("1" (expand "extend") (("1" (grind) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide -1) (("2" (skeep) (("2" (inst - "y") (("2" (assert) (("2" (hide 1) (("2" (expand "lower_bound?") (("2" (skeep) (("2" (inst - "s") (("2" (typepred "s") (("2" (expand "extend") (("2" (expand "restrict") (("2" (grind :exclude "PosRatSet") 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" (hide 2) (("2" (lemma "PosRatSet_nonempty") (("2" (inst?) (("2" (expand "nonempty?") (("2" (expand "empty?") (("2" (skosimp*) (("2" (inst - "x!1") (("2" (expand "member") (("2" (expand "restrict") (("2" (expand "extend") (("2" (propax) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide 2) (("2" (split) (("1" (lemma "PosRatSet_nonempty") (("1" (inst?) (("1" (expand "nonempty?") (("1" (expand "empty?") (("1" (skosimp*) (("1" (inst - "x!1") (("1" (expand "member") (("1" (expand "extend") (("1" (propax) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (expand "bounded_below?") (("2" (inst + "0") (("2" (grind) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((posint_plus_nnint_is_posint application-judgement "posint" integers nil) (glb_nat formula-decl nil integer_props nil) (empty? const-decl "bool" sets nil) (member const-decl "bool" sets nil) (PosRatSet_nonempty formula-decl nil clear_denominators nil) (glb_lem formula-decl nil bounded_real_defs nil) (s skolem-const-decl "(extend[real, nat, bool, FALSE] (restrict[real, nat, boolean] (extend[real, posnat, bool, FALSE](PosRatSet(x)))))" clear_denominators nil) (s!1 skolem-const-decl "(extend[real, posnat, bool, FALSE](PosRatSet(x)))" clear_denominators nil) (posrat_div_posrat_is_posrat application-judgement "posrat" rationals nil) (/ const-decl "[numfield, nznum -> numfield]" number_fields nil) (nznum nonempty-type-eq-decl nil number_fields nil) (/= const-decl "boolean" notequal nil) (numfield nonempty-type-eq-decl nil number_fields nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (lower_bound? const-decl "bool" bounded_real_defs nil) (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (NOT const-decl "[bool -> bool]" booleans nil) (x skolem-const-decl "posrat" clear_denominators nil) (restrict const-decl "R" restrict nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (PosRatSet const-decl "set[posnat]" clear_denominators nil) (posrat nonempty-type-eq-decl nil rationals nil) (nonneg_rat nonempty-type-eq-decl nil rationals nil) (extend const-decl "R" extend nil) (FALSE const-decl "bool" booleans nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (>= const-decl "bool" reals nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (glb const-decl "{x | greatest_lower_bound?(x, SB)}" bounded_real_defs nil) (greatest_lower_bound? const-decl "bool" bounded_real_defs nil) (bounded_below? const-decl "bool" bounded_real_defs nil) (nonempty? const-decl "bool" sets nil) (set type-eq-decl nil sets nil) (bool nonempty-type-eq-decl nil booleans nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (= const-decl "[T, T -> boolean]" equalities nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil) (AND const-decl "[bool, bool -> bool]" booleans nil)) nil)) (PosRatMeas_TCC3 0 (PosRatMeas_TCC3-1 nil 3599840492 ("" (skeep) (("" (lemma "PosRatSet_glb_posnat") (("" (inst - "x") (("" (skosimp*) (("" (replace -3 :dir rl) (("" (replace -2 + :dir rl) (("" (case "FORALL (kk:nat): 10^(kk+1)>=10") (("1" (inst - "pn!1-1") (("1" (assert) nil nil)) nil) ("2" (hide-all-but 1) (("2" (induct "kk") (("1" (grind) nil nil) ("2" (skeep) (("2" (assert) (("2" (expand "^") (("2" (expand "expt" +) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((PosRatSet_glb_posnat formula-decl nil clear_denominators nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (expt def-decl "real" exponentiation nil) (mult_divides2 application-judgement "(divides(m))" divides nil) (mult_divides1 application-judgement "(divides(n))" divides nil) (even_times_int_is_even application-judgement "even_int" integers nil) (posint_times_posint_is_posint application-judgement "posint" integers nil) (posrat_div_posrat_is_posrat application-judgement "posrat" rationals nil) (posnat_expt application-judgement "posnat" exponentiation nil) (even_plus_odd_is_odd application-judgement "odd_int" integers nil) (nat_induction formula-decl nil naturalnumbers nil) (pred type-eq-decl nil defined_types nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (int_minus_int_is_int application-judgement "int" integers nil) (posnat nonempty-type-eq-decl nil integers nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (- const-decl "[numfield, numfield -> numfield]" number_fields nil) (nnrat_exp application-judgement "nnrat" exponentiation nil) (posrat_exp application-judgement "posrat" exponentiation nil) (int_plus_int_is_int application-judgement "int" integers nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (nnint_plus_posint_is_posint application-judgement "posint" integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (int nonempty-type-eq-decl nil integers nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (OR const-decl "[bool, bool -> bool]" booleans nil) (/= const-decl "boolean" notequal nil) (^ const-decl "real" exponentiation nil) (numfield nonempty-type-eq-decl nil number_fields nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (posint_exp application-judgement "posint" exponentiation nil) (posrat nonempty-type-eq-decl nil rationals nil) (> const-decl "bool" reals nil) (nonneg_rat nonempty-type-eq-decl nil rationals nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil)) nil)) (PosRatMeas_increasing 0 (PosRatMeas_increasing-1 nil 3599838300 ("" (skeep) (("" (expand "PosRatMeas" :assert? none) (("" (name "mpx" "glb(extend[real, posnat, bool, FALSE](PosRatSet(x)))") (("" (replace -1) (("" (name "mpy" "glb(extend[real, posnat, bool, FALSE](PosRatSet(y)))") (("" (replace -1) (("" (lemma "PosRatSet_glb_posnat") (("" (inst-cp - "x") (("" (inst - "y") (("" (skolem - "pny") (("" (skolem - "pnx") (("" (assert) (("" (flatten) (("" (case "mpx < mpy") (("1" (case "10^(mpx) <= 10^mpy-10") (("1" (assert) (("1" (lift-if) (("1" (lift-if) (("1" (lift-if) (("1" (assert) nil nil)) nil)) nil)) nil)) nil) ("2" (hide 2) (("2" (case "10^mpy >= 10* 10^mpx AND 10^mpx >= 10") (("1" (flatten) (("1" (assert) nil nil)) nil) ("2" (hide 2) (("2" (case "FORALL (kk:nat): 10^(mpx+1+kk)>=10^(mpx+1)") (("1" (inst - "mpy-mpx-1") (("1" (assert) (("1" (split +) (("1" (expand "^" (-1 1)) (("1" (expand "expt" -1 2) (("1" (propax) nil nil)) nil)) nil) ("2" (case "FORALL (kk:nat): 10^(kk+1)>=10") (("1" (inst - "mpx-1") (("1" (assert) nil nil) ("2" (assert) (("2" (replace -8) (("2" (replace -6 + :dir rl) (("2" (assert) nil nil)) nil)) nil)) nil)) nil) ("2" (hide-all-but 1) (("2" (induct "kk") (("1" (grind) nil nil) ("2" (skeep) (("2" (expand "^") (("2" (expand "expt" +) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (replaces -6) (("2" (replaces -6) (("2" (replaces -3 :dir rl) (("2" (replaces -4 :dir rl) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil) ("2" (induct "kk") (("1" (assert) nil nil) ("2" (skeep) (("2" (assert) (("2" (expand "^" (-1 1)) (("2" (expand "expt" + 1) (("2" (assert) nil nil)) nil)) nil)) nil)) nil) ("3" (replaces -7) (("3" (replace -5 :dir rl) (("3" (assert) nil nil)) nil)) nil) ("4" (replaces -7) (("4" (replace -5 :dir rl) (("4" (assert) nil nil)) nil)) nil) ("5" (replaces -7) (("5" (replace -5 :dir rl) (("5" (assert) nil nil)) nil)) nil) ("6" (replaces -7) (("6" (replace -5 :dir rl) (("6" (assert) nil nil)) nil)) nil) ("7" (replaces -7) (("7" (replace -5 :dir rl) (("7" (assert) nil nil)) nil)) nil) ("8" (replaces -7) (("8" (replace -5 :dir rl) (("8" (assert) nil nil)) nil)) nil) ("9" (replaces -7) (("9" (replace -5 :dir rl) (("9" (assert) nil nil)) nil)) nil)) nil) ("3" (replaces -7) (("3" (replace -5 :dir rl) (("3" (assert) nil nil)) nil)) nil) ("4" (skeep) (("4" (replaces -7) (("4" (replace -5 :dir rl) (("4" (assert) nil nil)) nil)) nil)) nil)) nil)) nil) ("3" (replaces -7) (("3" (replace -5 :dir rl) (("3" (assert) nil nil)) nil)) nil)) nil)) nil) ("3" (replaces -6) (("3" (replace -3 :dir rl) (("3" (assert) nil nil)) nil)) nil) ("4" (replaces -6) (("4" (replace -3 :dir rl) (("4" (assert) nil nil)) nil)) nil)) nil) ("2" (hide 2) (("2" (assert) (("2" (skolem - "PNN") (("2" (typepred "PNN") (("2" (typepred "mpy") (("2" (expand "greatest_lower_bound?") (("2" (inst - "pny") (("2" (assert) (("2" (flatten) (("2" (typepred "mpx") (("2" (expand "greatest_lower_bound?") (("2" (flatten) (("2" (expand "lower_bound?" -1) (("2" (inst - "PNN") (("1" (assert) nil nil) ("2" (hide-all-but (-5 1)) (("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)) nil)) nil)) nil)) nil)) nil)) nil) ((PosRatMeas const-decl "nat" clear_denominators nil) (posint_exp application-judgement "posint" exponentiation nil) (rat_minus_rat_is_rat application-judgement "rat" rationals nil) (nnrat_exp application-judgement "nnrat" exponentiation nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (< const-decl "bool" reals nil) (real_minus_real_is_real application-judgement "real" reals nil) (x skolem-const-decl "posrat" clear_denominators nil) (mpx skolem-const-decl "{x_1 | greatest_lower_bound?(x_1, extend[real, posnat, bool, FALSE] (PosRatSet(x)))}" clear_denominators nil) (y skolem-const-decl "posrat" clear_denominators nil) (mpy skolem-const-decl "{x | greatest_lower_bound?(x, extend[real, posnat, bool, FALSE] (PosRatSet(y)))}" clear_denominators nil) (expt def-decl "real" exponentiation nil) (mult_divides2 application-judgement "(divides(m))" divides nil) (mult_divides1 application-judgement "(divides(n))" divides nil) (even_times_int_is_even application-judgement "even_int" integers nil) (posint_times_posint_is_posint application-judgement "posint" integers nil) (posrat_div_posrat_is_posrat application-judgement "posrat" rationals nil) (posnat_expt application-judgement "posnat" exponentiation nil) (even_plus_odd_is_odd application-judgement "odd_int" integers nil) (nat_induction formula-decl nil naturalnumbers nil) (pred type-eq-decl nil defined_types nil) (int_minus_int_is_int application-judgement "int" integers nil) (nnint_plus_posint_is_posint application-judgement "posint" integers nil) (int_plus_int_is_int application-judgement "int" integers nil) (minus_odd_is_odd application-judgement "odd_int" integers nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (real_plus_real_is_real application-judgement "real" reals nil) (IMPLIES const-decl "[bool, bool -> bool]" booleans nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (* const-decl "[numfield, numfield -> numfield]" number_fields nil) (nnrat_times_nnrat_is_nnrat application-judgement "nonneg_rat" rationals nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (AND const-decl "[bool, bool -> bool]" booleans nil) (- const-decl "[numfield, numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (^ const-decl "real" exponentiation nil) (/= const-decl "boolean" notequal nil) (OR const-decl "[bool, bool -> bool]" booleans nil) (<= const-decl "bool" reals nil) (NOT const-decl "[bool -> bool]" booleans nil) (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (PNN skolem-const-decl "(PosRatSet(x))" clear_denominators nil) (lower_bound? const-decl "bool" bounded_real_defs nil) (PosRatSet_glb_posnat formula-decl nil clear_denominators nil) (number nonempty-type-decl nil numbers nil) (boolean nonempty-type-decl nil booleans nil) (= const-decl "[T, T -> boolean]" equalities nil) (number_field_pred 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) (bool nonempty-type-eq-decl nil booleans nil) (set type-eq-decl nil sets nil) (nonempty? const-decl "bool" sets nil) (bounded_below? const-decl "bool" bounded_real_defs nil) (greatest_lower_bound? const-decl "bool" bounded_real_defs nil) (glb const-decl "{x | greatest_lower_bound?(x, SB)}" bounded_real_defs 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) (nonneg_int nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (posnat nonempty-type-eq-decl nil integers nil) (FALSE const-decl "bool" booleans nil) (extend const-decl "R" extend nil) (nonneg_rat nonempty-type-eq-decl nil rationals nil) (posrat nonempty-type-eq-decl nil rationals nil) (PosRatSet const-decl "set[posnat]" clear_denominators nil)) shostak)) (PosRatMeas_glb_minus_posnat_TCC1 0 (PosRatMeas_glb_minus_posnat_TCC1-1 nil 3599903317 ("" (subtype-tcc) nil nil) ((boolean nonempty-type-decl nil booleans nil) (bool nonempty-type-eq-decl nil booleans nil) (NOT const-decl "[bool -> bool]" booleans nil) (number nonempty-type-decl nil numbers nil) (number_field_pred 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) (nonneg_int nonempty-type-eq-decl nil integers nil) (posnat nonempty-type-eq-decl nil integers nil) (nonneg_rat nonempty-type-eq-decl nil rationals nil) (posrat nonempty-type-eq-decl nil rationals nil) (rat_minus_rat_is_rat application-judgement "rat" rationals nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil)) nil)) (PosRatMeas_glb_minus_posnat_TCC2 0 (PosRatMeas_glb_minus_posnat_TCC2-1 nil 3599903317 ("" (lemma "PosRatSet_nonempty") (("" (skeep) (("" (inst - "x-pn") (("1" (assert) (("1" (split) (("1" (expand "nonempty?") (("1" (expand "empty?") (("1" (skosimp*) (("1" (inst - "x!1") (("1" (expand "member") (("1" (expand "extend") (("1" (propax) nil nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (expand "bounded_below?") (("2" (inst + "-1") (("2" (grind) nil nil)) nil)) nil)) nil)) nil) ("2" (assert) nil nil)) nil)) nil)) nil) ((bounded_below? const-decl "bool" bounded_real_defs nil) (lower_bound? const-decl "bool" bounded_real_defs nil) (PosRatSet const-decl "set[posnat]" clear_denominators nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (posrat_div_posrat_is_posrat application-judgement "posrat" rationals nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (NOT const-decl "[bool -> bool]" booleans nil) (FALSE const-decl "bool" booleans nil) (set type-eq-decl nil sets nil) (- const-decl "[numfield -> numfield]" number_fields nil) (minus_odd_is_odd application-judgement "odd_int" integers nil) (nonempty? const-decl "bool" sets nil) (member const-decl "bool" sets nil) (extend const-decl "R" extend nil) (empty? const-decl "bool" sets nil) (boolean nonempty-type-decl nil booleans nil) (bool nonempty-type-eq-decl nil booleans nil) (AND const-decl "[bool, bool -> bool]" booleans nil) (number nonempty-type-decl nil numbers nil) (number_field_pred 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) (numfield nonempty-type-eq-decl nil number_fields nil) (- const-decl "[numfield, numfield -> numfield]" number_fields nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (rational nonempty-type-from-decl nil rationals nil) (nonneg_rat nonempty-type-eq-decl nil rationals nil) (> const-decl "bool" reals nil) (posrat nonempty-type-eq-decl nil rationals nil) (x skolem-const-decl "posrat" clear_denominators nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (int nonempty-type-eq-decl nil integers nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (posnat nonempty-type-eq-decl nil integers nil) (pn skolem-const-decl "posnat" clear_denominators nil) (rat_minus_rat_is_rat application-judgement "rat" rationals nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (PosRatSet_nonempty formula-decl nil clear_denominators nil)) nil)) (PosRatMeas_glb_minus_posnat 0 (PosRatMeas_glb_minus_posnat-1 nil 3599903321 ("" (skeep) (("" (invoke (name "mxi" "%1") (! 1 1)) (("1" (invoke (name "mx" "%1") (! 1 2 1)) (("1" (replace -1) (("1" (replace -2) (("1" (lemma "PosRatSet_glb_posnat") (("1" (inst-cp - "x") (("1" (inst - "x-pn") (("1" (skolem - "pxi") (("1" (skolem - "px") (("1" (flatten) (("1" (replace -5) (("1" (replace -6) (("1" (copy -3) (("1" (expand "PosRatSet" -1) (("1" (skeep -1) (("1" (case "mxi <= mx - pn2*pn") (("1" (case "pn2>=1") (("1" (mult-by -1 "pn") (("1" (assert) nil nil)) nil) ("2" (assert) nil nil)) nil) ("2" (hide 2) (("2" (typepred "mxi") (("2" (expand "greatest_lower_bound?") (("2" (flatten) (("2" (hide -2) (("2" (expand "lower_bound?") (("2" (inst - "mx - pn2*pn") (("2" (hide 2) (("2" (expand "extend" +) (("2" (assert) (("2" (split +) (("1" (flatten) (("1" (expand "PosRatSet" 1) (("1" (inst + "pn1-pn2*pn" "pn2") (("1" (assert) nil nil) ("2" (assert) (("2" (case "pn1 > pn2*pn") (("1" (assert) nil nil) ("2" (hide 2) (("2" (replace -5) (("2" (cross-mult -) (("2" (cross-mult -) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (assert) (("2" (replace -4 :dir rl) (("2" (replace -6 :dir rl) (("2" (assert) (("2" (case "px > pn2*pn") (("1" (assert) nil nil) ("2" (hide 2) (("2" (replace -2 +) (("2" (case "pn1 > pn*pn2") (("1" (assert) nil nil) ("2" (hide 2) (("2" (replace -1) (("2" (cross-mult -) 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)) nil)) nil)) nil)) nil) ("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (assert) nil nil)) nil)) nil) ((real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (rat_minus_rat_is_rat application-judgement "rat" rationals nil) (number nonempty-type-decl nil numbers nil) (boolean nonempty-type-decl nil booleans nil) (= const-decl "[T, T -> boolean]" equalities nil) (number_field_pred 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) (bool nonempty-type-eq-decl nil booleans nil) (set type-eq-decl nil sets nil) (nonempty? const-decl "bool" sets nil) (bounded_below? const-decl "bool" bounded_real_defs nil) (greatest_lower_bound? const-decl "bool" bounded_real_defs nil) (glb const-decl "{x | greatest_lower_bound?(x, SB)}" bounded_real_defs 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) (nonneg_int nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (posnat nonempty-type-eq-decl nil integers nil) (FALSE const-decl "bool" booleans nil) (extend const-decl "R" extend nil) (nonneg_rat nonempty-type-eq-decl nil rationals nil) (posrat nonempty-type-eq-decl nil rationals nil) (PosRatSet const-decl "set[posnat]" clear_denominators nil) (numfield nonempty-type-eq-decl nil number_fields nil) (- const-decl "[numfield, numfield -> numfield]" number_fields nil) (minus_odd_is_odd application-judgement "odd_int" integers nil) (PosRatSet_glb_posnat formula-decl nil clear_denominators nil) (x skolem-const-decl "posrat" clear_denominators nil) (pn skolem-const-decl "posnat" clear_denominators nil) (mx skolem-const-decl "{x_1 | greatest_lower_bound?(x_1, extend[real, posnat, bool, FALSE] (PosRatSet(x)))}" clear_denominators nil) (pn2 skolem-const-decl "posnat" clear_denominators nil) (div_cancel4 formula-decl nil real_props nil) (/= const-decl "boolean" notequal nil) (nonzero_real nonempty-type-eq-decl nil reals nil) (posrat_times_posrat_is_posrat application-judgement "posrat" rationals nil) (div_mult_pos_gt1 formula-decl nil extra_real_props nil) (posreal nonempty-type-eq-decl nil real_types nil) (rat_div_nzrat_is_rat application-judgement "rat" rationals nil) (pn1 skolem-const-decl "posnat" clear_denominators nil) (AND const-decl "[bool, bool -> bool]" booleans nil) (int_minus_int_is_int application-judgement "int" integers nil) (lower_bound? const-decl "bool" bounded_real_defs nil) (NOT const-decl "[bool -> bool]" booleans nil) (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (posrat_div_posrat_is_posrat application-judgement "posrat" rationals nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (mult_divides2 application-judgement "(divides(m))" divides nil) (mult_divides1 application-judgement "(divides(n))" divides nil) (posint_times_posint_is_posint application-judgement "posint" integers nil) (nonneg_real nonempty-type-eq-decl nil real_types nil) (both_sides_times_pos_ge1_imp formula-decl nil extra_real_props nil) (* const-decl "[numfield, numfield -> numfield]" number_fields nil) (<= const-decl "bool" reals nil) (real_minus_real_is_real application-judgement "real" reals nil)) nil)) (compute_posratpair_TCC1 0 (compute_posratpair_TCC1-1 nil 3599821439 ("" (subtype-tcc) nil nil) ((boolean nonempty-type-decl nil booleans nil) (bool nonempty-type-eq-decl nil booleans nil) (NOT const-decl "[bool -> bool]" booleans nil) (number nonempty-type-decl nil numbers nil) (number_field_pred 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) (nonneg_rat nonempty-type-eq-decl nil rationals nil) (> const-decl "bool" reals nil) (posrat nonempty-type-eq-decl nil rationals nil)) nil)) (compute_posratpair_TCC2 0 (compute_posratpair_TCC2-1 nil 3599821439 ("" (subtype-tcc) nil nil) ((boolean nonempty-type-decl nil booleans nil) (bool nonempty-type-eq-decl nil booleans nil) (NOT const-decl "[bool -> bool]" booleans nil) (number nonempty-type-decl nil numbers nil) (number_field_pred 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) (nonneg_rat nonempty-type-eq-decl nil rationals nil) (> const-decl "bool" reals nil) (posrat nonempty-type-eq-decl nil rationals nil) (posratpair_convert const-decl "posrat" clear_denominators nil) (nonneg_floor_is_nat application-judgement "nat" floor_ceil nil)) nil)) (compute_posratpair_TCC3 0 (compute_posratpair_TCC3-1 nil 3599821439 ("" (subtype-tcc) nil nil) ((boolean nonempty-type-decl nil booleans nil) (bool nonempty-type-eq-decl nil booleans nil) (NOT const-decl "[bool -> bool]" booleans nil) (number nonempty-type-decl nil numbers nil) (number_field_pred 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) (nonneg_rat nonempty-type-eq-decl nil rationals nil) (> const-decl "bool" reals nil) (posrat nonempty-type-eq-decl nil rationals nil) (nonneg_floor_is_nat application-judgement "nat" floor_ceil nil) (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil)) nil)) (compute_posratpair_TCC4 0 (compute_posratpair_TCC4-1 nil 3599821439 ("" (subtype-tcc) nil nil) ((boolean nonempty-type-decl nil booleans nil) (bool nonempty-type-eq-decl nil booleans nil) (NOT const-decl "[bool -> bool]" booleans nil) (number nonempty-type-decl nil numbers nil) (number_field_pred 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) (nonneg_rat nonempty-type-eq-decl nil rationals nil) (> const-decl "bool" reals nil) (posrat nonempty-type-eq-decl nil rationals nil) (rat_minus_rat_is_rat application-judgement "rat" rationals nil) (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (nonneg_floor_is_nat application-judgement "nat" floor_ceil nil)) nil)) (compute_posratpair_TCC5 0 (compute_posratpair_TCC5-1 nil 3599821439 ("" (skeep) (("" (expand "PosRatMeas") (("" (assert) (("" (lemma "PosRatMeas_glb_minus_posnat") (("" (inst?) (("" (assert) (("" (name "pnn" "floor(x)") (("" (replace -1) (("" (invoke (name "pe" "%1") (! -2 1)) (("1" (replace -1) (("1" (invoke (name "pz" "%1") (! -3 2 1)) (("1" (replace -1) (("1" (lemma "PosRatSet_glb_posnat") (("1" (inst-cp - "x") (("1" (inst - "x-pnn") (("1" (skolem - "epe") (("1" (skolem - "epz") (("1" (flatten) (("1" (assert) (("1" (lemma "both_sides_expt_gt1_lt_aux") (("1" (inst - "10" "pe-1" "pz-1") (("1" (expand "^" +) (("1" (assert) (("1" (replace -6) (("1" (replace -7) (("1" (replace -3 :dir rl) (("1" (replace -5 :dir rl) (("1" (assert) (("1" (case "EXISTS (k1:nat,k2:nat): expt(10,epe)=k1 AND expt(10,epz)=k2") (("1" (skeep -1) (("1" (assert) (("1" (case "NOT expt(10,epe) = expt(10,epz)-1") (("1" (assert) (("1" (replaces -1) (("1" (replaces -1) (("1" (assert) (("1" (hide-all-but (-1 +)) (("1" (hide 2) (("1" (case "FORALL (a1,a2:nat): a1<a2 IMPLIES a1=a2-1 OR a1<a2-1") (("1" (inst - "k1" "k2") (("1" (assert) nil nil)) nil) ("2" (hide-all-but 1) (("2" (grind) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (case "NOT divides(10,1)") (("1" (expand "divides" 1) (("1" (expand "expt" -1) (("1" (inst + "expt(10, epz - 1) - expt(10, epe - 1)") (("1" (assert) nil nil)) nil)) nil)) nil) ("2" (hide-all-but -1) (("2" (expand "divides") (("2" (skosimp*) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (inst + "expt(10,epe)" "expt(10,epz)") nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (assert) (("2" (replaces -5) (("2" (replaces -4 :dir rl) (("2" (assert) nil nil)) nil)) nil)) nil) ("3" (replaces -6) (("3" (replaces -2 :dir rl) (("3" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((nonneg_floor_is_nat application-judgement "nat" floor_ceil nil) (PosRatMeas const-decl "nat" clear_denominators nil) (PosRatMeas_glb_minus_posnat formula-decl nil clear_denominators nil) (minus_odd_is_odd application-judgement "odd_int" integers nil) (both_sides_expt_gt1_lt_aux formula-decl nil exponentiation nil) (posint_exp application-judgement "posint" exponentiation nil) (^ const-decl "real" exponentiation nil) (NOT const-decl "[bool -> bool]" booleans nil) (OR const-decl "[bool, bool -> bool]" booleans nil) (IMPLIES const-decl "[bool, bool -> bool]" booleans nil) (even_times_int_is_even application-judgement "even_int" integers nil) (mult_divides1 application-judgement "(divides(n))" divides nil) (mult_divides2 application-judgement "(divides(m))" divides nil) (posint_times_posint_is_posint application-judgement "posint" integers nil) (even_minus_odd_is_odd application-judgement "odd_int" integers nil) (divides const-decl "bool" divides nil) (expt def-decl "real" exponentiation nil) (posnat_expt application-judgement "posnat" exponentiation nil) (int_minus_int_is_int application-judgement "int" integers nil) (real_plus_real_is_real application-judgement "real" reals nil) (nonneg_real nonempty-type-eq-decl nil real_types nil) (posreal nonempty-type-eq-decl nil real_types nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (pz skolem-const-decl "{x_1 | greatest_lower_bound?(x_1, extend[real, posnat, bool, FALSE] (PosRatSet(x)))}" clear_denominators nil) (pe skolem-const-decl "{x_1 | greatest_lower_bound?(x_1, extend[real, posnat, bool, FALSE] (PosRatSet(x - pnn)))}" clear_denominators nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (real_minus_real_is_real application-judgement "real" reals nil) (pnn skolem-const-decl "{i | i <= x & x < 1 + i}" clear_denominators nil) (x skolem-const-decl "posrat" clear_denominators nil) (PosRatSet_glb_posnat formula-decl nil clear_denominators nil) (- const-decl "[numfield, numfield -> numfield]" number_fields nil) (PosRatSet const-decl "set[posnat]" clear_denominators nil) (extend const-decl "R" extend nil) (FALSE const-decl "bool" booleans nil) (glb const-decl "{x | greatest_lower_bound?(x, SB)}" bounded_real_defs nil) (greatest_lower_bound? const-decl "bool" bounded_real_defs nil) (bounded_below? const-decl "bool" bounded_real_defs nil) (nonempty? const-decl "bool" sets nil) (set type-eq-decl nil sets nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (= const-decl "[T, T -> boolean]" equalities nil) (posrat nonempty-type-eq-decl nil rationals nil) (nonneg_rat nonempty-type-eq-decl nil rationals nil) (floor const-decl "{i | i <= x & x < i + 1}" floor_ceil nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (< const-decl "bool" reals nil) (<= const-decl "bool" reals nil) (AND const-decl "[bool, bool -> bool]" booleans nil) (integer nonempty-type-from-decl nil integers nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil) (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (nnrat_exp application-judgement "nnrat" exponentiation nil) (rat_minus_rat_is_rat application-judgement "rat" rationals nil)) nil)) (compute_posratpair_TCC6 0 (compute_posratpair_TCC6-1 nil 3599821439 ("" (skeep) (("" (typepred "v(x-floor(x))") (("1" (expand "posratpair_convert") (("1" (name "d" "floor(x)") (("1" (replaces -1) (("1" (assert) (("1" (grind) nil nil)) nil)) nil)) nil)) nil) ("2" (assert) nil nil)) nil)) nil) ((floor const-decl "{i | i <= x & x < i + 1}" floor_ceil nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (<= const-decl "bool" reals nil) (AND const-decl "[bool, bool -> bool]" booleans nil) (integer nonempty-type-from-decl nil integers nil) (- const-decl "[numfield, numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (PosRatMeas const-decl "nat" clear_denominators nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (< const-decl "bool" reals nil) (posratpair_convert const-decl "posrat" clear_denominators nil) (posrat nonempty-type-eq-decl nil rationals nil) (> const-decl "bool" reals nil) (nonneg_rat nonempty-type-eq-decl nil rationals nil) (>= const-decl "bool" reals nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (PosRatPair type-eq-decl nil clear_denominators nil) (posnat nonempty-type-eq-decl nil integers nil) (= const-decl "[T, T -> boolean]" equalities nil) (number nonempty-type-decl nil numbers nil) (NOT const-decl "[bool -> bool]" booleans nil) (bool nonempty-type-eq-decl nil booleans nil) (boolean nonempty-type-decl nil booleans nil) (rat_minus_rat_is_rat application-judgement "rat" rationals nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (posrat_div_posrat_is_posrat application-judgement "posrat" rationals nil) (nnint_plus_posint_is_posint application-judgement "posint" integers nil) (nnint_times_nnint_is_nnint application-judgement "nonneg_int" integers nil) (mult_divides1 application-judgement "(divides(n))" divides nil) (mult_divides2 application-judgement "(divides(m))" divides nil) (posint_times_posint_is_posint application-judgement "posint" integers nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (+ const-decl "PosRatPair" clear_denominators nil) (nonneg_floor_is_nat application-judgement "nat" floor_ceil nil)) nil)) (compute_posratpair_TCC7 0 (compute_posratpair_TCC7-1 nil 3599821439 ("" (skeep) (("" (expand "PosRatMeas") (("" (assert) (("" (case "NOT 1/x>=1") (("1" (cross-mult 1) nil nil) ("2" (assert) (("2" (case "PosRatSet(1/x) = PosRatSet(x)") (("1" (assert) nil nil) ("2" (hide 4) (("2" (hide (-1 3)) (("2" (case "FORALL (y): FORALL (N:posnat): PosRatSet(y)(N) IMPLIES PosRatSet(1/y)(N)") (("1" (decompose-equality +) (("1" (iff) (("1" (ground) (("1" (inst - "1/x") (("1" (inst - "x!1") (("1" (assert) nil nil)) nil)) nil) ("2" (inst - "x") (("2" (inst - "x!1") (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide-all-but 1) (("2" (skeep) (("2" (skeep) (("2" (expand "PosRatSet") (("2" (skeep -) (("2" (inst + "pn2" "pn1") (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((PosRatMeas const-decl "nat" clear_denominators nil) (posrat nonempty-type-eq-decl nil rationals nil) (> const-decl "bool" reals nil) (nonneg_rat nonempty-type-eq-decl nil rationals nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (/ const-decl "[numfield, nznum -> numfield]" number_fields nil) (nznum nonempty-type-eq-decl nil number_fields nil) (/= const-decl "boolean" notequal nil) (numfield nonempty-type-eq-decl nil number_fields nil) (>= const-decl "bool" reals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (number nonempty-type-decl nil numbers nil) (NOT const-decl "[bool -> bool]" booleans nil) (bool nonempty-type-eq-decl nil booleans nil) (boolean nonempty-type-decl nil booleans nil) (posreal nonempty-type-eq-decl nil real_types nil) (nonneg_real nonempty-type-eq-decl nil real_types nil) (posrat_times_posrat_is_posrat application-judgement "posrat" rationals nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (div_mult_pos_ge1 formula-decl nil real_props nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (int nonempty-type-eq-decl nil integers nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (posnat nonempty-type-eq-decl nil integers nil) (set type-eq-decl nil sets nil) (= const-decl "[T, T -> boolean]" equalities nil) (PosRatSet const-decl "set[posnat]" clear_denominators nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (IMPLIES const-decl "[bool, bool -> bool]" booleans nil) (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (nonneg_floor_is_nat application-judgement "nat" floor_ceil nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (nnrat_exp application-judgement "nnrat" exponentiation nil) (rat_minus_rat_is_rat application-judgement "rat" rationals nil) (posrat_div_posrat_is_posrat application-judgement "posrat" rationals nil)) nil)) (compute_posratpair_TCC8 0 (compute_posratpair_TCC8-1 nil 3599821439 ("" (skeep) (("" (typepred "v(1/x)") (("" (rewrite "posratpair_div" :dir rl) (("" (replaces -1) (("" (expand "posratpair_convert") (("" (assert) nil nil)) nil)) nil)) nil)) nil)) nil) ((/ const-decl "[numfield, nznum -> numfield]" number_fields nil) (nznum nonempty-type-eq-decl nil number_fields nil) (/= const-decl "boolean" notequal nil) (numfield nonempty-type-eq-decl nil number_fields nil) (PosRatMeas const-decl "nat" clear_denominators nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (< const-decl "bool" reals nil) (posratpair_convert const-decl "posrat" clear_denominators nil) (posrat nonempty-type-eq-decl nil rationals nil) (> const-decl "bool" reals nil) (nonneg_rat nonempty-type-eq-decl nil rationals nil) (>= const-decl "bool" reals nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (PosRatPair type-eq-decl nil clear_denominators nil) (posnat nonempty-type-eq-decl nil integers nil) (= const-decl "[T, T -> boolean]" equalities nil) (number nonempty-type-decl nil numbers nil) (NOT const-decl "[bool -> bool]" booleans nil) (bool nonempty-type-eq-decl nil booleans nil) (boolean nonempty-type-decl nil booleans nil) (posrat_div_posrat_is_posrat application-judgement "posrat" rationals nil) (nonneg_floor_is_nat application-judgement "nat" floor_ceil nil) (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (posratpair_div formula-decl nil clear_denominators nil)) nil)) (rat_poly_to_int_rec_TCC1 0 (rat_poly_to_int_rec_TCC1-1 nil 3599920945 ("" (skeep) (("" (split) (("1" (inst + "1") (("1" (assert) nil nil)) nil) ("2" (assert) (("2" (skeep) (("2" (rewrite "one_divides") nil nil)) nil)) nil)) nil)) nil) ((posrat nonempty-type-eq-decl nil rationals nil) (> const-decl "bool" reals nil) (nonneg_rat nonempty-type-eq-decl nil rationals nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil) (upto nonempty-type-eq-decl nil naturalnumbers nil) (<= const-decl "bool" reals nil) (rat nonempty-type-eq-decl nil rationals nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (one_divides formula-decl nil divides nil)) nil)) (rat_poly_to_int_rec_TCC2 0 (rat_poly_to_int_rec_TCC2-1 nil 3599920945 ("" (skeep) (("" (assert) (("" (skeep) (("" (assert) (("" (case "NOT thisden*aq(0)/=0") (("1" (assert) nil nil) ("2" (split +) (("1" (grind) nil nil) ("2" (grind) nil nil) ("3" (flatten) (("3" (case "integer_pred(thisden*aq(0))") (("1" (case "EXISTS (kk:int): thisden*aq(0)=kk") (("1" (skeep -1) (("1" (replaces -1 +) (("1" (grind) nil nil)) nil)) nil) ("2" (inst + "thisden*aq(0)") nil nil)) nil) ("2" (hide 2) (("2" (typepred "compute_posratpair(abs(aq(0)))") (("2" (expand "posratpair_convert") (("2" (replace -3 :dir rl) (("2" (case "aq(0) > 0") (("1" (expand "abs") (("1" (assert) nil nil)) nil) ("2" (expand "abs") (("2" (assert) (("2" (cross-mult -1) (("2" (assert) (("2" (neg-formula -1) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((rat_abs_is_nonneg application-judgement "{r: nonneg_rat | r >= q}" real_defs nil) (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs nil) (minus_rat_is_rat application-judgement "rat" rationals nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (thisden skolem-const-decl "posnat" clear_denominators nil) (aq skolem-const-decl "[nat -> rat]" clear_denominators nil) (minus_int_is_int application-judgement "int" integers nil) (int_abs_is_nonneg application-judgement "{j: nonneg_int | j >= i}" real_defs nil) (= const-decl "[T, T -> boolean]" equalities nil) (- const-decl "[numfield -> numfield]" number_fields nil) (AND const-decl "[bool, bool -> bool]" booleans nil) (nonneg_real nonempty-type-eq-decl nil real_types nil) (compute_posratpair def-decl "{prp | posratpair_convert(prp) = x}" clear_denominators nil) (posratpair_convert const-decl "posrat" clear_denominators nil) (posrat nonempty-type-eq-decl nil rationals nil) (nonneg_rat nonempty-type-eq-decl nil rationals nil) (PosRatPair type-eq-decl nil clear_denominators nil) (div_cancel3 formula-decl nil real_props nil) (nonzero_real nonempty-type-eq-decl nil reals nil) (bijective? const-decl "bool" functions nil) (id const-decl "(bijective?[T, T])" identity nil) (TRUE const-decl "bool" booleans nil) (minus_odd_is_odd application-judgement "odd_int" integers nil) (both_sides_times1_imp formula-decl nil extra_real_props nil) (nzint_times_nzint_is_nzint application-judgement "nzint" integers nil) (mult_divides1 application-judgement "(divides(n))" divides nil) (mult_divides2 application-judgement "(divides(m))" divides nil) (minus_nzint_is_nzint application-judgement "nzint" integers nil) (posint_times_posint_is_posint application-judgement "posint" integers nil) (neg_neg formula-decl nil extra_tegies nil) (neg_mult formula-decl nil extra_tegies nil) (mult_neg formula-decl nil extra_tegies nil) (posrat_div_posrat_is_posrat application-judgement "posrat" rationals nil) (boolean nonempty-type-decl nil booleans nil) (bool nonempty-type-eq-decl nil booleans nil) (NOT const-decl "[bool -> bool]" booleans nil) (number nonempty-type-decl nil numbers nil) (/= const-decl "boolean" notequal nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (* const-decl "[numfield, numfield -> numfield]" 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) (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) (nonneg_int nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (posnat nonempty-type-eq-decl nil integers nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (rat nonempty-type-eq-decl nil rationals nil) (rat_times_rat_is_rat application-judgement "rat" rationals nil)) nil)) (rat_poly_to_int_rec_TCC3 0 (rat_poly_to_int_rec_TCC3-1 nil 3599920945 ("" (skeep) (("" (skeep) (("" (assert) (("" (split) (("1" (inst + "thisden") (("1" (skosimp*) nil nil)) nil) ("2" (skeep) (("2" (case "NOT j = 0") (("1" (assert) nil nil) ("2" (replaces -1) (("2" (replaces -1) (("2" (assert) (("2" (rewrite "abs_mult") (("2" (typepred "compute_posratpair(abs(aq(0)))") (("2" (expand "posratpair_convert") (("2" (replace -3 :dir rl) (("2" (cross-mult -1) (("2" (case "aq(0) > 0") (("1" (expand "abs") (("1" (assert) (("1" (expand "divides") (("1" (inst + "1") (("1" (assert) nil nil)) nil)) nil)) nil)) nil) ("2" (expand "abs") (("2" (assert) (("2" (neg-formula -1) (("2" (assert) (("2" (expand "divides") (("2" (inst + "-1") (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((posnat nonempty-type-eq-decl nil integers nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (posrat nonempty-type-eq-decl nil rationals nil) (> const-decl "bool" reals nil) (nonneg_rat nonempty-type-eq-decl nil rationals nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil) (upto nonempty-type-eq-decl nil naturalnumbers nil) (<= const-decl "bool" reals nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (= const-decl "[T, T -> boolean]" equalities nil) (NOT const-decl "[bool -> bool]" booleans nil) (rat nonempty-type-eq-decl nil rationals nil) (abs_mult formula-decl nil real_props nil) (nzint_abs_is_pos application-judgement "{j: posint | j >= i}" real_defs nil) (nnrat_times_nnrat_is_nnrat application-judgement "nonneg_rat" rationals nil) (abs_nat_rew formula-decl nil abs_rews "ints/") (posrat_div_posrat_is_posrat application-judgement "posrat" rationals nil) (div_cancel3 formula-decl nil real_props nil) (/= const-decl "boolean" notequal nil) (nonzero_real nonempty-type-eq-decl nil reals nil) (TRUE const-decl "bool" booleans nil) (id const-decl "(bijective?[T, T])" identity nil) (bijective? const-decl "bool" functions nil) (neg_neg formula-decl nil extra_tegies nil) (neg_mult formula-decl nil extra_tegies nil) (mult_neg formula-decl nil extra_tegies nil) (nzint_times_nzint_is_nzint application-judgement "nzint" integers nil) (mult_divides1 application-judgement "(divides(n))" divides nil) (mult_divides2 application-judgement "(divides(m))" divides nil) (minus_nzint_is_nzint application-judgement "nzint" integers nil) (posint_times_posint_is_posint application-judgement "posint" integers nil) (minus_odd_is_odd application-judgement "odd_int" integers nil) (both_sides_times1_imp formula-decl nil extra_real_props nil) (* const-decl "[numfield, numfield -> numfield]" number_fields nil) (divides const-decl "bool" divides nil) (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (minus_rat_is_rat application-judgement "rat" rationals nil) (PosRatPair type-eq-decl nil clear_denominators nil) (posratpair_convert const-decl "posrat" clear_denominators nil) (compute_posratpair def-decl "{prp | posratpair_convert(prp) = x}" clear_denominators nil) (nonneg_real nonempty-type-eq-decl nil real_types nil) (AND const-decl "[bool, bool -> bool]" booleans nil) (numfield nonempty-type-eq-decl nil number_fields nil) (- const-decl "[numfield -> numfield]" number_fields nil) (abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs nil) (rat_abs_is_nonneg application-judgement "{r: nonneg_rat | r >= q}" real_defs nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (rat_times_rat_is_rat application-judgement "rat" rationals nil)) nil)) (rat_poly_to_int_rec_TCC4 0 (rat_poly_to_int_rec_TCC4-1 nil 3599920945 ("" (subtype-tcc) nil nil) ((boolean nonempty-type-decl nil booleans nil) (bool nonempty-type-eq-decl nil booleans nil) (NOT const-decl "[bool -> bool]" booleans nil) (number nonempty-type-decl nil numbers nil) (number_field_pred 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) (nat nonempty-type-eq-decl nil naturalnumbers nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (rat_abs_is_nonneg application-judgement "{r: nonneg_rat | r >= q}" real_defs nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil)) nil)) (rat_poly_to_int_rec_TCC5 0 (rat_poly_to_int_rec_TCC5-1 nil 3599920945 ("" (subtype-tcc) nil nil) ((boolean nonempty-type-decl nil booleans nil) (bool nonempty-type-eq-decl nil booleans nil) (NOT const-decl "[bool -> bool]" booleans nil) (number nonempty-type-decl nil numbers nil) (number_field_pred 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) (nat nonempty-type-eq-decl nil naturalnumbers nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (int_minus_int_is_int application-judgement "int" integers nil)) nil)) (rat_poly_to_int_rec_TCC6 0 (rat_poly_to_int_rec_TCC6-1 nil 3599920945 ("" (termination-tcc) nil nil) nil nil)) (rat_poly_to_int_rec_TCC7 0 (rat_poly_to_int_rec_TCC7-1 nil 3599920945 ("" (skeep) (("" (assert) (("" (hide 2) (("" (split) (("1" (typepred "v(aq,n-1)") (("1" (propax) nil nil)) nil) ("2" (skeep) (("2" (typepred "v(aq,n-1)") (("2" (inst -2 "j") (("2" (assert) (("2" (skeep -1) (("2" (inst - "n") (("2" (assert) (("2" (replace -2) (("2" (assert) (("2" (case "n = j") (("1" (replaces -1) (("1" (replace -1) (("1" (rewrite "divides_zero") nil nil)) nil)) nil) ("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (int_minus_int_is_int application-judgement "int" integers nil) (boolean nonempty-type-decl nil booleans nil) (bool nonempty-type-eq-decl nil booleans nil) (NOT const-decl "[bool -> bool]" booleans nil) (number nonempty-type-decl nil numbers nil) (number_field_pred 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) (rational_pred const-decl "[real -> boolean]" rationals nil) (rational nonempty-type-from-decl nil rationals nil) (>= const-decl "bool" reals nil) (nonneg_rat nonempty-type-eq-decl nil rationals nil) (> const-decl "bool" reals nil) (posrat nonempty-type-eq-decl nil rationals nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (int nonempty-type-eq-decl nil integers nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (= const-decl "[T, T -> boolean]" equalities nil) (rat nonempty-type-eq-decl nil rationals nil) (< const-decl "bool" reals nil) (posnat nonempty-type-eq-decl nil integers nil) (AND const-decl "[bool, bool -> bool]" booleans nil) (numfield nonempty-type-eq-decl nil number_fields nil) (* const-decl "[numfield, numfield -> numfield]" number_fields nil) (<= const-decl "bool" reals nil) (upto nonempty-type-eq-decl nil naturalnumbers nil) (divides const-decl "bool" divides nil) (- const-decl "[numfield, numfield -> numfield]" number_fields nil) (divides_zero formula-decl nil divides nil) (nnrat_times_nnrat_is_nnrat application-judgement "nonneg_rat" rationals nil) (rat_times_rat_is_rat application-judgement "rat" rationals nil) (j skolem-const-decl "upto(n)" clear_denominators nil) (n skolem-const-decl "nat" clear_denominators nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil)) nil)) (rat_poly_to_int_rec_TCC8 0 (rat_poly_to_int_rec_TCC8-1 nil 3599920945 ("" (subtype-tcc) nil nil) ((boolean nonempty-type-decl nil booleans nil) (bool nonempty-type-eq-decl nil booleans nil) (NOT const-decl "[bool -> bool]" booleans nil) (number nonempty-type-decl nil numbers nil) (number_field_pred 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) (nat nonempty-type-eq-decl nil naturalnumbers nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (rat_abs_is_nonneg application-judgement "{r: nonneg_rat | r >= q}" real_defs nil) (int_minus_int_is_int application-judgement "int" integers nil) (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (rat_times_rat_is_rat application-judgement "rat" rationals nil) (divides const-decl "bool" divides nil) (upto nonempty-type-eq-decl nil naturalnumbers nil) (- const-decl "[numfield, numfield -> numfield]" number_fields nil) (<= const-decl "bool" reals nil) (* const-decl "[numfield, numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (AND const-decl "[bool, bool -> bool]" booleans nil) (rat nonempty-type-eq-decl nil rationals nil) (posnat nonempty-type-eq-decl nil integers nil) (= const-decl "[T, T -> boolean]" equalities nil) (posrat nonempty-type-eq-decl nil rationals nil) (> const-decl "bool" reals nil) (nonneg_rat nonempty-type-eq-decl nil rationals nil)) nil)) (rat_poly_to_int_rec_TCC9 0 (rat_poly_to_int_rec_TCC9-1 nil 3599920945 ("" (skeep) (("" (assert) (("" (hide 3) (("" (skeep) (("" (skeep) (("" (name "D" "currpoly`newpoly(n)") (("" (replaces -1) (("" (assert) (("" (typepred "compute_posratpair(abs(D))") (("" (expand "posratpair_convert") (("" (replace -3 :dir rl) (("" (cross-mult -1) (("" (case "D > 0") (("1" (expand "abs") (("1" (assert) nil nil)) nil) ("2" (expand "abs") (("2" (assert) (("2" (neg-formula -1) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((rat_times_rat_is_rat application-judgement "rat" rationals nil) (divides const-decl "bool" divides nil) (upto nonempty-type-eq-decl nil naturalnumbers nil) (- const-decl "[numfield, numfield -> numfield]" number_fields nil) (<= const-decl "bool" reals nil) (* const-decl "[numfield, numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (posrat nonempty-type-eq-decl nil rationals nil) (> const-decl "bool" reals nil) (nonneg_rat nonempty-type-eq-decl nil rationals nil) (>= const-decl "bool" reals nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (AND const-decl "[bool, bool -> bool]" booleans nil) (bool nonempty-type-eq-decl nil booleans nil) (rat nonempty-type-eq-decl nil rationals nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (posnat nonempty-type-eq-decl nil integers nil) (= const-decl "[T, T -> boolean]" equalities nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (rat_abs_is_nonneg application-judgement "{r: nonneg_rat | r >= q}" real_defs nil) (int_minus_int_is_int application-judgement "int" integers nil) (posrat_div_posrat_is_posrat application-judgement "posrat" rationals nil) (div_cancel3 formula-decl nil real_props nil) (/= const-decl "boolean" notequal nil) (nonzero_real nonempty-type-eq-decl nil reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (nnrat_times_nnrat_is_nnrat application-judgement "nonneg_rat" rationals nil) (bijective? const-decl "bool" functions nil) (id const-decl "(bijective?[T, T])" identity nil) (TRUE const-decl "bool" booleans nil) (minus_odd_is_odd application-judgement "odd_int" integers nil) (both_sides_times1_imp formula-decl nil extra_real_props nil) (nzint_times_nzint_is_nzint application-judgement "nzint" integers nil) (mult_divides1 application-judgement "(divides(n))" divides nil) (mult_divides2 application-judgement "(divides(m))" divides nil) (minus_nzint_is_nzint application-judgement "nzint" integers nil) (posint_times_posint_is_posint application-judgement "posint" integers nil) (neg_neg formula-decl nil extra_tegies nil) (neg_mult formula-decl nil extra_tegies nil) (mult_neg formula-decl nil extra_tegies nil) (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (minus_rat_is_rat application-judgement "rat" rationals nil) (abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs nil) (- const-decl "[numfield -> numfield]" number_fields nil) (nonneg_real nonempty-type-eq-decl nil real_types nil) (compute_posratpair def-decl "{prp | posratpair_convert(prp) = x}" clear_denominators nil) (posratpair_convert const-decl "posrat" clear_denominators nil) (PosRatPair type-eq-decl nil clear_denominators nil) (NOT const-decl "[bool -> bool]" booleans nil)) nil)) (rat_poly_to_int_rec_TCC10 0 (rat_poly_to_int_rec_TCC10-1 nil 3599920945 ("" (subtype-tcc) nil nil) ((boolean nonempty-type-decl nil booleans nil) (bool nonempty-type-eq-decl nil booleans nil) (NOT const-decl "[bool -> bool]" booleans nil) (number nonempty-type-decl nil numbers nil) (number_field_pred 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) (nat nonempty-type-eq-decl nil naturalnumbers nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (rat_abs_is_nonneg application-judgement "{r: nonneg_rat | r >= q}" real_defs nil) (int_minus_int_is_int application-judgement "int" integers nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (rat_times_rat_is_rat application-judgement "rat" rationals nil) (divides const-decl "bool" divides nil) (upto nonempty-type-eq-decl nil naturalnumbers nil) (- const-decl "[numfield, numfield -> numfield]" number_fields nil) (<= const-decl "bool" reals nil) (* const-decl "[numfield, numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (AND const-decl "[bool, bool -> bool]" booleans nil) (rat nonempty-type-eq-decl nil rationals nil) (posnat nonempty-type-eq-decl nil integers nil) (= const-decl "[T, T -> boolean]" equalities nil) (posrat nonempty-type-eq-decl nil rationals nil) (> const-decl "bool" reals nil) (nonneg_rat nonempty-type-eq-decl nil rationals nil) (/= const-decl "boolean" notequal nil)) nil)) (rat_poly_to_int_rec_TCC11 0 (rat_poly_to_int_rec_TCC11-1 nil 3599920945 ("" (skeep) (("" (skeep) (("" (hide 3) (("" (assert) (("" (skeep) (("" (assert) (("" (split) (("1" (typepred "v(aq,n-1)") (("1" (skeep) (("1" (inst + "thisden*cp") (("1" (skeep) (("1" (assert) (("1" (inst - "j") (("1" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (skeep) (("2" (assert) (("2" (case "NOT j = n") (("1" (typepred "v(aq,n-1)") (("1" (inst -2 "j") (("1" (flatten) (("1" (assert) (("1" (case "EXISTS (kk:int): v(aq,n-1)`newpoly(j) = kk") (("1" (skeep -1) (("1" (assert) (("1" (replace -1) (("1" (replace -5 :dir rl) (("1" (replace -1) (("1" (assert) (("1" (typepred "compute_gcd(thisden * currpoly`newpoly(n), currpoly`currgcd)") (("1" (hide -1) (("1" (typepred "gcd(thisden * currpoly`newpoly(n), currpoly`currgcd)") (("1" (replace -4) (("1" (invoke (name "ggg" "%1") (! 2 1)) (("1" (replace -1) (("1" (lemma "divides_transitive") (("1" (inst - "kk" "currpoly`currgcd" "ggg") (("1" (assert) (("1" (expand "divides") (("1" (skosimp*) (("1" (inst + "thisden*x!1") (("1" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide 3) (("2" (name "K" "currpoly`newpoly(n)") (("2" (replace -1) (("2" (typepred "compute_posratpair(abs(K))") (("2" (expand "posratpair_convert") (("2" (replace -8 :dir rl) (("2" (cross-mult -1) (("2" (case "K > 0") (("1" (expand "abs") (("1" (assert) nil nil)) nil) ("2" (expand "abs") (("2" (assert) (("2" (neg-formula -1) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (inst + "v(aq,n-1)`newpoly(j)") nil nil)) nil)) nil)) nil) ("2" (assert) nil nil)) nil)) nil) ("2" (assert) (("2" (replaces -1) (("2" (assert) (("2" (split) (("1" (name "K" "currpoly`newpoly(n)") (("1" (replace -1) (("1" (typepred "compute_posratpair(abs(K))") (("1" (expand "posratpair_convert") (("1" (replace -4 :dir rl) (("1" (cross-mult -1) (("1" (case "K > 0") (("1" (expand "abs") (("1" (assert) nil nil)) nil) ("2" (expand "abs") (("2" (assert) (("2" (neg-formula -1) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (name "K" "currpoly`newpoly(n)") (("2" (replace -1) (("2" (assert) (("2" (typepred "compute_gcd(thisden * K, currpoly`currgcd)") (("1" (typepred "gcd(thisden * K, currpoly`currgcd)") (("1" (replace -5) (("1" (propax) nil nil)) nil)) nil) ("2" (assert) (("2" (hide 2) (("2" (typepred "compute_posratpair(abs(K))") (("2" (expand "posratpair_convert") (("2" (replace -4 :dir rl) (("2" (cross-mult -1) (("2" (case "K > 0") (("1" (expand "abs") (("1" (assert) nil nil)) nil) ("2" (expand "abs") (("2" (assert) (("2" (neg-formula -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)) nil)) nil)) nil) ((rat_times_rat_is_rat application-judgement "rat" rationals nil) (int_minus_int_is_int application-judgement "int" integers nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (rat_abs_is_nonneg application-judgement "{r: nonneg_rat | r >= q}" real_defs nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (n skolem-const-decl "nat" clear_denominators nil) (j skolem-const-decl "upto(n)" clear_denominators nil) (IMPLIES const-decl "[bool, bool -> bool]" booleans nil) (/= const-decl "boolean" notequal nil) (gcd const-decl "{k: posnat | divides(k, i) AND divides(k, j)}" gcd "ints/") (compute_gcd def-decl "{kj: posnat | kj = gcd(i, j)}" gcd "ints/") (divides_transitive formula-decl nil divides nil) (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (PosRatPair type-eq-decl nil clear_denominators nil) (posratpair_convert const-decl "posrat" clear_denominators nil) (compute_posratpair def-decl "{prp | posratpair_convert(prp) = x}" clear_denominators nil) (nonneg_real nonempty-type-eq-decl nil real_types nil) (- const-decl "[numfield -> numfield]" number_fields nil) (abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs nil) (minus_rat_is_rat application-judgement "rat" rationals nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (mult_neg formula-decl nil extra_tegies nil) (neg_mult formula-decl nil extra_tegies nil) (neg_neg formula-decl nil extra_tegies nil) (posint_times_posint_is_posint application-judgement "posint" integers nil) (minus_nzint_is_nzint application-judgement "nzint" integers nil) (nzint_times_nzint_is_nzint application-judgement "nzint" integers nil) (both_sides_times1_imp formula-decl nil extra_real_props nil) (minus_odd_is_odd application-judgement "odd_int" integers nil) (TRUE const-decl "bool" booleans nil) (id const-decl "(bijective?[T, T])" identity nil) (bijective? const-decl "bool" functions nil) (nnrat_times_nnrat_is_nnrat application-judgement "nonneg_rat" rationals nil) (nonzero_real nonempty-type-eq-decl nil reals nil) (div_cancel3 formula-decl nil real_props nil) (posrat_div_posrat_is_posrat application-judgement "posrat" rationals nil) (mult_divides1 application-judgement "(divides(n))" divides nil) (mult_divides2 application-judgement "(divides(m))" divides nil) (- const-decl "[numfield, numfield -> numfield]" number_fields nil) (divides const-decl "bool" divides nil) (upto nonempty-type-eq-decl nil naturalnumbers nil) (<= const-decl "bool" reals nil) (* const-decl "[numfield, numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (AND const-decl "[bool, bool -> bool]" booleans nil) (posnat nonempty-type-eq-decl nil integers nil) (< const-decl "bool" reals nil) (rat nonempty-type-eq-decl nil rationals nil) (= const-decl "[T, T -> boolean]" equalities nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (posrat nonempty-type-eq-decl nil rationals nil) (> const-decl "bool" reals nil) (nonneg_rat nonempty-type-eq-decl nil rationals nil) (>= const-decl "bool" reals nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (number nonempty-type-decl nil numbers nil) (NOT const-decl "[bool -> bool]" booleans nil) (bool nonempty-type-eq-decl nil booleans nil) (boolean nonempty-type-decl nil booleans nil) (posrat_times_posrat_is_posrat application-judgement "posrat" rationals nil) (nonneg_int nonempty-type-eq-decl nil integers nil)) nil)) (rat_poly_to_int_rec_TCC12 0 (rat_poly_to_int_rec_TCC12-1 nil 3599920945 ("" (subtype-tcc) nil nil) ((boolean nonempty-type-decl nil booleans nil) (bool nonempty-type-eq-decl nil booleans nil) (NOT const-decl "[bool -> bool]" booleans nil) (number nonempty-type-decl nil numbers nil) (number_field_pred 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) (nat nonempty-type-eq-decl nil naturalnumbers nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (int_minus_int_is_int application-judgement "int" integers nil)) nil)) (rat_poly_to_int_rec_TCC13 0 (rat_poly_to_int_rec_TCC13-1 nil 3599920945 ("" (termination-tcc) nil nil) nil nil)) (rat_poly_to_int_TCC1 0 (rat_poly_to_int_TCC1-1 nil 3599920402 ("" (subtype-tcc) nil nil) ((boolean nonempty-type-decl nil booleans nil) (bool nonempty-type-eq-decl nil booleans nil) (NOT const-decl "[bool -> bool]" booleans nil) (number nonempty-type-decl nil numbers nil) (number_field_pred 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) (nat nonempty-type-eq-decl nil naturalnumbers nil) (nonneg_rat nonempty-type-eq-decl nil rationals nil) (> const-decl "bool" reals nil) (posrat nonempty-type-eq-decl nil rationals nil) (= const-decl "[T, T -> boolean]" equalities nil) (posnat nonempty-type-eq-decl nil integers nil) (rat nonempty-type-eq-decl nil rationals nil) (AND const-decl "[bool, bool -> bool]" booleans nil) (numfield nonempty-type-eq-decl nil number_fields nil) (* const-decl "[numfield, numfield -> numfield]" number_fields nil) (<= const-decl "bool" reals nil) (upto nonempty-type-eq-decl nil naturalnumbers nil) (divides const-decl "bool" divides nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (rat_times_rat_is_rat application-judgement "rat" rationals nil) (mult_divides2 application-judgement "(divides(m))" divides nil) (mult_divides1 application-judgement "(divides(n))" divides nil) (rat_div_nzrat_is_rat application-judgement "rat" rationals nil)) nil)) (rat_poly_to_int_TCC2 0 (rat_poly_to_int_TCC2-1 nil 3599920402 ("" (skeep) (("" (skeep) (("" (skeep) (("" (typepred "rptir") (("" (skeep -1) (("" (inst + "cp/mgcd") (("1" (skeep) (("1" (inst - "j") (("1" (lift-if) (("1" (ground) nil nil)) nil)) nil)) nil) ("2" (replace -5 :dir rl) (("2" (postpone) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((divides const-decl "bool" divides nil) (upto nonempty-type-eq-decl nil naturalnumbers nil) (<= const-decl "bool" reals nil) (* const-decl "[numfield, numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (AND const-decl "[bool, bool -> bool]" booleans nil) (rat nonempty-type-eq-decl nil rationals nil) (posnat nonempty-type-eq-decl nil integers nil) (= const-decl "[T, T -> boolean]" equalities nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (posrat nonempty-type-eq-decl nil rationals nil) (> const-decl "bool" reals nil) (nonneg_rat nonempty-type-eq-decl nil rationals nil) (>= const-decl "bool" reals nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (number nonempty-type-decl nil numbers nil) (NOT const-decl "[bool -> bool]" booleans nil) (bool nonempty-type-eq-decl nil booleans nil) (boolean nonempty-type-decl nil booleans nil) (posrat_div_posrat_is_posrat application-judgement "posrat" rationals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (/ const-decl "[numfield, nznum -> numfield]" number_fields nil) (nznum nonempty-type-eq-decl nil number_fields nil) (/= const-decl "boolean" notequal nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (rat_div_nzrat_is_rat application-judgement "rat" rationals nil) (rat_times_rat_is_rat application-judgement "rat" rationals nil)) nil)))
¤ Dauer der Verarbeitung: 0.96 Sekunden (vorverarbeitet am 2026-05-01) ¤*© Formatika GbR, Deutschland |
|
||||||||||||||
2026-05-26