| products/sources/formale Sprachen/PVS/Sturm/ |
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Quellcode-Bibliothek© Kompilation durch diese Firma[Weder Korrektheit noch Funktionsfähigkeit der Software werden zugesichert.]Datei: Sprache: LispUntersuchung PVS© |
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(clear_denominators
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(("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?") 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(("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?") 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(("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?") 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(("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?") 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(("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" --> -------------------- --> maximum size reached --> -------------------- ¤ Diese beiden folgenden Angebotsgruppen bietet das Unternehmen0.99Angebot Wie Sie bei der Firma Beratungs- und Dienstleistungen beauftragen können ¤ |
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