| products/sources/formale Sprachen/PVS/reals/ |
|
Quellcode-Bibliothek© Kompilation durch diese Firma[Weder Korrektheit noch Funktionsfähigkeit der Software werden zugesichert.]Datei: planner.tex Sprache: LispOriginal von: PVS© |
|
||||||
|
(binomial_identities
(binom_trinomial_revision_TCC1 0 (binom_trinomial_revision_TCC1-1 nil 3481019014 ("" (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_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)) nil)) (binom_trinomial_revision_TCC2 0 (binom_trinomial_revision_TCC2-1 nil 3481019014 ("" (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_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)) nil)) (binom_trinomial_revision_TCC3 0 (binom_trinomial_revision_TCC3-1 nil 3481019014 ("" (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_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)) nil)) (binom_trinomial_revision_TCC4 0 (binom_trinomial_revision_TCC4-1 nil 3481019014 ("" (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) (int_minus_int_is_int application-judgement "int" integers nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil)) nil)) (binom_trinomial_revision_TCC5 0 (binom_trinomial_revision_TCC5-1 nil 3481019014 ("" (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) (int_minus_int_is_int application-judgement "int" integers nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil)) nil)) (binom_trinomial_revision 0 (binom_trinomial_revision-1 nil 3481019014 ("" (expand "C") (("" (propax) nil nil)) nil) ((C const-decl "posnat" binomial nil) (posrat_div_posrat_is_posrat application-judgement "posrat" rationals 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)) shostak)) (binom_absorption_TCC1 0 (binom_absorption_TCC1-1 nil 3481019129 ("" (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_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)) nil)) (binom_absorption_TCC2 0 (binom_absorption_TCC2-1 nil 3481019129 ("" (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) (/= const-decl "boolean" notequal nil)) nil)) (binom_absorption_TCC3 0 (binom_absorption_TCC3-1 nil 3481019129 ("" (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) (int_minus_int_is_int application-judgement "int" integers nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil)) nil)) (binom_absorption_TCC4 0 (binom_absorption_TCC4-1 nil 3481019129 ("" (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) (int_minus_int_is_int application-judgement "int" integers nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil)) nil)) (binom_absorption 0 (binom_absorption-1 nil 3481019129 ("" (expand "C") (("" (expand "factorial" 1 1) (("" (expand "factorial" 1 2) (("" (skeep) (("" (ground) nil nil)) nil)) nil)) nil)) nil) ((factorial def-decl "posnat" factorial "ints/") (rat_times_rat_is_rat application-judgement "rat" rationals nil) (int_minus_int_is_int application-judgement "int" integers nil) (nnint_times_nnint_is_nnint application-judgement "nonneg_int" integers nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (C const-decl "posnat" binomial nil) (posrat_div_posrat_is_posrat application-judgement "posrat" rationals nil) (rat_div_nzrat_is_rat application-judgement "rat" rationals 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)) shostak)) (binom_upper_summation_TCC1 0 (binom_upper_summation_TCC1-1 nil 3481020000 ("" (subtype-tcc) nil nil) nil nil)) (binom_upper_summation_TCC2 0 (binom_upper_summation_TCC2-1 nil 3481020000 ("" (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_lt_is_strict_total_order name-judgement "(strict_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)) nil)) (binom_upper_summation_TCC3 0 (binom_upper_summation_TCC3-1 nil 3481020000 ("" (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) (posint_plus_nnint_is_posint application-judgement "posint" integers 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)) nil)) (binom_upper_summation 0 (binom_upper_summation-1 nil 3481019919 ("" (skeep) (("" (case "FORALL (j:nat): sigma(m, m+j, LAMBDA (k: nat): IF k < m OR k > m+j THEN 0 ELSE C(k, m) ENDIF) = C(m+j + 1, m + 1)") (("1" (inst - "n-m") (("1" (assert) nil nil) ("2" (assert) nil nil)) nil) ("2" (hide 2) (("2" (induct "j") (("1" (assert) (("1" (expand "sigma") (("1" (expand "sigma") (("1" (expand "C") (("1" (assert) nil nil)) nil)) nil)) nil)) nil) ("2" (skosimp*) (("2" (lemma "sigma_split") (("2" (inst - "LAMBDA (k: nat): IF k < m OR k > m + (j!1 + 1) THEN 0 ELSE C(k, m) ENDIF" "m+j!1+1" "m" "m+j!1") (("1" (assert) (("1" (replace -1) (("1" (hide -1) (("1" (expand "sigma" 1 1) (("1" (expand "sigma" 1 1) (("1" (lemma "sigma_restrict_eq") (("1" (inst - "LAMBDA (k: nat): IF k < m OR k > j!1 + m THEN 0 ELSE C(k, m) ENDIF" "LAMBDA (k: nat): IF k < m OR k > 1 + j!1 + m THEN 0 ELSE C(k, m) ENDIF" "j!1+m" "m") (("1" (split -) (("1" (replace -1 :dir rl) (("1" (replace -2) (("1" (lemma "C_n_plus_1") (("1" (inst - "1+j!1+m" "1+m") (("1" (assert) nil nil)) nil)) nil)) nil)) nil) ("2" (hide 2) (("2" (hide -1) (("2" (decompose-equality) (("1" (expand "restrict") (("1" (propax) nil nil)) nil) ("2" (skosimp*) (("2" (assert) nil nil)) nil) ("3" (skosimp*) (("3" (assert) nil nil)) nil)) nil)) nil)) nil)) nil) ("2" (skosimp*) (("2" (assert) nil nil)) nil) ("3" (skosimp*) (("3" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (skosimp*) (("2" (assert) nil nil)) nil)) nil)) nil)) nil) ("3" (skosimp*) (("3" (assert) nil nil)) nil)) nil)) nil) ("3" (skosimp*) (("3" (assert) nil nil)) nil)) nil)) nil) ((C const-decl "posnat" binomial nil) (posnat nonempty-type-eq-decl nil integers nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (< const-decl "bool" reals nil) (IF const-decl "[boolean, T, T -> T]" if_def nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (sigma def-decl "real" sigma nil) (T_high type-eq-decl nil sigma nil) (T_low type-eq-decl nil sigma nil) (<= const-decl "bool" reals nil) (OR const-decl "[bool, bool -> bool]" booleans nil) (= const-decl "[T, T -> boolean]" equalities nil) (nat nonempty-type-eq-decl nil naturalnumbers 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) (nnint_plus_posint_is_posint application-judgement "posint" integers nil) (sigma_nat application-judgement "nat" sigma_nat nil) (sigma_nnreal application-judgement "nnreal" sigma_nat nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (nnint_plus_nnint_is_nnint application-judgement "nonneg_int" integers nil) (NOT const-decl "[bool -> bool]" booleans nil) (AND const-decl "[bool, bool -> bool]" booleans nil) (IMPLIES const-decl "[bool, bool -> bool]" booleans nil) (int_plus_int_is_int application-judgement "int" integers nil) (m skolem-const-decl "nat" binomial_identities nil) (n skolem-const-decl "nat" binomial_identities nil) (- const-decl "[numfield, numfield -> numfield]" number_fields nil) (int_minus_int_is_int application-judgement "int" integers nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (pred type-eq-decl nil defined_types nil) (nat_induction formula-decl nil naturalnumbers 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) (factorial_0 formula-decl nil factorial "ints/") (sigma_split formula-decl nil sigma nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (restrict const-decl "[T -> real]" sigma 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) (C_n_plus_1 formula-decl nil binomial nil) (sigma_restrict_eq formula-decl nil sigma nil) (j!1 skolem-const-decl "nat" binomial_identities nil)) nil)) (binom_parallel_summation_TCC1 0 (binom_parallel_summation_TCC1-1 nil 3481020000 ("" (subtype-tcc) nil nil) nil nil)) (binom_parallel_summation_TCC2 0 (binom_parallel_summation_TCC2-1 nil 3481020000 ("" (subtype-tcc) nil nil) nil nil)) (binom_parallel_summation_TCC3 0 (binom_parallel_summation_TCC3-1 nil 3481020000 ("" (subtype-tcc) nil nil) ((posint_plus_nnint_is_posint application-judgement "posint" integers nil)) nil)) (binom_parallel_summation 0 (binom_parallel_summation-1 nil 3481020000 ("" (induct "n") (("1" (skeep) (("1" (expand "sigma") (("1" (expand "sigma") (("1" (expand "C") (("1" (assert) nil nil)) nil)) nil)) nil)) nil) ("2" (skeep) (("2" (skeep) (("2" (inst - "r") (("2" (expand "sigma" +) (("2" (lemma "sigma_restrict_eq") (("2" (inst - "LAMBDA (k: nat): IF k > j THEN 0 ELSE C(r + k, k) ENDIF" "LAMBDA (k: nat): IF k > 1 + j THEN 0 ELSE C(k + r, k) ENDIF" "j" "0") (("2" (split -) (("1" (replace -1 :dir rl) (("1" (hide -1) (("1" (replace -1) (("1" (hide -1) (("1" (lemma "C_n_plus_1") (("1" (inst - "1+j+r" "1+j") (("1" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide 2) (("2" (decompose-equality) (("2" (expand "restrict") (("2" (propax) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((sigma_restrict_eq formula-decl nil sigma nil) (C_n_plus_1 formula-decl nil binomial nil) (sigma_nat application-judgement "nat" sigma_nat nil) (sigma_nnreal application-judgement "nnreal" sigma_nat 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_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (restrict const-decl "[T -> real]" sigma nil) (factorial_0 formula-decl nil factorial "ints/") (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) (posrat_div_posrat_is_posrat application-judgement "posrat" rationals nil) (nat_induction formula-decl nil naturalnumbers nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (C const-decl "posnat" binomial nil) (posnat nonempty-type-eq-decl nil integers nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (IF const-decl "[boolean, T, T -> T]" if_def nil) (sigma def-decl "real" sigma nil) (T_high type-eq-decl nil sigma nil) (T_low type-eq-decl nil sigma nil) (<= const-decl "bool" reals nil) (OR const-decl "[bool, bool -> bool]" booleans nil) (= const-decl "[T, T -> boolean]" equalities nil) (pred type-eq-decl nil defined_types nil) (nat nonempty-type-eq-decl nil naturalnumbers 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) (nnint_plus_nnint_is_nnint application-judgement "nonneg_int" integers nil) (nnint_plus_posint_is_posint application-judgement "posint" integers nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil)) shostak)) (binom_vandermonde_convolution_TCC1 0 (binom_vandermonde_convolution_TCC1-1 nil 3481987592 ("" (subtype-tcc) nil nil) nil nil)) (binom_vandermonde_convolution_TCC2 0 (binom_vandermonde_convolution_TCC2-1 nil 3481987592 ("" (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) (int_minus_int_is_int application-judgement "int" integers nil) (nnint_plus_nnint_is_nnint application-judgement "nonneg_int" integers nil)) nil)) (binom_vandermonde_convolution_TCC3 0 (binom_vandermonde_convolution_TCC3-1 nil 3481987592 ("" (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) (int_minus_int_is_int application-judgement "int" integers nil) (nnint_plus_nnint_is_nnint application-judgement "nonneg_int" integers nil)) nil)) (binom_vandermonde_convolution_TCC4 0 (binom_vandermonde_convolution_TCC4-1 nil 3481987592 ("" (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) (int_minus_int_is_int application-judgement "int" integers nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (nnint_plus_nnint_is_nnint application-judgement "nonneg_int" integers nil)) nil)) (binom_vandermonde_convolution_TCC5 0 (binom_vandermonde_convolution_TCC5-1 nil 3481987592 ("" (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_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)) nil)) (binom_vandermonde_convolution 0 (binom_vandermonde_convolution-1 nil 3481987592 ("" (case "FORALL (m, n, p: nat): m+n >= p IMPLIES sigma(0, m, LAMBDA (k: nat): IF k > p OR k > m OR p - n > k THEN 0 ELSE C(m+n - p, m - k) * C(p, k) ENDIF) = C(m+n, m)") (("1" (skeep) (("1" (inst - "m" "n-m" "p") (("1" (assert) nil nil) ("2" (assert) nil nil)) nil)) nil) ("2" (hide 2) (("2" (induct "m") (("1" (skosimp*) (("1" (expand "sigma") (("1" (expand "sigma") (("1" (lift-if) (("1" (ground) (("1" (expand "C") (("1" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (skolem 1 "m") (("2" (flatten) (("2" (induct "n") (("1" (hide -) (("1" (skosimp*) (("1" (assert) (("1" (case "C(1+m,1+m) = 1") (("1" (replace -1) (("1" (hide -1) (("1" (name "fc" "LAMBDA (k: nat): IF k > p!1 OR k > 1 + m OR p!1 > k THEN 0 ELSE C(1 - p!1 + m, 1 - k + m) * C(p!1, k) ENDIF") (("1" (replace -1) (("1" (lemma "sigma_split") (("1" (inst - "fc" "1+m" "0" "p!1-1") (("1" (assert) (("1" (replace -1) (("1" (hide -1) (("1" (lemma "sigma_split") (("1" (inst - "fc" "1+m" "p!1" "p!1") (("1" (assert) (("1" (replace -1) (("1" (hide -1) (("1" (name "zerc" "LAMBDA (k:nat): 0") (("1" (lemma "sigma_zero") (("1" (inst - "p!1-1" "0") (("1" (lemma "sigma_zero") (("1" (inst - "1+m" "1+p!1") (("1" (lemma "sigma_restrict_eq") (("1" (inst - "fc" "zerc" "m+1" "1+p!1") (("1" (split -) (("1" (lemma "sigma_restrict_eq") (("1" (inst - "fc" "zerc" "p!1-1" "0") (("1" (split -) (("1" (case "sigma(p!1,p!1,fc) = 1") (("1" (assert) nil nil) ("2" (hide 2) (("2" (expand "sigma" +) (("2" (expand "sigma" +) (("2" (expand "fc" +) (("2" (expand "C" +) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide 2) (("2" (decompose-equality) (("2" (expand "restrict") (("2" (lift-if) (("2" (ground) (("2" (expand "fc") (("2" (expand "zerc") (("2" (propax) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide 2) (("2" (decompose-equality) (("2" (expand "restrict") (("2" (lift-if) (("2" (ground) (("2" (expand "fc") (("2" (expand "zerc") (("2" (propax) 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" (skosimp*) (("2" (assert) nil nil)) nil) ("3" (skosimp*) (("3" (assert) nil nil)) nil)) nil)) nil)) nil) ("2" (expand "C" 1) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil) ("2" (skolem 1 "n") (("2" (flatten) (("2" (skeep) (("2" (lemma "C_n_plus_1") (("2" (inst - "m+1+n" "m+1") (("2" (assert) (("2" (replace -1 1) (("2" (hide -1) (("2" (inst - "p") (("2" (assert) (("2" (case "1+m+n >= p") (("1" (assert) (("1" (name "fc" "LAMBDA (k: nat): IF k > p OR k > 1 + m OR -1 - n + p > k THEN 0 ELSE C(2 - p + m + n, 1 - k + m) * C(p, k) ENDIF") (("1" (replace -1) (("1" (name "gc" "LAMBDA (k: nat): IF k > p OR k > 1 + m OR p - n > k THEN 0 ELSE C(1 - p + m + n, 1 - k + m) * C(p, k) ENDIF") (("1" (replace -1) (("1" (replace -4 1 :dir rl) (("1" (inst - "n+1" "p") (("1" (assert) (("1" (name "rc" "LAMBDA (k: nat): IF k > p OR k > m OR -1 - n + p > k THEN 0 ELSE C(1 - p + m + n, m - k) * C(p, k) ENDIF") (("1" (replace -1) (("1" (replace -7 1 :dir rl) (("1" (case "NOT fc = rc + gc") (("1" (hide-all-but 1) (("1" (decompose-equality) (("1" (expand "+") (("1" (expand "fc") (("1" (expand "gc") (("1" (expand "rc") (("1" (lift-if) (("1" (lift-if) (("1" (lift-if) (("1" (assert) (("1" (ground) (("1" (case "x!1 = 1+m") (("1" (replace -1) (("1" (hide -1) (("1" (hide 2) (("1" (assert) (("1" (expand "C") (("1" (assert) nil nil)) nil)) nil)) nil)) nil)) nil) ("2" (assert) (("2" (lift-if) (("2" (assert) (("2" (ground) (("1" (expand "C") (("1" (assert) nil nil)) nil) ("2" (expand "C") (("2" (assert) (("2" (case "x!1 = p-n-1") (("1" (replace -1) (("1" (assert) nil nil)) nil) ("2" (assert) (("2" (lemma "C_n_plus_1") (("2" (inst - "1 - p + m + n" "1 - x!1 + m") (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (skosimp*) (("2" (expand "rc") (("2" (expand "gc") (("2" (expand "+") (("2" (lift-if) (("2" (lift-if) (("2" (ground) (("2" (lift-if) (("2" (ground) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (replace -1 1) (("2" (case "sigma(0,m,rc) = sigma(0,m+1,rc)") (("1" (replace -1 1) (("1" (lemma "sigma_sum") (("1" (inst - "rc" "gc" "1+m" "0") (("1" (expand "+" 1) (("1" --> -------------------- --> maximum size reached --> -------------------- ¤ Diese beiden folgenden Angebotsgruppen bietet das Unternehmen0.49Angebot Wie Sie bei der Firma Beratungs- und Dienstleistungen beauftragen können ¤ |
Lebenszyklus
Die hierunter aufgelisteten Ziele sind für diese Firma wichtig
ZieleEntwicklung einer Software für die statische QuellcodeanalyseBot Zugriff |
