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^© Kompilation durch diese Firma

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Datei: .project Sprache: Lisp

Original von: PVS^©

(ln_exp_series_alt
(ln_estimate_TCC1 0
  (ln_estimate_TCC1-1 nil 3270048045
   ("" (skosimp*) (("" (assert) nil nil)) nil)
   ((real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil))
   shostak))
(ln_estimate_TCC2 0
  (ln_estimate_TCC2-1 nil 3270048058
   ("" (skosimp*) (("" (inst + "n!1+1") (("" (assert) nil nil)) nil))
    nil)
   ((real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (minus_real_is_real application-judgement "real" reals nil))
   shostak))
(ln_estimate_TCC3 0
  (ln_estimate_TCC3-1 nil 3374414377 ("" (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)
    (/= const-decl "boolean" notequal nil))
   nil))
(ln_estimate_scaf4_TCC1 0
  (ln_estimate_scaf4_TCC1-1 nil 3309547516
   ("" (skosimp) (("" (assert) nil nil)) nil)
   ((real_minus_real_is_real application-judgement "real" reals nil))
   shostak))
(ln_estimate_scaf4_TCC2 0
  (ln_estimate_scaf4_TCC2-1 nil 3309547523
   ("" (skosimp) (("" (assert) nil nil)) nil) nil shostak))
(ln_estimate_scaf4_TCC3 0
  (ln_estimate_scaf4_TCC3-1 nil 3309547541
   ("" (skosimp) (("" (assert) nil nil)) nil)
   ((nnint_plus_posint_is_posint application-judgement "posint"
     integers nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil))
   shostak))
(ln_estimate_scaf4 0
  (ln_estimate_scaf4-1 nil 3309546853
   ("" (skosimp)
    (("" (name "SS" "sigma(0, n!1, LAMBDA (i: nat): x!1 ^ i)")
      (("" (replace -1)
        ((""
          (lemma "add_div"
           ("x" "SS" "n0x" "1" "y" "x!1^(n!1+1)" "n0y" "1-x!1"))
          (("" (replace -1 2)
            ((""
              (lemma "both_sides_div1"
               ("x" "1" "y" "SS * (1 - x!1) + x!1 ^ (n!1 + 1)" "n0z"
                "1-x!1"))
              (("" (replace -1 2)
                (("" (hide -1 -2)
                  ((""
                    (case "forall (n:nat): 1 = sigma(0, n, LAMBDA (i: nat): x!1 ^ i) *(1-x!1) + x!1 ^ (n+1)")
                    (("1" (inst - "n!1") (("1" (assert) nil nil)) nil)
                     ("2" (hide-all-but (1 2))
                      (("2" (induct "n")
                        (("1" (expand "sigma")
                          (("1" (assert)
                            (("1" (expand "^")
                              (("1"
                                (expand "expt")
                                (("1"
                                  (expand "expt")
                                  (("1"
                                    (expand "sigma")
                                    (("1" (propax) nil nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil)
                         ("2" (skosimp*)
                          (("2" (expand "sigma" 1)
                            (("2"
                              (name-replace "DRL101"
                               "sigma(0, j!1, LAMBDA (i: nat): x!1 ^ i)")
                              (("2"
                                (case-replace
                                 "(x!1 ^ (1 + j!1)) * x!1 = x!1 ^ (2 + j!1)")
                                (("1" (assert) nil nil)
                                 ("2"
                                  (hide-all-but 1)
                                  (("2"
                                    (expand "^")
                                    (("2"
                                      (expand "expt" 1 2)
                                      (("2" (assert) nil nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((^ const-decl "real" exponentiation nil)
    (/= const-decl "boolean" notequal nil)
    (sigma def-decl "real" sigma "reals/")
    (T_high type-eq-decl nil sigma "reals/")
    (T_low type-eq-decl nil sigma "reals/")
    (<= const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (>= const-decl "bool" reals nil)
    (OR const-decl "[bool, bool -> bool]" booleans 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)
    (= const-decl "[T, T -> boolean]" equalities 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)
    (add_div formula-decl nil real_props nil)
    (nonzero_real nonempty-type-eq-decl nil reals nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (both_sides_div1 formula-decl nil real_props nil)
    (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (minus_odd_is_odd application-judgement "odd_int" integers nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (expt def-decl "real" exponentiation nil)
    (sigma_0_neg formula-decl nil sigma_nat "reals/")
    (nat_induction formula-decl nil naturalnumbers nil)
    (pred type-eq-decl nil defined_types nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (real_le_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_div_nzreal_is_real application-judgement "real" reals nil)
    (real_minus_real_is_real application-judgement "real" reals nil))
   shostak))
(ln_estimate_scaf5_TCC1 0
  (ln_estimate_scaf5_TCC1-1 nil 3309550054
   ("" (skosimp) (("" (assert) nil nil)) nil)
   ((real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (real_minus_real_is_real application-judgement "real" reals nil))
   shostak))
(ln_estimate_scaf5_TCC2 0
  (ln_estimate_scaf5_TCC2-1 nil 3309550054
   ("" (skosimp) (("" (assert) nil nil)) nil)
   ((nnint_plus_posint_is_posint application-judgement "posint"
     integers nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (real_minus_real_is_real application-judgement "real" reals nil))
   shostak))
(ln_estimate_scaf5 0
  (ln_estimate_scaf5-1 nil 3309548279
   ("" (skosimp)
    (("" (lemma "ln_estimate_scaf4" ("x" "1-nzx!1" "n" "n!1"))
      (("" (assert) nil nil)) nil))
    nil)
   ((nzreal nonempty-type-eq-decl nil reals nil)
    (/= const-decl "boolean" notequal nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields 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)
    (ln_estimate_scaf4 formula-decl nil ln_exp_series_alt nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (nzreal_div_nzreal_is_nzreal application-judgement "nzreal"
     real_types nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (real_le_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_div_nzreal_is_real application-judgement "real" reals nil)
    (nnint_plus_posint_is_posint application-judgement "posint"
     integers nil))
   shostak))
(ln_estimate_bnd_TCC1 0
  (ln_estimate_bnd_TCC1-1 nil 3322390165 ("" (subtype-tcc) nil nil) nil
   nil))
(ln_estimate_bnd_TCC2 0
  (ln_estimate_bnd_TCC2-1 nil 3322390165 ("" (subtype-tcc) nil nil)
   ((/= const-decl "boolean" notequal nil)) nil))
(ln_estimate_bnd_TCC3 0
  (ln_estimate_bnd_TCC3-1 nil 3322390165
   ("" (skosimp*)
    (("" (typepred "n!1")
      (("" (name "NP1" "n!1+1")
        (("" (replace -1)
          (("" (lift-if)
            (("" (name "zP1" "z!1+1")
              (("" (replace -1)
                (("" (ground) (("" (mult-cases -2) nil nil)) nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    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)
    (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)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (< const-decl "bool" reals nil)
    (- const-decl "[numfield -> numfield]" number_fields nil)
    (<= const-decl "bool" reals nil)
    (real_gtm1_le1 nonempty-type-eq-decl nil ln_exp_series_alt 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)
    (zero_times3 formula-decl nil 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)
    (real_times_real_is_real application-judgement "real" reals nil)
    (nnint_plus_posint_is_posint application-judgement "posint"
     integers nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (posint nonempty-type-eq-decl nil integers nil))
   nil))
(ln_estimate_bnd 0
  (ln_estimate_bnd-1 nil 3322390178
   ("" (skosimp)
    (("" (lemma "ln_estimate_scaf9" ("px" "1+z!1" "n" "n!1"))
      (("" (replace -1)
        (("" (assert)
          (("" (hide -1)
            (("" (typepred "z!1")
              (("" (case "0 <=z!1")
                (("1" (hide -2)
                  (("1"
                    (lemma "ln_estimate_scaf10"
                     ("px" "1+z!1" "n" "n!1"))
                    (("1" (assert)
                      (("1" (expand "abs" 1 2) (("1" (assert) nil nil))
                        nil))
                      nil))
                    nil))
                  nil)
                 ("2"
                  (lemma "ln_estimate_scaf11" ("px" "1+z!1" "n" "n!1"))
                  (("2" (assert)
                    (("2" (expand "abs" 2 2) (("2" (assert) nil nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   nil nil))
(lnT_TCC1 0
  (lnT_TCC1-1 nil 3309361152 ("" (skosimp) (("" (assert) nil nil)) nil)
   ((nnint_plus_posint_is_posint application-judgement "posint"
     integers nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (minus_real_is_real application-judgement "real" reals nil))
   shostak))
(lnT_TCC2 0
  (lnT_TCC2-1 nil 3309361152
   (""
    (case "forall (n:nat,x:real): -1 <= x & x <= 1 => -1 <= x^n & x^n <= 1")
    (("1" (skosimp)
      (("1" (case-replace "x!1=0")
        (("1" (expand "^" 1)
          (("1" (expand "expt" 1) (("1" (propax) nil nil)) nil)) nil)
         ("2" (case-replace "n!1=0")
          (("1" (rewrite "expt_x1") (("1" (assert) nil nil)) nil)
           ("2" (inst - "n!1+1" "-x!1")
            (("2" (assert)
              (("2" (flatten)
                (("2" (rewrite "div_mult_pos_lt2" 3)
                  (("2" (rewrite "div_mult_pos_le1" 3)
                    (("2" (assert) nil nil)) nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     ("2" (hide 2)
      (("2" (skolem 1 ("_" "x"))
        (("2" (induct "n")
          (("1" (expand "^" 1)
            (("1" (expand "expt" 1) (("1" (propax) nil nil)) nil)) nil)
           ("2" (skosimp*)
            (("2" (assert)
              (("2" (flatten)
                (("2" (expand "^")
                  (("2" (expand "expt" 1)
                    (("2" (lemma "trichotomy" ("x" "x"))
                      (("2" (split -1)
                        (("1"
                          (lemma "both_sides_times_pos_le1" ("pz" "x"))
                          (("1" (inst-cp - "-1" "expt(x, j!1)")
                            (("1" (inst - "expt(x, j!1)" "1")
                              (("1" (assert) nil nil)) nil))
                            nil)
                           ("2" (assert) nil nil))
                          nil)
                         ("2" (replace -1) (("2" (assert) nil nil))
                          nil)
                         ("3"
                          (lemma "both_sides_times_neg_le1" ("nz" "x"))
                          (("1" (inst-cp - "expt(x, j!1)" "-1")
                            (("1" (inst - "1" "expt(x, j!1)")
                              (("1" (assert) nil nil)) nil))
                            nil)
                           ("2" (assert) nil nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((pred type-eq-decl nil defined_types nil)
    (nat_induction formula-decl nil naturalnumbers nil)
    (trichotomy formula-decl nil real_axioms nil)
    (both_sides_times_neg_le1 formula-decl nil real_props nil)
    (nonpos_real nonempty-type-eq-decl nil real_types nil)
    (negreal nonempty-type-eq-decl nil real_types nil)
    (nat_expt application-judgement "nat" exponentiation nil)
    (nnint_times_nnint_is_nnint application-judgement "nonneg_int"
     integers nil)
    (both_sides_times_pos_le1 formula-decl nil real_props 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_times_real_is_real application-judgement "real" reals nil)
    (real_div_nzreal_is_real application-judgement "real" reals nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (even_plus_odd_is_odd application-judgement "odd_int" integers nil)
    (expt_x1 formula-decl nil exponentiation nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (> const-decl "bool" reals nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (div_mult_pos_lt2 formula-decl nil real_props nil)
    (nzint_times_nzint_is_nzint application-judgement "nzint" integers
     nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (posint_times_posint_is_posint application-judgement "posint"
     integers nil)
    (div_mult_pos_le1 formula-decl nil real_props nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (int_expt application-judgement "int" exponentiation nil)
    (minus_int_is_int application-judgement "int" integers 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)
    (minus_even_is_even application-judgement "even_int" integers nil)
    (minus_real_is_real application-judgement "real" reals nil)
    (nnint_plus_posint_is_posint application-judgement "posint"
     integers nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (< const-decl "bool" reals nil)
    (real_gtm1_le1 nonempty-type-eq-decl nil ln_exp_series_alt nil)
    (minus_odd_is_odd application-judgement "odd_int" integers 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)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (int nonempty-type-eq-decl nil integers nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (>= const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (<= const-decl "bool" reals nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (- const-decl "[numfield -> numfield]" number_fields nil)
    (OR const-decl "[bool, bool -> bool]" booleans nil)
    (/= const-decl "boolean" notequal nil)
    (^ const-decl "real" exponentiation nil))
   shostak))
(ln_taylors_TCC1 0
  (ln_taylors_TCC1-1 nil 3270048072 ("" (grind) nil nil) nil shostak))
(ln_taylors_TCC2 0
  (ln_taylors_TCC2-1 nil 3270048235 ("" (grind) 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)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (- const-decl "[numfield -> numfield]" number_fields nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (< const-decl "bool" reals nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (between type-eq-decl nil taylor_help nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (minus_odd_is_odd application-judgement "odd_int" integers nil)
    (minus_real_is_real application-judgement "real" reals nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (/= const-decl "boolean" notequal nil))
   shostak))
(ln_taylors_TCC3 0
  (ln_taylors_TCC3-1 nil 3270063121
   ("" (skosimp*) (("" (assert) nil nil)) nil)
   ((nnint_plus_posint_is_posint application-judgement "posint"
     integers nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (minus_real_is_real application-judgement "real" reals nil)
    (real_div_nzreal_is_real application-judgement "real" reals nil))
   shostak))
(ln_taylors 0
  (ln_taylors-1 nil 3270058061
   ("" (skosimp*)
    ((""
      (lemma "Taylors[posreal]"
       ("f" "ln" "n" "n!1" "bb" "xgm1!1+1" "aa" "1"))
      (("1" (lemma "nderiv_ln" ("n" "n!1+1"))
        (("1" (replace -1)
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                                                 ("x"
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                                                  "n0z"
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