Quellcode-Bibliothek

^© Kompilation durch diese Firma

[Weder Korrektheit noch Funktionsfähigkeit der Software werden zugesichert.]

Datei: euclidean.prf Sprache: Lisp

Original von: PVS^©

(integral_pulse
(IMP_integral_prep_TCC1 0
  (IMP_integral_prep_TCC1-1 nil 3260699953
   ("" (skosimp*)
    (("" (lemma "connected_domain")
      (("" (inst -1 "x!1" "y!1" "z!1") (("" (assert) nil nil)) nil))
      nil))
    nil)
   ((connected_domain formula-decl nil integral_pulse nil)) nil))
(IMP_integral_prep_TCC2 0
  (IMP_integral_prep_TCC2-1 nil 3260699953
   ("" (lemma "not_one_element") (("" (propax) nil nil)) nil)
   ((not_one_element formula-decl nil integral_pulse nil)) nil))
(EX3p_TCC1 0
  (EX3p_TCC1-1 nil 3262360238
   ("" (skosimp*) (("" (assert) nil nil)) nil)
   ((real_ge_is_total_order name-judgement "(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)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil))
   shostak))
(EX3p_TCC2 0
  (EX3p_TCC2-1 nil 3262360239 ("" (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)
    (T_pred const-decl "[real -> boolean]" integral_pulse nil)
    (T formal-subtype-decl nil integral_pulse nil)
    (partition type-eq-decl nil integral_def nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (below type-eq-decl nil naturalnumbers nil)
    (< const-decl "bool" reals 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)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (finite_sequence type-eq-decl nil finite_sequences nil)
    (closed_interval type-eq-decl nil intervals_real "reals/")
    (<= const-decl "bool" reals nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (below type-eq-decl nil nat_types nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (> const-decl "bool" reals nil))
   shostak))
(EX3p_TCC3 0
  (EX3p_TCC3-1 nil 3262360239 ("" (subtype-tcc) nil nil) nil shostak))
(EX3p_TCC4 0
  (EX3p_TCC4-1 nil 3262360239 ("" (assuming-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)
    (T_pred const-decl "[real -> boolean]" integral_pulse nil)
    (T formal-subtype-decl nil integral_pulse nil)
    (upto nonempty-type-eq-decl nil naturalnumbers 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)
    (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)
    (partition type-eq-decl nil integral_def nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (below type-eq-decl nil naturalnumbers nil)
    (< const-decl "bool" reals 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)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (finite_sequence type-eq-decl nil finite_sequences nil)
    (closed_interval type-eq-decl nil intervals_real "reals/")
    (<= const-decl "bool" reals nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (below type-eq-decl nil nat_types nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (> const-decl "bool" reals nil))
   shostak))
(EX3p_TCC5 0
  (EX3p_TCC5-1 nil 3262360240 ("" (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)
    (T_pred const-decl "[real -> boolean]" integral_pulse nil)
    (T formal-subtype-decl nil integral_pulse nil)
    (upto nonempty-type-eq-decl nil naturalnumbers nil)
    (integer nonempty-type-from-decl nil 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)
    (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)
    (partition type-eq-decl nil integral_def nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (below type-eq-decl nil naturalnumbers nil)
    (< const-decl "bool" reals 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)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (finite_sequence type-eq-decl nil finite_sequences nil)
    (closed_interval type-eq-decl nil intervals_real "reals/")
    (<= const-decl "bool" reals nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (below type-eq-decl nil nat_types nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (> const-decl "bool" reals nil))
   shostak))
(EX3p_TCC6 0
  (EX3p_TCC6-1 nil 3262360240 ("" (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)
    (T_pred const-decl "[real -> boolean]" integral_pulse nil)
    (T formal-subtype-decl nil integral_pulse 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_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_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (partition type-eq-decl nil integral_def nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (below type-eq-decl nil naturalnumbers nil)
    (< const-decl "bool" reals 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)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (finite_sequence type-eq-decl nil finite_sequences nil)
    (closed_interval type-eq-decl nil intervals_real "reals/")
    (<= const-decl "bool" reals nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (below type-eq-decl nil nat_types nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (> const-decl "bool" reals nil))
   shostak))
(EX3p_TCC7 0
  (EX3p_TCC7-1 nil 3352532343 ("" (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)
    (T_pred const-decl "[real -> boolean]" integral_pulse nil)
    (T formal-subtype-decl nil integral_pulse 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_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_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (partition type-eq-decl nil integral_def nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (below type-eq-decl nil naturalnumbers nil)
    (< const-decl "bool" reals 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)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (finite_sequence type-eq-decl nil finite_sequences nil)
    (closed_interval type-eq-decl nil intervals_real "reals/")
    (<= const-decl "bool" reals nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (below type-eq-decl nil nat_types nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (> const-decl "bool" reals nil))
   nil))
(EX3p 0
  (EX3p-1 nil 3262360246
   ("" (skosimp*)
    ((""
      (case "FORALL (P: partition(a!1,b!1),p,q:nat):
                                       0 < p AND p+q <= length(P) - 1 IMPLIES
                                       sigma(p, p+q, (LAMBDA (n: upto(length(P) - 1)):
                                       IF n = 0 THEN 0 ELSE seq(P)(n) - seq(P)(n - 1) ENDIF)) =
                                              seq(P)(p+q) - seq(P)(p-1)")
      (("1" (inst -1 "P!1" "p!1" "q!1-p!1")
        (("1" (assert) nil nil) ("2" (assert) nil nil)) nil)
       ("2" (hide 2)
        (("2" (induct "q")
          (("1" (skosimp*)
            (("1" (expand "sigma")
              (("1" (ground)
                (("1" (expand "sigma") (("1" (propax) nil nil)) nil))
                nil))
              nil))
            nil)
           ("2" (skosimp*)
            (("2" (inst - "P!2" "p!2")
              (("2" (assert)
                (("2" (expand "sigma" 1)
                  (("2" (replace -1) (("2" (assert) nil nil)) nil))
                  nil))
                nil))
              nil))
            nil)
           ("3" (hide 2)
            (("3" (skosimp*) (("3" (assert) nil nil)) nil)) nil)
           ("4" (skosimp*) (("4" (assert) nil nil)) nil)
           ("5" (skosimp*) (("5" (assert) nil nil)) nil)
           ("6" (skosimp*) (("6" (assert) nil nil)) nil)
           ("7" (skosimp*) nil nil)
           ("8" (skosimp*) (("8" (assert) nil nil)) nil))
          nil))
        nil)
       ("3" (skosimp*) (("3" (assert) nil nil)) nil)
       ("4" (skosimp*) (("4" (assert) nil nil)) nil)
       ("5" (skosimp*) (("5" (assert) nil nil)) nil)
       ("6" (skosimp*) (("6" (assert) nil nil)) nil)
       ("7" (skosimp*) nil nil)
       ("8" (hide 2)
        (("8" (skosimp*)
          (("8" (inst + "0") (("8" (assert) nil nil)) nil)) nil))
        nil))
      nil))
    nil)
   ((IF const-decl "[boolean, T, T -> T]" if_def nil)
    (sigma def-decl "real" sigma "reals/")
    (T_high type-eq-decl nil sigma "reals/")
    (T_low type-eq-decl nil sigma "reals/")
    (upto nonempty-type-eq-decl nil naturalnumbers nil)
    (OR const-decl "[bool, bool -> bool]" booleans nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (partition type-eq-decl nil integral_def nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (below type-eq-decl nil naturalnumbers nil)
    (< const-decl "bool" reals 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)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (> const-decl "bool" reals nil)
    (finite_sequence type-eq-decl nil finite_sequences nil)
    (closed_interval type-eq-decl nil intervals_real "reals/")
    (<= const-decl "bool" reals nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (T formal-subtype-decl nil integral_pulse nil)
    (T_pred const-decl "[real -> boolean]" integral_pulse 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)
    (below type-eq-decl nil nat_types nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
     integers nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (integer nonempty-type-from-decl nil integers nil)
    (int_plus_int_is_int application-judgement "int" integers 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)
    (p!1 skolem-const-decl "nat" integral_pulse nil)
    (q!1 skolem-const-decl "nat" integral_pulse nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (a!1 skolem-const-decl "T" integral_pulse nil)
    (b!1 skolem-const-decl "T" integral_pulse nil)
    (pred type-eq-decl nil defined_types nil)
    (nat_induction formula-decl nil naturalnumbers nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (minus_odd_is_odd application-judgement "odd_int" integers nil)
    (nnint_plus_posint_is_posint application-judgement "posint"
     integers nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil))
   shostak))
(EXse_TCC1 0
  (EXse_TCC1-1 nil 3262447218
   ("" (skosimp*) (("" (assert) nil nil)) nil)
   ((int_minus_int_is_int application-judgement "int" integers 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))
   shostak))
(EXse 0
  (EXse-3 nil 3280253181
   ("" (skosimp*)
    (("" (expand "Rie_sec")
      (("" (typepred "P!1")
        (("" (assert)
          (("" (inst - "ii!1-1")
            (("" (name "FF" "f!1(xis!1(ii!1 - 1))")
              (("" (replace -1)
                (("" (lemma "width_lem")
                  (("" (expand "finseq_appl")
                    (("" (inst -1 "a!1" "b!1" "P!1" "ii!1-1")
                      (("" (assert)
                        (("" (case " FF >= 0 AND FF <= 1")
                          (("1" (flatten)
                            (("1" (assert)
                              (("1"
                                (mult-ineq -2 -3)
                                (("1"
                                  (assert)
                                  (("1"
                                    (expand "abs")
                                    (("1"
                                      (move-terms -9 l 1)
                                      (("1"
                                        (assert)
                                        (("1"
                                          (case-replace "FF = 0")
                                          (("1" (assert) nil nil)
                                           ("2"
                                            (mult-by -9 "FF")
                                            (("2" (assert) nil nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil)
                           ("2" (inst - "xis!1(ii!1-1)")
                            (("2" (ground) nil nil)) nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((real_times_real_is_real application-judgement "real" reals nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (Rie_sec const-decl "real" integral_def nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (int_abs_is_nonneg application-judgement "{j: nonneg_int | j >= i}"
     real_defs 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)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (xis? const-decl "bool" integral_def nil)
    (width_lem formula-decl nil integral_def nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (IFF const-decl "[bool, bool -> bool]" booleans nil)
    (FF skolem-const-decl "real" integral_pulse nil)
    (both_sides_times_pos_lt1 formula-decl nil real_props nil)
    (le_times_le_any1 formula-decl nil extra_real_props nil)
    (abs_nat formula-decl nil abs_lems "reals/")
    (abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs
         nil)
    (posreal_times_posreal_is_posreal application-judgement "posreal"
     real_types nil)
    (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (width const-decl "posreal" integral_def nil)
    (int_plus_int_is_int application-judgement "int" integers nil)
    (finseq_appl const-decl "[below[length(fs)] -> T]" finite_sequences
     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)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (below type-eq-decl nil nat_types nil)
    (T_pred const-decl "[real -> boolean]" integral_pulse nil)
    (T formal-subtype-decl nil integral_pulse nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (<= const-decl "bool" reals nil)
    (closed_interval type-eq-decl nil intervals_real "reals/")
    (finite_sequence type-eq-decl nil finite_sequences 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)
    (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) (< const-decl "bool" reals nil)
    (below type-eq-decl nil naturalnumbers nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (partition type-eq-decl nil integral_def nil))
   nil)
  (EXse-2 nil 3262529290
   ("" (skosimp*)
    (("" (expand "Rie_sec")
      (("" (typepred "P!1")
        (("" (assert)
          (("" (inst - "ii!1-1")
            (("" (name "FF" "f!1(xis!1`seq(ii!1 - 1))")
              (("1" (replace -1)
                (("1" (lemma "width_lem")
                  (("1" (expand "finseq_appl")
                    (("1" (inst -1 "a!1" "b!1" "P!1" "ii!1-1")
                      (("1" (assert)
                        (("1" (case " FF >= 0 AND FF <= 1")
                          (("1" (flatten)
                            (("1" (assert)
                              (("1"
                                (mult-ineq -2 -3)
                                (("1"
                                  (assert)
                                  (("1"
                                    (expand "abs")
                                    (("1"
                                      (move-terms -9 l 1)
                                      (("1"
                                        (assert)
                                        (("1"
                                          (case-replace "FF = 0")
                                          (("1" (assert) nil nil)
                                           ("2"
                                            (mult-by -9 "FF")
                                            (("2" (assert) nil nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil)
                           ("2" (inst - "xis!1`seq(ii!1-1)")
                            (("1" (ground) nil nil)
                             ("2" (assert)
                              (("2"
                                (typepred "xis!1")
                                (("2" (assert) nil nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil)
               ("2" (typepred "xis!1")
                (("2" (assert)
                  (("2" (flatten) (("2" (assert) nil nil)) nil)) nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((Rie_sec const-decl "real" integral_def nil)
    (xis? const-decl "bool" integral_def nil)
    (width_lem formula-decl nil integral_def nil)
    (width const-decl "posreal" integral_def nil)
    (partition type-eq-decl nil integral_def nil))
   nil)
  (EXse-1 nil 3262440806
   ("" (skosimp*)
    (("" (expand "section")
      (("" (typepred "P!1")
        (("" (inst - "ii!1-1")
          (("1"
            (name "FF" "f!1(x_in(seq(P!1)(ii!1 - 1), seq(P!1)(ii!1)))")
            (("1" (replace -1)
              (("1" (lemma "width_lem")
                (("1" (expand "finseq_appl")
                  (("1" (inst -1 "a!1" "b!1" "P!1" "ii!1-1")
                    (("1" (assert)
                      (("1" (case " FF >= 0 AND FF <= 1")
                        (("1" (flatten)
                          (("1" (assert)
                            (("1" (mult-ineq -2 -3)
                              (("1"
                                (assert)
                                (("1"
                                  (expand "abs")
                                  (("1"
                                    (move-terms -9 l 1)
                                    (("1"
                                      (assert)
                                      (("1"
                                        (case-replace "FF = 0")
                                        (("1" (assert) nil nil)
                                         ("2"
                                          (mult-by -9 "FF")
                                          (("2" (assert) nil nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil)
                         ("2"
                          (inst -
                           "x_in(seq(P!1)(ii!1-1), seq(P!1)(ii!1))")
                          (("2" (ground) nil nil)) nil))
                        nil))
                      nil)
                     ("2" (assert) nil nil))
                    nil))
                  nil))
                nil))
              nil)
             ("2" (assert) nil nil) ("3" (propax) nil nil)
             ("4" (assert) nil nil))
            nil)
           ("2" (assert) nil nil))
          nil))
        nil))
      nil))
    nil)
   ((width const-decl "posreal" integral_def nil)
    (width_lem formula-decl nil integral_def nil)
    (x_in const-decl "{t: T | aa <= t AND t <= bb}" integral_def nil)
    (partition type-eq-decl nil integral_def nil))
   shostak))
(Example_3_TCC1 0
  (Example_3_TCC1-1 nil 3262529445
   ("" (skosimp*) (("" (assert) nil nil)) 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))
   shostak))
(Example_3 0
  (Example_3-5 nil 3282559921
   ("" (auto-rewrite "xis?")
    (("" (auto-rewrite "xis_lem")
      (("" (skosimp*)
        (("" (rewrite "integral_def")
          (("" (expand "integral?")
            (("" (skosimp*)
              (("" (inst + "epsi!1/1000")
                (("" (skosimp*)
                  (("" (typepred "R!1")
                    (("" (expand "Riemann_sum?")
                      (("" (skosimp*)
                        (("" (replace -1)
                          (("" (hide -1)
                            (("" (lemma "Rie_sum_alt_lem")
                              ((""
                                (inst - "a!1" "b!1" "f!1")
                                ((""
                                  (assert)
                                  ((""
                                    (inst?)
                                    ((""
                                      (replace -1)
                                      ((""
                                        (hide -1)
                                        ((""
                                          (name "N" "length(P!1)")
                                          ((""
                                            (case
                                             "(EXISTS (k: below(N-1)): xl!1 < seq(P!1)(k) AND seq(P!1)(k+1) < xh!1)")
                                            (("1"
                                              (skosimp*)
                                              (("1"
                                                (case
                                                 "EXISTS (p,q: nat): p >= 1 AND p <= length(P!1) -1
                                                                                                                                                                                                      AND seq(P!1)(p-1) <= xl!1 AND xl!1 < seq(P!1)(p)
                                                                                                                                                                                                      AND    q >=  1 AND q <= length(P!1) - 1
                                                                                                                                                                                                      AND seq(P!1)(q-1) < xh!1 AND xh!1 <= seq(P!1)(q) AND p+1 <= q-1")
                                                (("1"
                                                  (skosimp*)
                                                  (("1"
                                                    (expand
                                                     "Rie_sum_alt")
                                                    (("1"
                                                      (expand
                                                       "Rie_sec")
                                                      (("1"
                                                        (assert)
                                                        (("1"
                                                          (name
                                                           "SEC"
                                                           " LAMBDA (n: upto(length(P!1) - 1)):
                                                                                                                                                                                                                                                                                                                                                                                                                   IF n = 0 THEN 0
                                                                                                                                                                                                                                                                                                                                                                                                                   ELSE seq(P!1)(n) *
                                                                                                                                                                                                                                                                                                                                                                       f!1(xis!1(n - 1))
                                                                                                                                                                                                                                                                                                                                                                                                                         -
                                                                                                                                                                                                                                                                                                                                                                                                                         seq(P!1)(n - 1) *
                                                                                                                                                                                                                                                                                                                                                                                                                          f!1(xis!1(n - 1))
                                                                                                                                                                                                                                                                                                                                                                                                                   ENDIF")
                                                          (("1"
                                                            (replace
                                                             -1)
                                                            (("1"
                                                              (name
                                                               "SS"
                                                               "sigma[upto(length(P!1) - 1)](1, length(P!1) - 1, SEC)")
                                                              (("1"
                                                                (replace
                                                                 -1)
                                                                (("1"
                                                                  (case
                                                                   "sigma(p!1+1,q!1-1,SEC) <= SS AND SS <= sigma(p!1,q!1,SEC)")
                                                                  (("1"
                                                                    (flatten)
                                                                    (("1"
                                                                      (case
                                                                       "sigma(p!1+1, q!1 - 1, SEC) = seq(P!1)(q!1-1) - seq(P!1)(p!1)")
                                                                      (("1"
                                                                        (case
                                                                         "sigma(p!1, q!1, SEC) <= seq(P!1)(q!1) - seq(P!1)(p!1-1)")
                                                                        (("1"
                                                                          (case-replace
                                                                           "abs(-1 * SS - xl!1 + xh!1) = abs(SS - xh!1 + xl!1)")
                                                                          (("1"
                                                                            (hide
                                                                             -1)
                                                                            (("1"
                                                                              (expand
                                                                               "abs")
                                                                              (("1"
                                                                                (lift-if)
                                                                                (("1"
                                                                                  (hide
                                                                                   -6
                                                                                   -22)
                                                                                  (("1"
                                                                                    (lemma
                                                                                     "width_lem")
                                                                                    (("1"
                                                                                      (expand
                                                                                       "finseq_appl")
                                                                                      (("1"
                                                                                        (inst-cp
                                                                                         -
                                                                                         "a!1"
                                                                                         "b!1"
                                                                                         "P!1"
                                                                                         "p!1-1")
                                                                                        (("1"
                                                                                          (inst-cp
                                                                                           -
                                                                                           "a!1"
                                                                                           "b!1"
                                                                                           "P!1"
                                                                                           "p!1")
                                                                                          (("1"
                                                                                            (inst
                                                                                             -
                                                                                             "a!1"
                                                                                             "b!1"
                                                                                             "P!1"
                                                                                             "q!1-1")
                                                                                            (("1"
                                                                                              (ground)
                                                                                              nil
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil)
                                                                           ("2"
                                                                            (hide-all-but
                                                                             1)
                                                                            (("2"
                                                                              (lemma
                                                                               "abs_neg")
                                                                              (("2"
                                                                                (inst
                                                                                 -
                                                                                 "SS - xh!1 + xl!1")
                                                                                (("2"
                                                                                  (assert)
                                                                                  nil
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil)
                                                                         ("2"
                                                                          (lemma
                                                                           "EX3p")
                                                                          (("2"
                                                                            (inst
                                                                             -1
                                                                             "a!1"
                                                                             "b!1")
                                                                            (("2"
                                                                              (inst?)
                                                                              (("2"
                                                                                (assert)
                                                                                (("2"
                                                                                  (inst
                                                                                   -1
                                                                                   "P!1"
                                                                                   "p!1"
                                                                                   "q!1")
                                                                                  (("2"
                                                                                    (assert)
                                                                                    (("2"
                                                                                      (assert)
                                                                                      (("2"
                                                                                        (replace
                                                                                         -1
                                                                                         +
                                                                                         rl)
                                                                                        (("2"
                                                                                          (rewrite
                                                                                           "sigma_le")
                                                                                          (("1"
                                                                                            (hide
                                                                                             2)
                                                                                            (("1"
                                                                                              (skosimp*)
                                                                                              (("1"
                                                                                                (replace
                                                                                                 -6
                                                                                                 +
                                                                                                 rl)
                                                                                                (("1"
                                                                                                  (assert)
                                                                                                  (("1"
                                                                                                    (hide
                                                                                                     -1
                                                                                                     -2
                                                                                                     -3
                                                                                                     -4
                                                                                                     -5
                                                                                                     -6)
                                                                                                    (("1"
                                                                                                      (case
                                                                                                       "f!1(xis!1(n!1 - 1)) <= 1")
                                                                                                      (("1"
                                                                                                        (assert)
                                                                                                        (("1"
                                                                                                          (mult-by
                                                                                                           -1
                                                                                                           "seq(P!1)(n!1) - seq(P!1)(n!1 - 1)")
                                                                                                          (("1"
                                                                                                            (assert)
                                                                                                            nil
                                                                                                            nil)
                                                                                                           ("2"
                                                                                                            (hide
                                                                                                             2)
                                                                                                            (("2"
                                                                                                              (typepred
                                                                                                               "xis!1")
                                                                                                              (("2"
                                                                                                                (assert)
                                                                                                                (("2"
                                                                                                                  (inst
                                                                                                                   -
                                                                                                                   "n!1-1")
                                                                                                                  (("2"
                                                                                                                    (assert)
                                                                                                                    (("2"
                                                                                                                      (flatten)
                                                                                                                      (("2"
                                                                                                                        (assert)
                                                                                                                        nil
                                                                                                                        nil))
                                                                                                                      nil))
                                                                                                                    nil))
                                                                                                                  nil))
                                                                                                                nil))
                                                                                                              nil))
                                                                                                            nil))
                                                                                                          nil))
                                                                                                        nil)
                                                                                                       ("2"
                                                                                                        (hide
                                                                                                         2)
                                                                                                        (("2"
                                                                                                          (reveal
                                                                                                           -8)
                                                                                                          (("2"
                                                                                                            (inst
                                                                                                             -
                                                                                                             "xis!1(n!1 - 1)")
                                                                                                            (("2"
                                                                                                              (assert)
                                                                                                              nil
                                                                                                              nil))
                                                                                                            nil))
                                                                                                          nil))
                                                                                                        nil))
                                                                                                      nil))
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil)
                                                                                           ("2"
                                                                                            (skosimp*)
                                                                                            (("2"
                                                                                              (assert)
                                                                                              nil
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil)
                                                                       ("2"
                                                                        (lemma
                                                                         "EX3p")
                                                                        (("2"
                                                                          (inst
                                                                           -1
                                                                           "a!1"
                                                                           "b!1")
                                                                          (("2"
                                                                            (assert)
                                                                            (("2"
                                                                              (inst
                                                                               -1
                                                                               "P!1"
                                                                               "p!1+1"
                                                                               "q!1-1")
                                                                              (("2"
                                                                                (assert)
                                                                                (("2"
                                                                                  (case
                                                                                   "1 + p!1 <= q!1 - 1")
                                                                                  (("1"
                                                                                    (assert)
                                                                                    (("1"
                                                                                      (hide
                                                                                       2)
                                                                                      (("1"
                                                                                        (replace
                                                                                         -2
                                                                                         +
                                                                                         rl)
                                                                                        (("1"
                                                                                          (hide
                                                                                           -2)
                                                                                          (("1"
                                                                                            (rewrite
                                                                                             "sigma_restrict_eq")
                                                                                            (("1"
                                                                                              (hide
                                                                                               2)
                                                                                              (("1"
                                                                                                (expand
                                                                                                 "restrict")
                                                                                                (("1"
                                                                                                  (apply-extensionality
                                                                                                   1
                                                                                                   :hide?
                                                                                                   t)
                                                                                                  (("1"
                                                                                                    (lift-if)
                                                                                                    (("1"
                                                                                                      (ground)
                                                                                                      (("1"
                                                                                                        (replace
                                                                                                         -5
                                                                                                         +
                                                                                                         rl)
                                                                                                        (("1"
                                                                                                          (assert)
                                                                                                          (("1"
                                                                                                            (inst
                                                                                                             -
                                                                                                             "xis!1(x!1 - 1)")
                                                                                                            (("1"
                                                                                                              (hide
                                                                                                               -2
                                                                                                               -3
                                                                                                               -4
                                                                                                               -5)
                                                                                                              (("1"
                                                                                                                (lemma
                                                                                                                 "parts_order")
                                                                                                                (("1"
                                                                                                                  (inst-cp
                                                                                                                   -1
                                                                                                                   "a!1"
                                                                                                                   "b!1"
                                                                                                                   "P!1"
                                                                                                                   "p!1"
                                                                                                                   "x!1-1")
                                                                                                                  (("1"
                                                                                                                    (inst-cp
                                                                                                                     -1
                                                                                                                     "a!1"
                                                                                                                     "b!1"
                                                                                                                     "P!1"
                                                                                                                     "x!1"
                                                                                                                     "q!1-1")
                                                                                                                    (("1"
                                                                                                                      (hide
                                                                                                                       -1)
--> --------------------

--> maximum size reached

--> --------------------

¤ Dauer der Verarbeitung: 0.874 Sekunden (vorverarbeitet) ¤

Download des Quellennavigators
Download des sprechenden Kalenders
in der Quellcodebibliothek suchen

Haftungshinweis

Die Informationen auf dieser Webseite wurden nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit, noch Qualität der bereit gestellten Informationen zugesichert.

Bemerkung:

Die farbliche Syntaxdarstellung ist noch experimentell.