Quellcode-Bibliothek

^© Kompilation durch diese Firma

[Weder Korrektheit noch Funktionsfähigkeit der Software werden zugesichert.]

Datei: harmonic_polynomials.prf Sprache: Lisp

Original von: PVS^©

(harmonic_polynomials
(harmonic_poly_real_TCC1 0
  (harmonic_poly_real_TCC1-1 nil 3261618989
   ("" (skosimp*) (("" (inst + "1") (("" (assert) nil nil)) nil)) nil)
   ((number nonempty-type-decl nil numbers nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (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)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil))
   shostak))
(harmonic_poly_real_TCC2 0
  (harmonic_poly_real_TCC2-1 nil 3261619116
   ("" (skosimp*)
    (("" (lemma "even_div2")
      (("" (inst?)
        (("" (assert)
          (("" (lemma "even_iff_not_odd")
            (("" (inst?) (("" (assert) nil nil)) nil)) nil))
          nil))
        nil))
      nil))
    nil)
   ((even_div2 formula-decl nil naturalnumbers nil)
    (nnrat_div_posrat_is_nnrat application-judgement "nonneg_rat"
     rationals nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (even_iff_not_odd formula-decl nil naturalnumbers 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))
   shostak))
(harmonic_poly_real_TCC3 0
  (harmonic_poly_real_TCC3-1 nil 3261619130
   ("" (skosimp*)
    (("" (lemma "even_div2")
      (("" (inst?)
        (("" (assert)
          (("" (lemma "odd_iff_not_even")
            (("" (inst?) (("" (assert) nil nil)) nil)) nil))
          nil))
        nil))
      nil))
    nil)
   ((even_div2 formula-decl nil naturalnumbers nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (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))
   shostak))
(harmonic_poly_real_TCC4 0
  (harmonic_poly_real_TCC4-1 nil 3261619140 ("" (grind) nil nil)
   ((even_times_int_is_even application-judgement "even_int" integers
     nil)
    (mult_divides1 application-judgement "(divides(n))" divides nil)
    (mult_divides2 application-judgement "(divides(m))" divides nil)
    (/= const-decl "boolean" notequal nil)
    (odd? const-decl "bool" integers nil))
   shostak))
(harmonic_poly_real_TCC5 0
  (harmonic_poly_real_TCC5-1 nil 3261619149 ("" (grind) nil nil)
   ((even_times_int_is_even application-judgement "even_int" integers
     nil)
    (mult_divides1 application-judgement "(divides(n))" divides nil)
    (mult_divides2 application-judgement "(divides(m))" divides nil)
    (/= const-decl "boolean" notequal nil)
    (odd? const-decl "bool" integers nil))
   shostak))
(harmonic_poly_real_TCC6 0
  (harmonic_poly_real_TCC6-1 nil 3261619159 ("" (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)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (int nonempty-type-eq-decl nil integers nil)
    (>= const-decl "bool" reals nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (/= const-decl "boolean" notequal nil)
    (odd? const-decl "bool" integers nil)
    (even_times_int_is_even application-judgement "even_int" integers
     nil)
    (mult_divides1 application-judgement "(divides(n))" divides nil)
    (mult_divides2 application-judgement "(divides(m))" divides nil))
   shostak))
(harmonic_poly_real_TCC7 0
  (harmonic_poly_real_TCC7-1 nil 3261620027 ("" (grind) nil nil)
   ((even_times_int_is_even application-judgement "even_int" integers
     nil)
    (mult_divides1 application-judgement "(divides(n))" divides nil)
    (mult_divides2 application-judgement "(divides(m))" divides nil)
    (/= const-decl "boolean" notequal nil)
    (odd? const-decl "bool" integers nil))
   shostak))
(harmonic_poly_imag_TCC1 0
  (harmonic_poly_imag_TCC1-1 nil 3261619175
   ("" (skosimp*)
    (("" (lemma "odd_div2" ("x" "i!1"))
      (("" (rewrite "even_or_odd") (("" (assert) nil nil)) nil)) nil))
    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)
    (odd_div2 formula-decl nil naturalnumbers nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (rat_div_nzrat_is_rat application-judgement "rat" rationals nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (even_or_odd formula-decl nil naturalnumbers nil))
   shostak))
(harmonic_poly_imag_TCC2 0
  (harmonic_poly_imag_TCC2-1 nil 3261619184 ("" (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)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (int nonempty-type-eq-decl nil integers nil)
    (>= const-decl "bool" reals nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (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)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (even? const-decl "bool" integers nil))
   shostak))
(harmonic_poly_imag_TCC3 0
  (harmonic_poly_imag_TCC3-1 nil 3261619194 ("" (grind) nil nil)
   ((even? const-decl "bool" integers nil)
    (/= const-decl "boolean" notequal nil))
   shostak))
(harmonic_poly_imag_TCC4 0
  (harmonic_poly_imag_TCC4-1 nil 3261619204 ("" (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)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (int nonempty-type-eq-decl nil integers nil)
    (>= const-decl "bool" reals nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (even? const-decl "bool" integers nil)
    (/= const-decl "boolean" notequal nil))
   shostak))
(harmonic_poly_imag_TCC5 0
  (harmonic_poly_imag_TCC5-1 nil 3261620046 ("" (grind) nil nil)
   ((even? const-decl "bool" integers nil)
    (/= const-decl "boolean" notequal nil))
   shostak))
(harmonic_polynomial_real_n1 0
  (harmonic_polynomial_real_n1-1 nil 3261619224
   ("" (skolem 1 ("x" "y"))
    (("" (expand "harmonic_poly_real")
      (("" (expand "sigma")
        (("" (expand "sigma")
          (("" (rewrite "expt_x0")
            (("" (rewrite "expt_x1")
              (("" (rewrite "C_0")
                (("" (case "odd?(0)")
                  (("1" (expand "odd?") (("1" (propax) nil nil)) nil)
                   ("2" (assert)
                    (("2" (expand "sigma") (("2" (propax) nil nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((harmonic_poly_real const-decl "real" harmonic_polynomials nil)
    (expt_x1 formula-decl nil exponentiation nil)
    (posint_times_posint_is_posint application-judgement "posint"
     integers nil)
    (odd? const-decl "bool" integers nil)
    (even_times_int_is_even application-judgement "even_int" integers
     nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (sigma_0_neg formula-decl nil sigma_nat nil)
    (C_0 formula-decl nil binomial 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)
    (rat_exp application-judgement "rat" exponentiation nil)
    (mult_divides2 application-judgement "(divides(m))" divides nil)
    (mult_divides1 application-judgement "(divides(n))" divides nil)
    (nzint_times_nzint_is_nzint application-judgement "nzint" integers
     nil)
    (nzreal_exp application-judgement "nzreal" exponentiation nil)
    (int_exp application-judgement "int" exponentiation nil)
    (- const-decl "[numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields 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)
    (expt_x0 formula-decl nil exponentiation nil)
    (minus_odd_is_odd application-judgement "odd_int" integers nil)
    (sigma def-decl "real" sigma nil))
   shostak))
(harmonic_polynomial_imag_n1 0
  (harmonic_polynomial_imag_n1-1 nil 3261619351
   ("" (skolem 1 ("x" "y"))
    (("" (expand "harmonic_poly_imag")
      (("" (expand "sigma")
        (("" (expand "sigma")
          (("" (rewrite "expt_x1")
            (("" (rewrite "expt_x0")
              (("" (rewrite "C_n")
                (("" (case "even?(1)")
                  (("1" (expand "even?") (("1" (propax) nil nil)) nil)
                   ("2" (assert)
                    (("2" (expand "sigma") (("2" (propax) nil nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((int_minus_int_is_int application-judgement "int" integers nil)
    (harmonic_poly_imag const-decl "real" harmonic_polynomials nil)
    (- const-decl "[numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (expt_x0 formula-decl nil exponentiation nil)
    (minus_odd_is_odd application-judgement "odd_int" integers nil)
    (even? const-decl "bool" integers nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (sigma_0_neg formula-decl nil sigma_nat nil)
    (posint_times_posint_is_posint application-judgement "posint"
     integers nil)
    (C_n formula-decl nil binomial 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)
    (rat_exp application-judgement "rat" exponentiation nil)
    (mult_divides2 application-judgement "(divides(m))" divides nil)
    (mult_divides1 application-judgement "(divides(n))" divides nil)
    (nzint_times_nzint_is_nzint application-judgement "nzint" integers
     nil)
    (nzreal_exp application-judgement "nzreal" exponentiation nil)
    (int_exp application-judgement "int" exponentiation 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)
    (expt_x1 formula-decl nil exponentiation nil)
    (sigma def-decl "real" sigma nil))
   shostak))
(harmonic_polynomial_real_rec 0
  (harmonic_polynomial_real_rec-1 nil 3261620367
   ("" (skolem 1 ("n" "x" "y"))
    (("" (expand "harmonic_poly_real")
      (("" (expand "harmonic_poly_imag")
        ((""
          (name "F1" "LAMBDA (i: nat):
              IF i > 1 + n OR odd?(i) THEN 0
              ELSE C(1 + n, i) * (-1) ^ (i / 2) *
                    (IF i = 0 THEN x ^ (1 + n)
                     ELSIF i = 1 + n THEN y ^ (1 + n)
                     ELSE (x ^ (1 - i + n)) * y ^ i
                     ENDIF)
              ENDIF")
          (("1" (replace -1)
            (("1"
              (lemma "sigma_scal[nat]"
               ("low" "0" "high" "n" "a" "x" "F" " LAMBDA (i: nat):
                IF i > n OR odd?(i) THEN 0
                ELSE C(n, i) * (-1) ^ (i / 2) *
                      (IF i = 0 THEN x ^ n
                       ELSIF i = n THEN y ^ n
                       ELSE x ^ (n - i) * y ^ i
                       ENDIF)
                ENDIF"))
              (("1" (replace -1 1 rl)
                (("1" (hide -1)
                  (("1"
                    (name "F2" "LAMBDA (i_1: nat):
               x *
                (LAMBDA (i: nat):
                   IF i > n OR odd?(i) THEN 0
                   ELSE C(n, i) * (-1) ^ (i / 2) *
                         (IF i = 0 THEN x ^ n
                          ELSIF i = n THEN y ^ n
                          ELSE x ^ (n - i) * y ^ i
                          ENDIF)
                   ENDIF)
                    (i_1)")
                    (("1" (replace -1)
                      (("1"
                        (name "F3" "LAMBDA (i: nat):
                 IF i > n OR even?(i) THEN 0
                 ELSE C(n, i) * (-1) ^ ((i - 1) / 2) *
                       (IF i = n THEN y ^ n ELSE x ^ (n - i) * y ^ i ENDIF)
                 ENDIF")
                        (("1" (replace -1)
                          (("1"
                            (lemma "sigma_scal[nat]"
                             ("low" "0" "high" "n" "F" "F3" "a" "y"))
                            (("1" (replace -1 1 rl)
                              (("1"
                                (case
                                 "sigma(0, n, F2) = sigma(0, n+1, F2)")
                                (("1"
                                  (replace -1 1)
                                  (("1"
                                    (case
                                     "FORALL (n:nat): sigma(0, n, LAMBDA (i: nat): y * F3(i)) = sigma(0,n+1, LAMBDA (i:nat): IF i = 0 THEN 0 ELSE y*F3(i-1) ENDIF)")
                                    (("1"
                                      (inst - "n")
                                      (("1"
                                        (replace -1 1)
                                        (("1"
                                          (lemma
                                           "sigma_minus[nat]"
                                           ("low"
                                            "0"
                                            "high"
                                            "n+1"
                                            "F"
                                            "F2"
                                            "G"
                                            "LAMBDA (i: nat): IF i = 0 THEN 0 ELSE y * F3(i - 1) ENDIF"))
                                          (("1"
                                            (replace -1 1)
                                            (("1"
                                              (hide -1 -2 -3 -4)
                                              (("1"
                                                (lemma
                                                 "sigma_eq[nat]"
                                                 ("low"
                                                  "0"
                                                  "high"
                                                  "n+1"
                                                  "F"
                                                  "F1"
                                                  "G"
                                                  "LAMBDA (i_1: nat):
               F2(i_1) -
                (LAMBDA (i: nat): IF i = 0 THEN 0 ELSE y * F3(i - 1) ENDIF)
                    (i_1)"))
                                                (("1"
                                                  (split -1)
                                                  (("1"
                                                    (assert)
                                                    nil
                                                    nil)
                                                   ("2"
                                                    (hide 2)
                                                    (("2"
                                                      (skosimp*)
                                                      (("2"
                                                        (typepred
                                                         "n!1")
                                                        (("2"
                                                          (expand "F1")
                                                          (("2"
                                                            (hide
                                                             -5
                                                             -4
                                                             -3)
                                                            (("2"
                                                              (expand
                                                               "F2")
                                                              (("2"
                                                                (expand
                                                                 "F3")
                                                                (("2"
                                                                  (case
                                                                   "n!1=0")
                                                                  (("1"
                                                                    (replace
                                                                     -1)
                                                                    (("1"
                                                                      (rewrite
                                                                       "C_0")
                                                                      (("1"
                                                                        (rewrite
                                                                         "C_0")
                                                                        (("1"
                                                                          (rewrite
                                                                           "expt_x0")
                                                                          (("1"
                                                                            (case
                                                                             "odd?(0)")
                                                                            (("1"
                                                                              (expand
                                                                               "odd?")
                                                                              (("1"
                                                                                (propax)
                                                                                nil
                                                                                nil))
                                                                              nil)
                                                                             ("2"
                                                                              (assert)
                                                                              (("2"
                                                                                (expand
                                                                                 "^")
                                                                                (("2"
                                                                                  (expand
                                                                                   "expt"
                                                                                   2
                                                                                   1)
                                                                                  (("2"
                                                                                    (assert)
                                                                                    nil
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil)
                                                                   ("2"
                                                                    (assert)
                                                                    (("2"
                                                                      (case
                                                                       "n!1= 1+n")
                                                                      (("1"
                                                                        (assert)
                                                                        (("1"
                                                                          (replace
                                                                           -1)
                                                                          (("1"
                                                                            (rewrite
                                                                             "C_n")
                                                                            (("1"
                                                                              (rewrite
                                                                               "C_n")
                                                                              (("1"
                                                                                (case
                                                                                 "even?(n)")
                                                                                (("1"
                                                                                  (case
                                                                                   "odd?(n+1)")
                                                                                  (("1"
                                                                                    (assert)
                                                                                    nil
                                                                                    nil)
                                                                                   ("2"
                                                                                    (hide-all-but
                                                                                     (-1
                                                                                      1))
                                                                                    (("2"
                                                                                      (expand
                                                                                       "even?")
                                                                                      (("2"
                                                                                        (skosimp*)
                                                                                        (("2"
                                                                                          (replace
                                                                                           -1)
                                                                                          (("2"
                                                                                            (expand
                                                                                             "odd?")
                                                                                            (("2"
                                                                                              (inst
                                                                                               +
                                                                                               "j!1")
                                                                                              nil
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil)
                                                                                 ("2"
                                                                                  (assert)
                                                                                  (("2"
                                                                                    (case
                                                                                     "NOT (odd?(1+n))")
                                                                                    (("1"
                                                                                      (assert)
                                                                                      (("1"
                                                                                        (rewrite
                                                                                         "even_or_odd")
                                                                                        (("1"
                                                                                          (hide
                                                                                           1)
                                                                                          (("1"
                                                                                            (expand
                                                                                             "odd?")
                                                                                            (("1"
                                                                                              (skosimp*)
                                                                                              (("1"
                                                                                                (replace
                                                                                                 -1)
                                                                                                (("1"
                                                                                                  (lemma
                                                                                                   "div_cancel1"
                                                                                                   ("x"
                                                                                                    "j!1"
                                                                                                    "n0z"
                                                                                                    "2"))
                                                                                                  (("1"
                                                                                                    (replace
                                                                                                     -1)
                                                                                                    (("1"
                                                                                                      (lemma
                                                                                                       "div_cancel1"
                                                                                                       ("x"
                                                                                                        "j!1+1"
                                                                                                        "n0z"
                                                                                                        "2"))
                                                                                                      (("1"
                                                                                                        (replace
                                                                                                         -1)
                                                                                                        (("1"
                                                                                                          (replace
                                                                                                           -3
                                                                                                           2
                                                                                                           rl)
                                                                                                          (("1"
                                                                                                            (replace
                                                                                                             -3
                                                                                                             *
                                                                                                             rl)
                                                                                                            (("1"
                                                                                                              (typepred
                                                                                                               "n")
                                                                                                              (("1"
                                                                                                                (expand
                                                                                                                 "^"
                                                                                                                 2)
                                                                                                                (("1"
                                                                                                                  (assert)
                                                                                                                  (("1"
                                                                                                                    (expand
                                                                                                                     "expt"
                                                                                                                     2
                                                                                                                     1)
                                                                                                                    (("1"
                                                                                                                      (expand
                                                                                                                       "expt"
                                                                                                                       2
                                                                                                                       2)
                                                                                                                      (("1"
                                                                                                                        (assert)
                                                                                                                        nil
                                                                                                                        nil))
                                                                                                                      nil))
                                                                                                                    nil))
                                                                                                                  nil))
                                                                                                                nil))
                                                                                                              nil))
                                                                                                            nil))
                                                                                                          nil))
                                                                                                        nil))
                                                                                                      nil))
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil)
                                                                                     ("2"
                                                                                      (hide-all-but
                                                                                       (-1
                                                                                        1))
                                                                                      (("2"
                                                                                        (expand
                                                                                         "odd?")
                                                                                        (("2"
                                                                                          (skosimp*)
                                                                                          (("2"
                                                                                            (replace
                                                                                             -1)
                                                                                            (("2"
                                                                                              (expand
                                                                                               "even?")
                                                                                              (("2"
                                                                                                (inst
                                                                                                 +
                                                                                                 "j!1")
                                                                                                nil
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil)
                                                                       ("2"
                                                                        (assert)
                                                                        (("2"
                                                                          (case
                                                                           "odd?(n!1)")
                                                                          (("1"
                                                                            (case
                                                                             "even?(n!1-1)")
                                                                            (("1"
                                                                              (assert)
                                                                              nil
                                                                              nil)
                                                                             ("2"
                                                                              (hide-all-but
                                                                               (1
                                                                                -1))
                                                                              (("2"
                                                                                (expand
                                                                                 "odd?")
                                                                                (("2"
                                                                                  (skosimp*)
                                                                                  (("2"
                                                                                    (replace
                                                                                     -1)
                                                                                    (("2"
                                                                                      (expand
                                                                                       "even?")
                                                                                      (("2"
                                                                                        (inst
                                                                                         +
                                                                                         "j!1")
                                                                                        nil
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil)
                                                                           ("2"
                                                                            (case
                                                                             "NOT (even?(n!1-1))")
                                                                            (("1"
                                                                              (assert)
                                                                              (("1"
                                                                                (rewrite
                                                                                 "even_or_odd")
                                                                                (("1"
                                                                                  (hide
                                                                                   1)
                                                                                  (("1"
                                                                                    (expand
                                                                                     "odd?")
                                                                                    (("1"
                                                                                      (skosimp*)
                                                                                      (("1"
                                                                                        (lemma
                                                                                         "div_cancel1"
                                                                                         ("x"
                                                                                          "1+j!1"
                                                                                          "n0z"
                                                                                          "2"))
                                                                                        (("1"
                                                                                          (lemma
                                                                                           "div_cancel1"
                                                                                           ("x"
                                                                                            "j!1"
                                                                                            "n0z"
                                                                                            "2"))
                                                                                          (("1"
                                                                                            (case
                                                                                             "(n!1 - 2) / 2 = j!1")
                                                                                            (("1"
                                                                                              (replace
                                                                                               -1)
                                                                                              (("1"
                                                                                                (case
                                                                                                 "(n!1) / 2 = j!1+1")
                                                                                                (("1"
                                                                                                  (replace
                                                                                                   -1)
                                                                                                  (("1"
                                                                                                    (case
                                                                                                     "n!1=n")
                                                                                                    (("1"
                                                                                                      (replace
                                                                                                       -1)
                                                                                                      (("1"
                                                                                                        (rewrite
                                                                                                         "C_n")
                                                                                                        (("1"
                                                                                                          (rewrite
                                                                                                           "C_n_1")
                                                                                                          (("1"
                                                                                                            (rewrite
                                                                                                             "C_n_1")
                                                                                                            (("1"
                                                                                                              (lemma
                                                                                                               "expt_plus"
                                                                                                               ("n0x"
                                                                                                                "-1"
                                                                                                                "i"
                                                                                                                "1"
                                                                                                                "j"
                                                                                                                "j!1"))
                                                                                                              (("1"
                                                                                                                (rewrite
                                                                                                                 "expt_x1"
                                                                                                                 -1)
                                                                                                                (("1"
                                                                                                                  (replace
                                                                                                                   -1)
                                                                                                                  (("1"
                                                                                                                    (name-replace
                                                                                                                     "K1"
                                                                                                                     "(-1)^j!1")
                                                                                                                    (("1"
                                                                                                                      (rewrite
                                                                                                                       "expt_x1"
                                                                                                                       3)
                                                                                                                      (("1"
                                                                                                                        (expand
                                                                                                                         "^"
                                                                                                                         3)
                                                                                                                        (("1"
                                                                                                                          (expand
                                                                                                                           "expt"
                                                                                                                           3
                                                                                                                           1)
                                                                                                                          (("1"
                                                                                                                            (grind)
                                                                                                                            nil
                                                                                                                            nil))
                                                                                                                          nil))
                                                                                                                        nil))
                                                                                                                      nil))
                                                                                                                    nil))
                                                                                                                  nil))
                                                                                                                nil))
                                                                                                              nil))
                                                                                                            nil))
                                                                                                          nil))
                                                                                                        nil))
                                                                                                      nil)
                                                                                                     ("2"
                                                                                                      (assert)
                                                                                                      (("2"
                                                                                                        (lemma
                                                                                                         "C_n_plus_1"
                                                                                                         ("n"
                                                                                                          "n"
                                                                                                          "k"
                                                                                                          "n!1"))
                                                                                                        (("2"
                                                                                                          (replace
                                                                                                           -1
                                                                                                           4)
                                                                                                          (("2"
                                                                                                            (lemma
                                                                                                             "expt_plus"
                                                                                                             ("n0x"
                                                                                                              "-1"
                                                                                                              "i"
                                                                                                              "1"
                                                                                                              "j"
                                                                                                              "j!1"))
                                                                                                            (("2"
                                                                                                              (rewrite
                                                                                                               "expt_x1"
                                                                                                               -1)
                                                                                                              (("2"
                                                                                                                (replace
                                                                                                                 -1
                                                                                                                 4)
                                                                                                                (("2"
                                                                                                                  (name-replace
                                                                                                                   "K10"
                                                                                                                   "(-1)^j!1")
                                                                                                                  (("2"
                                                                                                                    (name-replace
                                                                                                                     "K11"
                                                                                                                     "C(n,n!1-1)")
                                                                                                                    (("2"
                                                                                                                      (name-replace
                                                                                                                       "K12"
                                                                                                                       "C(n,n!1)")
                                                                                                                      (("2"
                                                                                                                        (expand
                                                                                                                         "^"
                                                                                                                         4)
                                                                                                                        (("2"
                                                                                                                          (expand
                                                                                                                           "expt"
                                                                                                                           4
                                                                                                                           7)
                                                                                                                          (("2"
                                                                                                                            (expand
                                                                                                                             "expt"
--> --------------------

--> maximum size reached

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

¤ Dauer der Verarbeitung: 0.27 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.