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products/Sources/formale Sprachen/PVS/exact_real_arith/ (Beweissystem der NASA Version 6.0.9^©) Datei vom 28.9.2014 mit Größe 3 kB

Quelle int.prf Sprache: Lisp

(int
(cauchy_int_TCC1 0
  (cauchy_int_TCC1-1 nil 3287600938 ("" (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)
    (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)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (>= const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (^ const-decl "real" exponentiation nil)
    (cauchy_prop const-decl "bool" cauchy nil)
    (cauchy_real? const-decl "bool" cauchy nil)
    (posnat_expt application-judgement "posnat" exponentiation nil)
    (mult_divides1 application-judgement "(divides(n))" divides nil)
    (mult_divides2 application-judgement "(divides(m))" divides nil))
   nil))
(cauchy_nat_TCC1 0
  (cauchy_nat_TCC1-1 nil 3287600939
   ("" (expand "cauchy_nnreal?")
    (("" (skosimp*)
      (("" (inst + "n!1")
        (("" (expand "cauchy_prop") (("" (propax) nil nil)) nil)) nil))
      nil))
    nil)
   ((nnint_times_nnint_is_nnint application-judgement "nonneg_int"
     integers nil)
    (mult_divides1 application-judgement "(divides(n))" divides nil)
    (mult_divides2 application-judgement "(divides(m))" divides nil)
    (cauchy_prop const-decl "bool" cauchy nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (int nonempty-type-eq-decl nil integers nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (nnreal type-eq-decl nil real_types nil)
    (>= const-decl "bool" reals nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (real nonempty-type-from-decl nil reals nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (cauchy_nnreal? const-decl "bool" cauchy nil)
    (posint_exp application-judgement "posint" exponentiation nil))
   shostak))
(int_lemma 0
  (int_lemma-1 nil 3287600938 ("" (grind) nil nil)
   ((^ const-decl "real" exponentiation nil)
    (cauchy_int const-decl "cauchy_real" int nil)
    (cauchy_prop const-decl "bool" cauchy nil)
    (mult_divides2 application-judgement "(divides(m))" divides nil)
    (mult_divides1 application-judgement "(divides(n))" divides nil)
    (posnat_expt application-judgement "posnat" exponentiation nil))
   nil))
(nat_lemma 0
  (nat_lemma-1 nil 3287601015
   ("" (expand "cauchy_prop")
    (("" (skosimp*)
      (("" (expand "cauchy_nat") (("" (propax) nil nil)) nil)) nil))
    nil)
   ((cauchy_nat const-decl "cauchy_nnreal" int nil)
    (mult_divides2 application-judgement "(divides(m))" divides nil)
    (mult_divides1 application-judgement "(divides(n))" divides nil)
    (nnint_times_nnint_is_nnint application-judgement "nonneg_int"
     integers nil)
    (cauchy_prop const-decl "bool" cauchy nil)
    (posint_exp application-judgement "posint" exponentiation nil))
   shostak)))

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