Quelle add.prf Sprache: Lisp

(add
(cauchy_add_TCC1 0
  (cauchy_add_TCC1-1 nil 3507981237
   ("" (skosimp*)
    (("" (typepred "cx!1" "cy!1")
      (("" (expand "cauchy_real?")
        (("" (skosimp*)
          (("" (inst 1 "x!1+x!2")
            (("" (expand "cauchy_prop")
              (("" (skosimp*)
                (("" (inst -1 "2+p!1")
                  (("" (inst -2 "2+p!1") (("" (grind) nil nil)) nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((cauchy_real nonempty-type-eq-decl nil cauchy nil)
    (cauchy_real? const-decl "bool" cauchy nil)
    (nat nonempty-type-eq-decl nil naturalnumbers 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)
    (real nonempty-type-from-decl nil reals nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number nonempty-type-decl nil numbers nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (posint_exp application-judgement "posint" exponentiation nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (cauchy_prop const-decl "bool" cauchy nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers 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)
    (posnat_expt application-judgement "posnat" exponentiation nil)
    (posrat_div_posrat_is_posrat application-judgement "posrat"
     rationals nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (posint_times_posint_is_posint application-judgement "posint"
     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)
    (rat_div_nzrat_is_rat application-judgement "rat" rationals nil)
    (rat_plus_rat_is_rat application-judgement "rat" rationals nil)
    (round const-decl "int" prelude_aux nil)
    (^ const-decl "real" exponentiation nil)
    (expt def-decl "real" exponentiation nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (int_plus_int_is_int application-judgement "int" integers nil))
   nil))
(add_lemma 0
  (add_lemma-1 nil 3507981237
   ("" (skosimp*)
    (("" (expand "cauchy_prop")
      (("" (skosimp*)
        (("" (inst -1 "2+p!1")
          (("" (inst -2 "2+p!1")
            (("" (expand "cauchy_add") (("" (grind) nil nil)) nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((posint_exp application-judgement "posint" exponentiation nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (cauchy_prop const-decl "bool" cauchy nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (number nonempty-type-decl nil numbers nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (int nonempty-type-eq-decl nil integers nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (>= const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (int_plus_int_is_int application-judgement "int" integers nil)
    (cauchy_add const-decl "cauchy_real" add nil)
    (expt def-decl "real" exponentiation nil)
    (^ const-decl "real" exponentiation nil)
    (round const-decl "int" prelude_aux nil)
    (rat_plus_rat_is_rat application-judgement "rat" rationals nil)
    (rat_div_nzrat_is_rat application-judgement "rat" rationals nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (mult_divides2 application-judgement "(divides(m))" divides nil)
    (mult_divides1 application-judgement "(divides(n))" divides nil)
    (even_times_int_is_even application-judgement "even_int" integers
     nil)
    (posint_times_posint_is_posint application-judgement "posint"
     integers nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (posrat_div_posrat_is_posrat application-judgement "posrat"
     rationals nil)
    (posnat_expt application-judgement "posnat" exponentiation 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))
   nil)))

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Beweissystem der NASA

Beweissystem Isabelle

NIST Cobol Testsuite

Cephes Mathematical Library

Wiener Entwicklungsmethode

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