Quelle factorial.prf Sprache: Lisp

(factorial
(factorial_product_TCC1 0
  (factorial_product_TCC1-1 nil 3536929858 ("" (subtype-tcc) nil nil)
   ((real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil))
   nil))
(factorial_product_TCC2 0
  (factorial_product_TCC2-1 nil 3536929858 ("" (subtype-tcc) nil nil)
   nil nil))
(factorial_product_TCC3 0
  (factorial_product_TCC3-1 nil 3536930474 ("" (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)
    (>= const-decl "bool" reals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (int nonempty-type-eq-decl nil integers nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (integer nonempty-type-from-decl nil integers 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))
   nil))
(factorial_product 0
  (factorial_product-1 nil 3536930226
   ("" (skeep)
    (("" (rewrite "product_it_product" :dir rl)
      (("" (expand "product_it")
        (("" (lemma "for_induction")
          (("" (inst? -1)
            ((""
              (inst -1 "LAMBDA(i:upto(n),a:real) : a = factorial(i)")
              (("" (assert)
                (("" (hide 2)
                  (("" (skeep)
                    (("" (expand "factorial" +) (("" (assert) nil nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((product_it_product formula-decl nil product nil)
    (OR const-decl "[bool, bool -> bool]" booleans nil)
    (<= const-decl "bool" reals nil)
    (T_high type-eq-decl nil product nil)
    (T_low type-eq-decl nil product 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)
    (for_induction formula-decl nil for_iterate "structures/")
    (factorial def-decl "posnat" factorial "ints/")
    (posnat nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (PRED type-eq-decl nil defined_types nil)
    (upto nonempty-type-eq-decl nil naturalnumbers nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (int_plus_int_is_int application-judgement "int" integers nil)
    (mult_divides1 application-judgement "(divides(n))" divides nil)
    (mult_divides2 application-judgement "(divides(m))" divides nil)
    (factorial_0 formula-decl nil factorial "ints/")
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (subrange type-eq-decl nil integers nil)
    (ForBody type-eq-decl nil for_iterate "structures/")
    (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (product_it const-decl "real" product nil))
   shostak))
(product_factorial_TCC1 0
  (product_factorial_TCC1-1 nil 3536930474 ("" (subtype-tcc) nil 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))
   nil))
(product_factorial_TCC2 0
  (product_factorial_TCC2-1 nil 3536930474 ("" (subtype-tcc) nil nil)
   nil nil))
(product_factorial_TCC3 0
  (product_factorial_TCC3-1 nil 3536930474 ("" (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)
    (> 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)
    (integer nonempty-type-from-decl nil integers nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props 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))
   nil))
(product_factorial 0
  (product_factorial-1 nil 3536930495
   ("" (skeep)
    (("" (rewrite "product_it_product" :dir rl)
      (("" (expand "product_it")
        (("" (lemma "for_induction")
          (("" (inst? -1)
            ((""
              (inst -1 "LAMBDA(i:upto(p),a:real) : a = factorial(i)")
              (("" (assert)
                (("" (hide 2)
                  (("" (skeep)
                    (("" (expand "factorial" +) (("" (assert) nil nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((product_it_product formula-decl nil product nil)
    (OR const-decl "[bool, bool -> bool]" booleans nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (<= const-decl "bool" reals nil)
    (T_high type-eq-decl nil product nil)
    (T_low type-eq-decl nil product 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)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (for_induction formula-decl nil for_iterate "structures/")
    (factorial def-decl "posnat" factorial "ints/")
    (= const-decl "[T, T -> boolean]" equalities nil)
    (PRED type-eq-decl nil defined_types nil)
    (upto nonempty-type-eq-decl nil naturalnumbers nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (int_plus_int_is_int application-judgement "int" integers nil)
    (mult_divides1 application-judgement "(divides(n))" divides nil)
    (mult_divides2 application-judgement "(divides(m))" divides nil)
    (factorial_0 formula-decl nil factorial "ints/")
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (subrange type-eq-decl nil integers nil)
    (ForBody type-eq-decl nil for_iterate "structures/")
    (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (product_it const-decl "real" product nil))
   nil)))

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