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Datei: Sprache: Lisp

Original von: PVS^©

(floor_more
(floor_small_nat 0
  (floor_small_nat-1 nil 3507028517
   ("" (skosimp*)
    (("" (rewrite "floor_small")
      (("1" (lift-if)
        (("1" (ground)
          (("1" (use "pos_div_ge") (("1" (assert) nil)))))))
       ("2" (expand "abs") (("2" (propax) nil))))))
    nil)
   ((floor_small formula-decl nil floor_ceil 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)
    (integer nonempty-type-from-decl nil 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)
    (/= const-decl "boolean" notequal nil)
    (nonzero_integer nonempty-type-eq-decl nil integers nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (minus_odd_is_odd application-judgement "odd_int" integers nil)
    (nnrat_div_posrat_is_nnrat application-judgement "nonneg_rat"
     rationals nil)
    (nonneg_floor_is_nat application-judgement "nat" floor_ceil nil)
    (nzint_abs_is_pos application-judgement "{j: posint | j >= i}"
     real_defs 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)
    (abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs
         nil))
   nil))
(floor_max 0
  (floor_max-1 nil 3507028517
   ("" (skosimp*)
    (("" (case "n!1 / m!1 <= n!1")
      (("1" (assert) nil)
       ("2" (hide 2)
        (("2" (rewrite "div_mult_pos_le1")
          (("2" (lemma "both_sides_times_pos_gt1")
            (("2" (inst -1 "n!1" "m!1" "1")
              (("1" (assert) nil)
               ("2" (case "n!1=0")
                (("1" (assert) nil) ("2" (assert) nil))))))))))))))
    nil)
   ((posnat nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (nonneg_int nonempty-type-eq-decl nil integers 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)
    (/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
    (nznum nonempty-type-eq-decl nil number_fields nil)
    (/= const-decl "boolean" notequal nil)
    (numfield nonempty-type-eq-decl nil number_fields 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)
    (nnrat_div_posrat_is_nnrat application-judgement "nonneg_rat"
     rationals nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (nonneg_floor_is_nat application-judgement "nat" floor_ceil nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (div_mult_pos_le1 formula-decl nil real_props 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)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (n!1 skolem-const-decl "nat" floor_more nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (both_sides_times_pos_gt1 formula-decl nil real_props nil))
   nil)))

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