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Datei: mod_div_lems.prf Sprache: Lisp

Original von: PVS^©

(mod_div_lems
(mod_div 0
  (mod_div-1 nil 3407856356 ("" (grind) nil nil)
   ((nonneg_floor_is_nat application-judgement "nat" floor_ceil 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)
    (int_abs_is_nonneg application-judgement "{j: nonneg_int | j >= i}"
     real_defs nil)
    (nzint_abs_is_pos application-judgement "{j: posint | j >= i}"
     real_defs nil)
    (div const-decl "integer" div nil)
    (abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs
         nil)
    (sgn const-decl "int" real_defs nil)
    (mod const-decl "{k | abs(k) < abs(j)}" mod nil))
   shostak))
(mod_rem 0
  (mod_rem-1 nil 3407856353
   ("" (skosimp*)
    (("" (lemma "floor_neg")
      (("" (inst -1 "i!1/j!1")
        (("" (expand "rem")
          (("" (expand "div")
            (("" (expand "mod")
              (("" (expand "sgn")
                (("" (lift-if)
                  (("" (lift-if)
                    (("" (assert)
                      (("" (lift-if)
                        (("" (expand "abs")
                          (("" (expand "integer?")
                            (("" (ground)
                              (("1"
                                (lift-if)
                                (("1" (ground) nil nil))
                                nil)
                               ("2"
                                (lift-if)
                                (("2" (ground) nil nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((floor_neg formula-decl nil floor_ceil nil)
    (mult_divides1 application-judgement "(divides(n))" divides nil)
    (mult_divides2 application-judgement "(divides(m))" divides nil)
    (rem const-decl "{k | abs(k) < abs(j)}" rem nil)
    (mod const-decl "{k | abs(k) < abs(j)}" mod nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (minus_int_is_int application-judgement "int" integers nil)
    (abs_nat_rew formula-decl nil abs_rews nil)
    (minus_nzint_is_nzint application-judgement "nzint" integers nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs
         nil)
    (minus_rat_is_rat application-judgement "rat" rationals nil)
    (int_plus_int_is_int application-judgement "int" integers nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (integer? const-decl "bool" integers nil)
    (sgn const-decl "int" real_defs nil)
    (minus_odd_is_odd application-judgement "odd_int" integers nil)
    (div const-decl "integer" div 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)
    (nonzero_integer nonempty-type-eq-decl nil integers 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)
    (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)
    (rat_div_nzrat_is_rat application-judgement "rat" rationals nil))
   nil)))

¤ Dauer der Verarbeitung: 0.15 Sekunden (vorverarbeitet) ¤

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