Quelle min_fseq.prf Sprache: Lisp

(min_fseq
(Imin_TCC1 0
  (Imin_TCC1-1 nil 3284470600
   (""
    (inst 1 "(LAMBDA ((s: ne_fseq), (ii: dom(s)), (jj:abv(ii, s))):
                        Imin[length(s),T,<=](seq(s),ii,jj))")
    (("" (skosimp*)
      (("" (expand "restrict")
        ((""
          (typepred "Imin[length(s!1), T, <=]
               (LAMBDA (s: below(length(s!1))): seq(s!1)(s), ii!1, jj!1)")
          (("" (inst?) (("1" (assert) nil nil) ("2" (assert) nil nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((NOT const-decl "[bool -> bool]" booleans nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (s!1 skolem-const-decl "ne_fseq[T]" min_fseq nil)
    (j!1 skolem-const-decl "nat" min_fseq nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (restrict const-decl "R" restrict nil)
    (Imin const-decl
     "{i: subrange(ii, jj) | (FORALL j: ii <= j AND j <= jj IMPLIES A(i) <= A(j))}"
     min_array_def nil)
    (abv type-eq-decl nil min_array_def nil)
    (below type-eq-decl nil naturalnumbers nil)
    (<= formal-const-decl "(total_order?[T])" min_fseq nil)
    (total_order? const-decl "bool" orders nil)
    (pred type-eq-decl nil defined_types nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (subrange type-eq-decl nil integers nil)
    (abv type-eq-decl nil min_fseq nil) (< const-decl "bool" reals nil)
    (<= const-decl "bool" reals nil)
    (AND const-decl "[bool, bool -> bool]" booleans 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)
    (dom type-eq-decl nil min_fseq nil)
    (ne_fseq type-eq-decl nil fseqs 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)
    (fseq type-eq-decl nil fseqs nil)
    (barray type-eq-decl nil fseqs nil)
    (T formal-nonempty-type-decl nil min_fseq nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil))
   nil))
(Imin_seq_1_TCC1 0
  (Imin_seq_1_TCC1-1 nil 3284470600 ("" (subtype-tcc) nil nil) nil
   nil))
(Imin_seq_1 0
  (Imin_seq_1-1 nil 3284470600
   ("" (skosimp*)
    (("" (typepred "Imin(s!1, ii!1, ii!1)")
      (("1" (inst?) (("1" (assert) nil) ("2" (assert) nil)))
       ("2" (skosimp*) (("2" (assert) nil))))))
    nil)
   ((Imin const-decl "{i: subrange(ii, jj) |
         (FORALL j: ii <= j AND j <= jj IMPLIES seq(s)(i) <= seq(s)(j))}"
     min_fseq nil)
    (<= formal-const-decl "(total_order?[T])" min_fseq nil)
    (total_order? const-decl "bool" orders nil)
    (pred type-eq-decl nil defined_types nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (subrange type-eq-decl nil integers nil)
    (abv type-eq-decl nil min_fseq nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (dom type-eq-decl nil min_fseq nil)
    (ne_fseq type-eq-decl nil fseqs nil)
    (> const-decl "bool" reals nil) (fseq type-eq-decl nil fseqs nil)
    (barray type-eq-decl nil fseqs nil)
    (T formal-nonempty-type-decl nil min_fseq nil)
    (< const-decl "bool" reals 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 "bool" reals 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)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil))
   nil))
(imin_TCC1 0
  (imin_TCC1-1 nil 3284470600
   ("" (inst 1 "(LAMBDA s: Imin(s,0,length(s)-1))")
    (("" (skosimp*)
      (("" (typepred "Imin(s!1, 0, length(s!1) - 1)")
        (("1" (assert)
          (("1" (skosimp*) (("1" (inst?) (("1" (assert) nil)))))))
         ("2" (hide 2) (("2" (skosimp*) (("2" (assert) nil))))))))))
    nil)
   ((real_le_is_total_order name-judgement "(total_order?[real])"
     real_props 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)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (Imin const-decl "{i: subrange(ii, jj) |
         (FORALL j: ii <= j AND j <= jj IMPLIES seq(s)(i) <= seq(s)(j))}"
     min_fseq nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (subrange type-eq-decl nil integers nil)
    (abv type-eq-decl nil min_fseq nil)
    (<= const-decl "bool" reals nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (<= formal-const-decl "(total_order?[T])" min_fseq nil)
    (total_order? const-decl "bool" orders nil)
    (pred type-eq-decl nil defined_types nil)
    (dom type-eq-decl nil min_fseq nil) (< const-decl "bool" reals 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)
    (ne_fseq type-eq-decl nil fseqs 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)
    (fseq type-eq-decl nil fseqs nil)
    (barray type-eq-decl nil fseqs nil)
    (T formal-nonempty-type-decl nil min_fseq nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (int_minus_int_is_int application-judgement "int" integers nil))
   nil))
(min_TCC1 0
  (min_TCC1-1 nil 3284470600
   ("" (inst 1 "(LAMBDA s: seq(s)(imin(s)))")
    (("" (skosimp*)
      (("" (prop)
        (("1" (skosimp*)
          (("1" (typepred "imin(s!1)") (("1" (inst?) nil)))))
         ("2" (inst?) nil))))))
    nil)
   ((NOT const-decl "[bool -> bool]" booleans nil)
    (imin const-decl
     "{i: dom(s) | (FORALL (ii: dom(s)): seq(s)(i) <= seq(s)(ii))}"
     min_fseq nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (<= formal-const-decl "(total_order?[T])" min_fseq nil)
    (total_order? const-decl "bool" orders nil)
    (pred type-eq-decl nil defined_types nil)
    (dom type-eq-decl nil min_fseq nil) (< const-decl "bool" reals 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)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (ne_fseq type-eq-decl nil fseqs 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)
    (fseq type-eq-decl nil fseqs nil)
    (barray type-eq-decl nil fseqs nil)
    (T formal-nonempty-type-decl nil min_fseq nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil))
   nil))
(min_seq_lem 0
  (min_seq_lem-1 nil 3284470600
   ("" (skosimp*) (("" (typepred "min(s!1)") (("" (inst?) nil)))) nil)
   ((min const-decl "{t: T |
         (FORALL (ii: dom(s)): t <= seq(s)(ii)) AND
          (EXISTS (jj: dom(s)): seq(s)(jj) = t)}" min_fseq nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (<= formal-const-decl "(total_order?[T])" min_fseq nil)
    (total_order? const-decl "bool" orders nil)
    (pred type-eq-decl nil defined_types nil)
    (dom type-eq-decl nil min_fseq nil)
    (ne_fseq type-eq-decl nil fseqs nil)
    (> const-decl "bool" reals nil) (fseq type-eq-decl nil fseqs nil)
    (barray type-eq-decl nil fseqs nil)
    (T formal-nonempty-type-decl nil min_fseq nil)
    (< const-decl "bool" reals 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))
   nil))
(min_seq_in? 0
  (min_seq_in?-1 nil 3284470600
   ("" (skosimp*)
    (("" (expand "in?")
      (("" (typepred "min(s!1)")
        (("" (skosimp*)
          (("" (hide -1) (("" (inst?) (("" (assert) nil))))))))))))
    nil)
   ((in? const-decl "bool" fsq nil)
    (below type-eq-decl nil naturalnumbers 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)
    (>= const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (< const-decl "bool" reals nil)
    (T formal-nonempty-type-decl nil min_fseq nil)
    (barray type-eq-decl nil fseqs nil)
    (fseq type-eq-decl nil fseqs nil) (> const-decl "bool" reals nil)
    (ne_fseq type-eq-decl nil fseqs nil)
    (dom type-eq-decl nil min_fseq nil)
    (pred type-eq-decl nil defined_types nil)
    (total_order? const-decl "bool" orders nil)
    (<= formal-const-decl "(total_order?[T])" min_fseq nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (min const-decl "{t: T |
         (FORALL (ii: dom(s)): t <= seq(s)(ii)) AND
          (EXISTS (jj: dom(s)): seq(s)(jj) = t)}" min_fseq nil))
   nil))
(min_seq_def 0
  (min_seq_def-1 nil 3284470600
   ("" (skosimp*)
    (("" (prop)
      (("1" (rewrite "min_seq_lem") nil)
       ("2" (rewrite "min_seq_in?") nil))))
    nil)
   ((dom type-eq-decl nil min_fseq nil) (< const-decl "bool" reals 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)
    (ne_fseq type-eq-decl nil fseqs 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)
    (fseq type-eq-decl nil fseqs nil)
    (barray type-eq-decl nil fseqs nil)
    (T formal-nonempty-type-decl nil min_fseq nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (min_seq_lem formula-decl nil min_fseq nil)
    (min_seq_in? formula-decl nil min_fseq nil))
   nil))
(min_seq_it_is 0
  (min_seq_it_is-1 nil 3284470600
   ("" (skosimp*)
    (("" (typepred "min(s!1)")
      (("" (expand "in?")
        (("" (skosimp*)
          (("" (replace -2 * rl)
            (("" (hide -2)
              (("" (replace -3)
                (("" (hide -3)
                  (("" (inst?)
                    (("" (inst -2 "jj!1")
                      (("" (typepred "<=")
                        (("" (expand "total_order?")
                          (("" (expand "partial_order?")
                            (("" (flatten)
                              ((""
                                (expand "antisymmetric?")
                                ((""
                                  (inst?)
                                  ((""
                                    (assert)
                                    nil))))))))))))))))))))))))))))))))
    nil)
   ((min const-decl "{t: T |
         (FORALL (ii: dom(s)): t <= seq(s)(ii)) AND
          (EXISTS (jj: dom(s)): seq(s)(jj) = t)}" min_fseq nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (<= formal-const-decl "(total_order?[T])" min_fseq nil)
    (total_order? const-decl "bool" orders nil)
    (pred type-eq-decl nil defined_types nil)
    (dom type-eq-decl nil min_fseq nil)
    (ne_fseq type-eq-decl nil fseqs nil)
    (> const-decl "bool" reals nil) (fseq type-eq-decl nil fseqs nil)
    (barray type-eq-decl nil fseqs nil)
    (T formal-nonempty-type-decl nil min_fseq nil)
    (< const-decl "bool" reals 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)
    (antisymmetric? const-decl "bool" relations nil)
    (partial_order? const-decl "bool" orders nil)
    (below type-eq-decl nil naturalnumbers nil)
    (in? const-decl "bool" fsq nil))
   nil))
(imin_seq_lem 0
  (imin_seq_lem-1 nil 3284470600
   ("" (skosimp*)
    (("" (typepred "imin(s!1)")
      (("" (typepred "min(s!1)")
        (("" (skosimp*)
          (("" (replace -2 * rl)
            (("" (hide -2)
              (("" (inst?)
                (("" (inst -3 "jj!1")
                  (("" (typepred "min_fseq.<=")
                    (("" (expand "total_order?")
                      (("" (expand "partial_order?")
                        (("" (flatten)
                          (("" (expand "antisymmetric?")
                            (("" (inst?) (("" (assert) nil nil)) nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((imin const-decl
     "{i: dom(s) | (FORALL (ii: dom(s)): seq(s)(i) <= seq(s)(ii))}"
     min_fseq nil)
    (<= formal-const-decl "(total_order?[T])" min_fseq nil)
    (total_order? const-decl "bool" orders nil)
    (pred type-eq-decl nil defined_types nil)
    (dom type-eq-decl nil min_fseq 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)
    (ne_fseq type-eq-decl nil fseqs nil)
    (> const-decl "bool" reals nil) (fseq type-eq-decl nil fseqs nil)
    (barray type-eq-decl nil fseqs nil)
    (T formal-nonempty-type-decl nil min_fseq nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (< const-decl "bool" reals 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)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (antisymmetric? const-decl "bool" relations nil)
    (partial_order? const-decl "bool" orders nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (min const-decl "{t: T |
         (FORALL (ii: dom(s)): t <= seq(s)(ii)) AND
          (EXISTS (jj: dom(s)): seq(s)(jj) = t)}" min_fseq nil))
   nil))
(imin_seq_1 0
  (imin_seq_1-1 nil 3284470600
   ("" (skosimp*) (("" (typepred "imin(s!1)") (("" (assert) nil))))
    nil)
   ((imin const-decl
     "{i: dom(s) | (FORALL (ii: dom(s)): seq(s)(i) <= seq(s)(ii))}"
     min_fseq nil)
    (<= formal-const-decl "(total_order?[T])" min_fseq nil)
    (total_order? const-decl "bool" orders nil)
    (pred type-eq-decl nil defined_types nil)
    (dom type-eq-decl nil min_fseq 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)
    (ne_fseq type-eq-decl nil fseqs nil)
    (> const-decl "bool" reals nil) (fseq type-eq-decl nil fseqs nil)
    (barray type-eq-decl nil fseqs nil)
    (T formal-nonempty-type-decl nil min_fseq nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (< const-decl "bool" reals 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)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil))
   nil))
(min_seq_2 0
  (min_seq_2-2 nil 3410628708
   ("" (skosimp*)
    (("" (typepred "min(s!1)")
      (("" (skosimp*)
        (("" (replace -2 * rl)
          (("" (hide -2)
            (("" (inst-cp -1 "0")
              (("" (inst -1 "1")
                (("1" (lift-if)
                  (("1" (ground)
                    (("1" (typepred "jj!1")
                      (("1" (case-replace "jj!1 = 0 OR jj!1 = 1")
                        (("1" (prop)
                          (("1" (assert) nil nil)
                           ("2" (replace -1)
                            (("2" (hide -1)
                              (("2"
                                (typepred "min_fseq.<=")
                                (("2"
                                  (expand "total_order?")
                                  (("2"
                                    (expand "partial_order?")
                                    (("2"
                                      (flatten)
                                      (("2"
                                        (expand "antisymmetric?")
                                        (("2"
                                          (inst?)
                                          (("2" (assert) nil nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil)
                         ("2" (assert) nil nil))
                        nil))
                      nil))
                    nil))
                  nil)
                 ("2" (assert) nil nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((min const-decl "{t: T |
         (FORALL (ii: dom(s)): t <= seq(s)(ii)) AND
          (EXISTS (jj: dom(s)): seq(s)(jj) = t)}" min_fseq nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (<= formal-const-decl "(total_order?[T])" min_fseq nil)
    (total_order? const-decl "bool" orders nil)
    (pred type-eq-decl nil defined_types nil)
    (dom type-eq-decl nil min_fseq nil)
    (ne_fseq type-eq-decl nil fseqs nil)
    (> const-decl "bool" reals nil) (fseq type-eq-decl nil fseqs nil)
    (barray type-eq-decl nil fseqs nil)
    (T formal-nonempty-type-decl nil min_fseq nil)
    (< const-decl "bool" reals 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)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (antisymmetric? const-decl "bool" relations nil)
    (partial_order? const-decl "bool" orders nil)
    (OR const-decl "[bool, bool -> bool]" booleans nil)
    (s!1 skolem-const-decl "ne_fseq[T]" min_fseq nil))
   nil)
  (min_seq_2-1 nil 3284470600
   ("" (skosimp*)
    (("" (typepred "min(s!1)")
      (("" (skosimp*)
        (("" (replace -2 * rl)
          (("" (hide -2)
            (("" (inst-cp -1 "0")
              (("" (inst -1 "1")
                (("1" (lift-if)
                  (("1" (ground)
                    (("1" (typepred "jj!1")
                      (("1" (case-replace "jj!1 = 0 OR jj!1 = 1")
                        (("1" (prop)
                          (("1" (assert) nil)
                           ("2" (replace -1)
                            (("2" (hide -1)
                              (("2"
                                (typepred "min_seq.<=")
                                (("2"
                                  (expand "total_order?")
                                  (("2"
                                    (expand "partial_order?")
                                    (("2"
                                      (flatten)
                                      (("2"
                                        (expand "antisymmetric?")
                                        (("2"
                                          (inst?)
                                          (("2"
                                            (assert)
                                            nil)))))))))))))))))))
                         ("2" (assert) nil)))))))))
                 ("2" (assert) nil))))))))))))))
    nil)
   ((fseq type-eq-decl nil fseqs nil)) nil)))

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Wiener Entwicklungsmethode

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