Quelle path_circ.prf Sprache: Lisp

(path_circ
(path_reduc_TCC1 0
  (path_reduc_TCC1-1 nil 3253636829 ("" (subtype-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)
    (set type-eq-decl nil sets nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (dbl const-decl "set[T]" doubletons nil)
    (doubleton type-eq-decl nil doubletons nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (finite_set type-eq-decl nil finite_sets nil)
    (pregraph type-eq-decl nil graphs nil)
    (graph type-eq-decl nil graphs 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)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (below type-eq-decl nil nat_types nil)
    (finseq type-eq-decl nil finite_sequences nil)
    (prewalk type-eq-decl nil walks nil)
    (path? const-decl "bool" paths nil)
    (Path type-eq-decl nil paths 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)
    (below type-eq-decl nil naturalnumbers nil)
    (G!1 skolem-const-decl "graph[T]" path_circ nil)
    (walk? const-decl "bool" walks nil)
    (edge? const-decl "bool" graphs nil)
    (finseq_appl const-decl "[below[length(fs)] -> T]" finite_sequences
     nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (nil application-judgement "finite_set[T]" path_circ nil)
    (T formal-type-decl nil path_circ nil)
    (verts_in? const-decl "bool" walks nil)
    (/= const-decl "boolean" notequal nil))
   nil))
(path_reduc 0
  (path_reduc-1 nil 3253636829
   ("" (skosimp*)
    (("" (typepred "p!1")
      (("" (install-rewrites "paths") (("" (grind) nil nil)) nil))
      nil))
    nil)
   ((Path type-eq-decl nil paths nil)
    (path? const-decl "bool" paths nil)
    (graph type-eq-decl nil graphs nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (pregraph type-eq-decl nil graphs nil)
    (finite_set type-eq-decl nil finite_sets nil)
    (doubleton type-eq-decl nil doubletons nil)
    (dbl const-decl "set[T]" doubletons nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (/= const-decl "boolean" notequal nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (set type-eq-decl nil sets nil)
    (prewalk type-eq-decl nil walks nil)
    (finseq type-eq-decl nil finite_sequences nil)
    (T formal-type-decl nil path_circ nil)
    (below type-eq-decl nil nat_types 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)
    (nil application-judgement "finite_set[T]" path_circ nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (verts_in? const-decl "bool" walks nil)
    (finseq_appl const-decl "[below[length(fs)] -> T]" finite_sequences
     nil)
    (edge? const-decl "bool" graphs nil)
    (walk? const-decl "bool" walks nil)
    (reducible? const-decl "bool" circuits nil)
    (reduced? const-decl "bool" circuits nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers 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)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields 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, numfield -> numfield]" number_fields nil)
    (< const-decl "bool" reals nil)
    (below type-eq-decl nil naturalnumbers nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (posnat nonempty-type-eq-decl nil integers nil))
   nil))
(trunc_long 0
  (trunc_long-1 nil 3253636829
   ("" (expand "trunc1") (("" (skosimp*) (("" (grind) nil nil)) nil))
    nil)
   ((real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (int_min application-judgement "{k: int | k <= i AND k <= j}"
     real_defs nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (int_plus_int_is_int application-judgement "int" integers nil)
    (nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
     integers nil)
    (O const-decl "finseq" finite_sequences nil)
    (^ const-decl "finseq" finite_sequences nil)
    (min const-decl "{p: real | p <= m AND p <= n}" real_defs nil)
    (trunc1 const-decl "prewalk" walks nil))
   nil))
(trunc_walk 0
  (trunc_walk-1 nil 3253636829
   ("" (skosimp*)
    (("" (expand "trunc1")
      (("" (expand "walk?")
        (("" (flatten)
          (("" (prop)
            (("1" (grind) nil nil)
             ("2" (skosimp*)
              (("2" (expand "finseq_appl")
                (("2" (inst - "n!1")
                  (("2" (expand* "^" min empty_seq)
                    (("2" (assert) nil nil)) nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((trunc1 const-decl "prewalk" walks nil)
    (nil application-judgement "finite_set[T]" path_circ 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)
    (int_min application-judgement "{k: int | k <= i AND k <= j}"
     real_defs nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (edge? const-decl "bool" graphs nil)
    (/= const-decl "boolean" notequal nil)
    (finseq_appl const-decl "[below[length(fs)] -> T]" finite_sequences
     nil)
    (verts_in? const-decl "bool" walks nil)
    (T formal-type-decl nil path_circ nil)
    (^ const-decl "finseq" finite_sequences nil)
    (min const-decl "{p: real | p <= m AND p <= n}" real_defs nil)
    (empty_seq const-decl "finseq" finite_sequences nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props 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)
    (below type-eq-decl nil nat_types nil)
    (finseq type-eq-decl nil finite_sequences nil)
    (> const-decl "bool" reals nil)
    (prewalk type-eq-decl nil walks nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (< const-decl "bool" reals nil)
    (IF const-decl "[boolean, T, T -> T]" if_def nil)
    (below type-eq-decl nil naturalnumbers nil)
    (walk? const-decl "bool" walks nil))
   nil))
(walks_concat_red_TCC1 0
  (walks_concat_red_TCC1-1 nil 3253636829 ("" (subtype-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)
    (set type-eq-decl nil sets nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (dbl const-decl "set[T]" doubletons nil)
    (doubleton type-eq-decl nil doubletons nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (finite_set type-eq-decl nil finite_sets nil)
    (pregraph type-eq-decl nil graphs nil)
    (graph type-eq-decl nil graphs 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)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (below type-eq-decl nil nat_types nil)
    (finseq type-eq-decl nil finite_sequences nil)
    (prewalk type-eq-decl nil walks nil)
    (T formal-type-decl nil path_circ nil)
    (verts_in? const-decl "bool" walks nil)
    (finseq_appl const-decl "[below[length(fs)] -> T]" finite_sequences
     nil)
    (/= const-decl "boolean" notequal nil)
    (edge? const-decl "bool" graphs nil)
    (walk? const-decl "bool" walks nil)
    (nil application-judgement "finite_set[T]" path_circ nil))
   nil))
(walks_concat_red_TCC2 0
  (walks_concat_red_TCC2-1 nil 3253636829 ("" (subtype-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)
    (set type-eq-decl nil sets nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (dbl const-decl "set[T]" doubletons nil)
    (doubleton type-eq-decl nil doubletons nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (finite_set type-eq-decl nil finite_sets nil)
    (pregraph type-eq-decl nil graphs nil)
    (graph type-eq-decl nil graphs 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)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (below type-eq-decl nil nat_types nil)
    (finseq type-eq-decl nil finite_sequences nil)
    (prewalk type-eq-decl nil walks nil)
    (T formal-type-decl nil path_circ nil)
    (verts_in? const-decl "bool" walks nil)
    (finseq_appl const-decl "[below[length(fs)] -> T]" finite_sequences
     nil)
    (/= const-decl "boolean" notequal nil)
    (edge? const-decl "bool" graphs nil)
    (walk? const-decl "bool" walks nil)
    (reducible? const-decl "bool" circuits nil)
    (reduced? const-decl "bool" circuits nil)
    (nil application-judgement "finite_set[T]" path_circ nil))
   nil))
(walks_concat_red_TCC3 0
  (walks_concat_red_TCC3-1 nil 3253636829 ("" (subtype-tcc) nil nil)
   ((T formal-type-decl nil path_circ nil)
    (verts_in? const-decl "bool" walks nil)
    (finseq_appl const-decl "[below[length(fs)] -> T]" finite_sequences
     nil)
    (/= const-decl "boolean" notequal nil)
    (edge? const-decl "bool" graphs nil)
    (walk? const-decl "bool" walks nil)
    (reducible? const-decl "bool" circuits nil)
    (reduced? const-decl "bool" circuits nil)
    (nil application-judgement "finite_set[T]" path_circ nil))
   nil))
(walks_concat_red_TCC4 0
  (walks_concat_red_TCC4-1 nil 3253636829 ("" (subtype-tcc) nil nil)
   ((T formal-type-decl nil path_circ nil)
    (verts_in? const-decl "bool" walks nil)
    (finseq_appl const-decl "[below[length(fs)] -> T]" finite_sequences
     nil)
    (/= const-decl "boolean" notequal nil)
    (edge? const-decl "bool" graphs nil)
    (walk? const-decl "bool" walks nil)
    (reducible? const-decl "bool" circuits nil)
    (reduced? const-decl "bool" circuits nil)
    (nil application-judgement "finite_set[T]" path_circ nil))
   nil))
(walks_concat_red_TCC5 0
  (walks_concat_red_TCC5-1 nil 3253636829 ("" (subtype-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)
    (set type-eq-decl nil sets nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (dbl const-decl "set[T]" doubletons nil)
    (doubleton type-eq-decl nil doubletons nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (finite_set type-eq-decl nil finite_sets nil)
    (pregraph type-eq-decl nil graphs nil)
    (graph type-eq-decl nil graphs 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)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (below type-eq-decl nil nat_types nil)
    (finseq type-eq-decl nil finite_sequences nil)
    (prewalk type-eq-decl nil walks nil)
    (int_minus_int_is_int application-judgement "int" integers 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)
    (T formal-type-decl nil path_circ nil)
    (verts_in? const-decl "bool" walks nil)
    (finseq_appl const-decl "[below[length(fs)] -> T]" finite_sequences
     nil)
    (/= const-decl "boolean" notequal nil)
    (edge? const-decl "bool" graphs nil)
    (walk? const-decl "bool" walks nil)
    (reducible? const-decl "bool" circuits nil)
    (reduced? const-decl "bool" circuits nil)
    (nil application-judgement "finite_set[T]" path_circ nil))
   nil))
(walks_concat_red_TCC6 0
  (walks_concat_red_TCC6-1 nil 3253636829 ("" (subtype-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)
    (set type-eq-decl nil sets nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (dbl const-decl "set[T]" doubletons nil)
    (doubleton type-eq-decl nil doubletons nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (finite_set type-eq-decl nil finite_sets nil)
    (pregraph type-eq-decl nil graphs nil)
    (graph type-eq-decl nil graphs 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)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (below type-eq-decl nil nat_types nil)
    (finseq type-eq-decl nil finite_sequences nil)
    (prewalk type-eq-decl nil walks 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)
    (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)
    (T formal-type-decl nil path_circ nil)
    (verts_in? const-decl "bool" walks nil)
    (finseq_appl const-decl "[below[length(fs)] -> T]" finite_sequences
     nil)
    (/= const-decl "boolean" notequal nil)
    (edge? const-decl "bool" graphs nil)
    (walk? const-decl "bool" walks nil)
    (reducible? const-decl "bool" circuits nil)
    (reduced? const-decl "bool" circuits nil)
    (nil application-judgement "finite_set[T]" path_circ nil))
   nil))
(walks_concat_red_TCC7 0
  (walks_concat_red_TCC7-1 nil 3253636829
   ("" (lemma "trunc_long")
    (("" (lemma "verts_in?_concat")
      (("" (lemma "trunc_walk")
        (("" (skosimp*)
          (("" (inst -3 "u!1" "w!1")
            (("" (inst -2 "G!1" "trunc1(u!1)" "w!1")
              (("1" (inst -1 "G!1" "u!1") (("1" (grind) nil nil)) nil)
               ("2" (grind) nil nil) ("3" (grind) nil nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((T formal-type-decl nil path_circ nil)
    (verts_in?_concat formula-decl nil walks nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (>= const-decl "bool" reals nil)
    (u!1 skolem-const-decl "prewalk[T]" path_circ nil)
    (trunc1 const-decl "prewalk" walks nil)
    (Longprewalk type-eq-decl nil walks nil)
    (G!1 skolem-const-decl "graph[T]" path_circ nil)
    (verts_in? const-decl "bool" walks nil)
    (graph type-eq-decl nil graphs nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (pregraph type-eq-decl nil graphs nil)
    (finite_set type-eq-decl nil finite_sets nil)
    (doubleton type-eq-decl nil doubletons nil)
    (dbl const-decl "set[T]" doubletons nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (/= const-decl "boolean" notequal nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (set type-eq-decl nil sets nil) (Seq type-eq-decl nil walks nil)
    (nil application-judgement "finite_set[T]" path_circ nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (int_min application-judgement "{k: int | k <= i AND k <= j}"
     real_defs nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (int_plus_int_is_int application-judgement "int" integers nil)
    (nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
     integers nil)
    (reduced? const-decl "bool" circuits nil)
    (reducible? const-decl "bool" circuits nil)
    (O const-decl "finseq" finite_sequences nil)
    (^ const-decl "finseq" finite_sequences nil)
    (min const-decl "{p: real | p <= m AND p <= n}" real_defs nil)
    (walk? const-decl "bool" walks nil)
    (edge? const-decl "bool" graphs nil)
    (finseq_appl const-decl "[below[length(fs)] -> T]" finite_sequences
     nil)
    (empty_seq const-decl "finseq" finite_sequences nil)
    (below type-eq-decl nil naturalnumbers nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (IF const-decl "[boolean, T, T -> T]" if_def 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)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (odd_plus_odd_is_even application-judgement "even_int" integers
     nil)
    (even_minus_odd_is_odd application-judgement "odd_int" integers
     nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (i!1 skolem-const-decl
     "below(IF 0 > length(u!1) - 2 THEN 0 ELSE length(u!1) - 1 ENDIF)"
     path_circ nil)
    (w!1 skolem-const-decl "prewalk[T]" path_circ nil)
    (minus_odd_is_odd application-judgement "odd_int" integers nil)
    (i!2 skolem-const-decl "below(length(u!1) + w!1`length - 1)"
     path_circ nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (prewalk type-eq-decl nil walks 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)
    (finseq type-eq-decl nil finite_sequences nil)
    (below type-eq-decl nil nat_types nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (trunc_walk formula-decl nil path_circ nil)
    (trunc_long formula-decl nil path_circ nil))
   nil))
(walks_concat_red 0
  (walks_concat_red-1 nil 3253636829
   ("" (expand "trunc1")
    (("" (skosimp*)
      (("" (expand "reduced?" 2)
        (("" (expand "reducible?" -)
          (("" (skolem! -8)
            (("" (case "k!1 < length(u!1)-1")
              (("1" (hide -3)
                (("1" (expand "reduced?" -5)
                  (("1" (expand "reducible?" 1)
                    (("1" (inst 1 "k!1")
                      (("1" (assert)
                        (("1" (expand "finseq_appl")
                          (("1" (grind) nil nil)) nil))
                        nil))
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    (real_gt_is_strict_total_order name-judgement
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    (T formal-type-decl nil path_circ nil)
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    (number nonempty-type-decl nil numbers nil)
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    (real_gt_is_strict_total_order name-judgement
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   nil))
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    (graph type-eq-decl nil graphs nil)
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    (int_minus_int_is_int application-judgement "int" integers nil)
    (real_gt_is_strict_total_order name-judgement
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    (edge? const-decl "bool" graphs nil)
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    (from? const-decl "bool" walks nil)
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    (dbl const-decl "set[T]" doubletons nil)
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    (graph type-eq-decl nil graphs nil)
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    (int_minus_int_is_int application-judgement "int" integers nil)
    (real_gt_is_strict_total_order name-judgement
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    (edge? const-decl "bool" graphs nil)
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    (path? const-decl "bool" paths nil)
    (from? const-decl "bool" walks nil)
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    (real_pred const-decl "[number_field -> boolean]" reals nil)
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     real_props nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
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     "(strict_total_order?[real])" real_props nil)
    (finseq_appl const-decl "[below[length(fs)] -> T]" finite_sequences
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    (T formal-type-decl nil path_circ nil)
    (verts_in? const-decl "bool" walks nil)
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    (walk? const-decl "bool" walks nil)
    (path? const-decl "bool" paths nil)
    (from? const-decl "bool" walks nil)
    (path_from? const-decl "bool" paths nil)
    (nil application-judgement "finite_set[T]" path_circ nil))
   nil))
(red_compos_TCC4 0
  (red_compos_TCC4-1 nil 3253636829 ("" (subtype-tcc) nil nil)
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    (NOT const-decl "[bool -> bool]" booleans nil)
    (set type-eq-decl nil sets nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
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    (doubleton type-eq-decl nil doubletons nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (finite_set type-eq-decl nil finite_sets nil)
    (pregraph type-eq-decl nil graphs nil)
    (graph type-eq-decl nil graphs nil)
    (number nonempty-type-decl nil numbers nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
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    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (> const-decl "bool" reals nil)
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    (int_plus_int_is_int application-judgement "int" integers nil)
    (int_min application-judgement "{k: int | k <= i AND k <= j}"
     real_defs nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
     integers nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (min const-decl "{p: real | p <= m AND p <= n}" real_defs nil)
    (^ const-decl "finseq" finite_sequences nil)
    (below type-eq-decl nil naturalnumbers nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields 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_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (G!1 skolem-const-decl "graph[T]" path_circ nil)
    (finseq_appl const-decl "[below[length(fs)] -> T]" finite_sequences
     nil)
    (T formal-type-decl nil path_circ nil)
    (verts_in? const-decl "bool" walks nil)
    (edge? const-decl "bool" graphs nil)
    (walk? const-decl "bool" walks nil)
    (path? const-decl "bool" paths nil)
    (from? const-decl "bool" walks nil)
    (path_from? const-decl "bool" paths nil)
    (trunc1 const-decl "prewalk" walks nil)
    (rev const-decl "finseq[T]" doubletons nil)
    (O const-decl "finseq" finite_sequences nil)
    (nil application-judgement "finite_set[T]" path_circ nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (/= const-decl "boolean" notequal nil))
   nil))
(red_compos 0
  (red_compos-1 nil 3253636829
   ("" (skosimp*)
    (("" (lemma "path_reduc")
      (("" (lemma "path?_rev")
        (("" (lemma "walks_concat_red")
          (("" (lemma "index_rev")
            (("" (inst -1 "q!1")
              (("" (inst -3 "G!1" "q!1")
                (("" (inst-cp -4 "G!1" "p!1")
                  (("1" (inst -2 "G!1" "p!1" "rev(q!1)")
                    (("1" (lemma "path_from_l")
                      (("1" (inst-cp -1 "G!1" "p!1" "s!1" "t!1")
                        (("1" (inst-cp -1 "G!1" "q!1" "s!1" "t!1")
                          (("1" (hide -1)
                            (("1" (hide -6)
                              (("1"
                                (reveal -1)
                                (("1"
                                  (inst -1 "G!1" "rev(q!1)")
                                  (("1"
                                    (expand "path_from?")
                                    (("1"
                                      (flatten)
                                      (("1"
                                        (expand "from?")
                                        (("1"
                                          (expand "finseq_appl")
                                          (("1"
                                            (flatten)
                                            (("1"
                                              (assert)
                                              (("1" (grind) nil nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil)
                                   ("2" (grind) nil nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil)
                     ("2" (assert) (("2" (grind) nil nil)) nil))
                    nil)
                   ("2" (grind) nil nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((path_reduc formula-decl nil path_circ nil)
    (walks_concat_red formula-decl nil path_circ nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (below type-eq-decl nil nat_types nil)
    (finseq type-eq-decl nil finite_sequences 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)
    (bool nonempty-type-eq-decl nil booleans nil)
    (> const-decl "bool" reals nil)
    (prewalk type-eq-decl nil walks nil)
    (path? const-decl "bool" paths nil)
    (G!1 skolem-const-decl "graph[T]" path_circ nil)
    (p!1 skolem-const-decl "prewalk[T]" path_circ nil)
    (Path type-eq-decl nil paths nil)
    (path_from_l formula-decl nil paths nil)
    (finseq_appl const-decl "[below[length(fs)] -> T]" finite_sequences
     nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
     integers nil)
    (int_plus_int_is_int application-judgement "int" integers nil)
    (int_min application-judgement "{k: int | k <= i AND k <= j}"
     real_defs nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (nil application-judgement "finite_set[T]" path_circ nil)
    (verts_in? const-decl "bool" walks nil)
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    (from? const-decl "bool" walks nil)
    (path_from? const-decl "bool" paths nil)
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    (q!1 skolem-const-decl "prewalk[T]" path_circ nil)
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    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
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    (doubleton type-eq-decl nil doubletons nil)
    (dbl const-decl "set[T]" doubletons nil)
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    (AND const-decl "[bool, bool -> bool]" booleans nil)
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    (path?_rev formula-decl nil paths nil)
    (T formal-type-decl nil path_circ nil))
   nil))
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  (cycl_red_compos_TCC1-1 nil 3253636829 ("" (subtype-tcc) nil nil)
   ((boolean nonempty-type-decl nil booleans nil)
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    (finseq type-eq-decl nil finite_sequences nil)
    (prewalk type-eq-decl nil walks 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)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (/= const-decl "boolean" notequal nil)
    (T formal-type-decl nil path_circ nil)
    (verts_in? const-decl "bool" walks nil)
    (finseq_appl const-decl "[below[length(fs)] -> T]" finite_sequences
     nil)
    (edge? const-decl "bool" graphs nil)
    (walk? const-decl "bool" walks nil)
    (path? const-decl "bool" paths nil)
    (from? const-decl "bool" walks nil)
    (path_from? const-decl "bool" paths nil)
    (nil application-judgement "finite_set[T]" path_circ nil))
   nil))
(cycl_red_compos_TCC2 0
--> --------------------

--> maximum size reached

--> --------------------

quality100%

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