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Datei: repulsive_iterative.prf   Sprache: Lisp

Original von: PVS©
(repulsive_iterative
 (man_pos_seq_TCC1 0
  (man_pos_seq_TCC1-1 nil 3574766784 ("" (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)
    (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)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (> const-decl "bool" reals nil)
    (posreal nonempty-type-eq-decl nil real_types 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)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (posnat nonempty-type-eq-decl nil 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)
    (int_minus_int_is_int application-judgement "int" integers nil))
   nil))
 (man_pos_seq_TCC2 0
  (man_pos_seq_TCC2-1 nil 3574766784 ("" (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)
    (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)
    (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))
   nil))
 (man_pos_seq_TCC3 0
  (man_pos_seq_TCC3-1 nil 3574766784 ("" (termination-tcc) nil nil) nil
   nil))
 (man_pos_seq_test 0
  (man_pos_seq_test-1 nil 3574766788 ("" (grind) nil nil)
   ((man_pos_seq def-decl "Vect2" repulsive_iterative nil)
    (* const-decl "Vector" vectors_2D "vectors/")
    (+ const-decl "Vector" vectors_2D "vectors/")
    (real_plus_real_is_real application-judgement "real" reals nil)
    (real_times_real_is_real application-judgement "real" reals nil))
   shostak))
 (manuever_position_at_def 0
  (manuever_position_at_def-1 nil 3575022941
   ("" (induct "m")
    (("1" (assert)
      (("1" (skeep)
        (("1" (expand "maneuver_position_at")
          (("1" (name "iz" "floor(0)")
            (("1" (case "NOT iz = 0")
              (("1" (hide 2) (("1" (grind) nil nil)) nil)
               ("2" (replaces -2)
                (("2" (replace -1)
                  (("2" (grind) (("2" (decompose-equality) nil nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     ("2" (skeep)
      (("2" (skeep)
        (("2" (inst?)
          (("2" (expand "man_pos_seq" +)
            (("2" (assert)
              (("2" (replace -1 :dir rl)
                (("2" (hide -1)
                  (("2" (assert)
                    (("2" (expand "maneuver_position_at")
                      (("2"
                        (case "floor((j * timestep + timestep) / timestep) = floor(j * timestep / timestep)+1")
                        (("1" (replaces -1)
                          (("1" (assert)
                            (("1" (expand "man_pos_seq" + 1)
                              (("1"
                                (grind
                                 :exclude
                                 ("man_pos_seq" "floor"))
                                nil
                                nil))
                              nil))
                            nil))
                          nil)
                         ("2" (hide 2) (("2" (grind) nil nil)) nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((nnreal_plus_posreal_is_posreal application-judgement "posreal"
     real_types nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
    (nznum nonempty-type-eq-decl nil number_fields nil)
    (/= const-decl "boolean" notequal nil)
    (nnreal_div_posreal_is_nnreal application-judgement "nnreal"
     real_types nil)
    (posreal_div_posreal_is_posreal application-judgement "posreal"
     real_types nil)
    (nonneg_floor_is_nat application-judgement "nat" floor_ceil nil)
    (posint_min application-judgement "{k: posint | k <= i AND k <= j}"
     real_defs nil)
    (posreal_times_posreal_is_posreal application-judgement "posreal"
     real_types nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (odd_plus_even_is_odd application-judgement "odd_int" integers nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (min const-decl "{p: real | p <= m AND p <= n}" real_defs nil)
    (* const-decl "Vector" vectors_2D "vectors/")
    (+ const-decl "Vector" vectors_2D "vectors/")
    (floor const-decl "{i | i <= x & x < i + 1}" floor_ceil nil)
    (< const-decl "bool" reals nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (integer nonempty-type-from-decl nil integers nil)
    (nat_induction formula-decl nil naturalnumbers nil)
    (man_pos_seq def-decl "Vect2" repulsive_iterative nil)
    (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (maneuver_position_at const-decl "Vect2" repulsive_iterative nil)
    (nnreal type-eq-decl nil real_types nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (<= const-decl "bool" reals nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (VelSeq type-eq-decl nil repulsive_iterative nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (Vect2 type-eq-decl nil vectors_2D_def "vectors/")
    (posnat nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (pred type-eq-decl nil defined_types nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (>= const-decl "bool" reals nil)
    (bool nonempty-type-eq-decl nil booleans 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)
    (boolean nonempty-type-decl nil booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (nnint_plus_posint_is_posint application-judgement "posint"
     integers nil)
    (nnreal_times_nnreal_is_nnreal application-judgement "nnreal"
     real_types nil))
   shostak))
 (repulsive_criteria_iterative_TCC1 0
  (repulsive_criteria_iterative_TCC1-1 nil 3575207629
   ("" (subtype-tcc) nil nil)
   ((/= const-decl "boolean" notequal nil)
    (det const-decl "real" det_2D "vectors/")
    (* const-decl "real" vectors_2D "vectors/")
    (repulsive_criteria const-decl "bool" repulsive nil)
    (real_times_real_is_real application-judgement "real" reals nil))
   nil))
 (repulsive_criteria_iterative_TCC2 0
  (repulsive_criteria_iterative_TCC2-1 nil 3575207629
   ("" (subtype-tcc) nil nil)
   ((/= const-decl "boolean" notequal nil)
    (det const-decl "real" det_2D "vectors/")
    (* const-decl "real" vectors_2D "vectors/")
    (repulsive_criteria const-decl "bool" repulsive nil)
    (real_times_real_is_real application-judgement "real" reals nil))
   nil))
 (repulsive_criteria_iterative_repulsive 0
  (repulsive_criteria_iterative_repulsive-1 nil 3575046820
   ("" (skeep)
    (("" (expand "repulsive_iterative?")
      (("" (flatten)
        (("" (expand "repulsive_criteria_iterative")
          (("" (flatten)
            (("" (case "s*v>=0")
              (("1" (assert)
                (("1" (hide 1)
                  (("1"
                    (case "FORALL (i:subrange(1,Nsteps)): man_pos_seq(s,timestep,velseq)(i)*velseq(i)>=0")
                    (("1" (lemma "definitions.dot_nneg_divergent")
                      (("1" (skeep)
                        (("1"
                          (case "FORALL (i:subrange(1,Nsteps-1)): norm(man_pos_seq(s, timestep, velseq)(1 + i)) >= norm(man_pos_seq(s, timestep, velseq)(i))")
                          (("1"
                            (case "FORALL (i:subrange(1,Nsteps)): norm(man_pos_seq(s, timestep, velseq)(i)) >= norm(s)")
                            (("1"
                              (name "ii"
                                    "min(floor(t/timestep)+1,Nsteps)")
                              (("1"
                                (inst - "ii")
                                (("1"
                                  (case
                                   "norm(maneuver_position_at(s,timestep,velseq,Nsteps)(t))>=norm(man_pos_seq(s,timestep,velseq)(ii))")
                                  (("1" (assert) nil nil)
                                   ("2"
                                    (hide (-2 2))
                                    (("2"
                                      (case "velseq(ii)=zero")
                                      (("1"
                                        (expand "maneuver_position_at")
                                        (("1"
                                          (replace -2)
                                          (("1"
                                            (replace -1)
                                            (("1" (assert) nil nil))
                                            nil))
                                          nil))
                                        nil)
                                       ("2"
                                        (inst
                                         -
                                         "velseq(ii)"
                                         "man_pos_seq(s,timestep,velseq)(ii)")
                                        (("1"
                                          (flatten)
                                          (("1"
                                            (hide -4)
                                            (("1"
                                              (expand
                                               "maneuver_position_at"
                                               +)
                                              (("1"
                                                (split -)
                                                (("1"
                                                  (expand "divergent?")
                                                  (("1"
                                                    (replace -2)
                                                    (("1"
                                                      (inst
                                                       -
                                                       "t-timestep*(ii-1)")
                                                      (("1"
                                                        (expand "dist")
                                                        (("1"
                                                          (rewrite
                                                           "sq_dist_norm")
                                                          (("1"
                                                            (rewrite
                                                             "sq_dist_norm")
                                                            (("1"
                                                              (rewrite
                                                               "sqrt_sq")
                                                              (("1"
                                                                (rewrite
                                                                 "sqrt_sq")
                                                                (("1"
                                                                  (assert)
                                                                  nil
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil)
                                                       ("2"
                                                        (assert)
                                                        (("2"
                                                          (case
                                                           "t = timestep*(ii-1)")
                                                          (("1"
                                                            (case
                                                             "NOT t - timestep * floor(t / timestep) = 0")
                                                            (("1"
                                                              (assert)
                                                              nil
                                                              nil)
                                                             ("2"
                                                              (replaces
                                                               -1)
                                                              (("2"
                                                                (case
                                                                 "t-ii*timestep+timestep = 0")
                                                                (("1"
                                                                  (replace
                                                                   -1)
                                                                  (("1"
                                                                    (assert)
                                                                    nil
                                                                    nil))
                                                                  nil)
                                                                 ("2"
                                                                  (assert)
                                                                  nil
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil)
                                                           ("2"
                                                            (assert)
                                                            (("2"
                                                              (case
                                                               "t>=timestep*(ii-1)")
                                                              (("1"
                                                                (assert)
                                                                nil
                                                                nil)
                                                               ("2"
                                                                (name
                                                                 "pj"
                                                                 "1+floor(t/timestep)")
                                                                (("2"
                                                                  (case
                                                                   "pj>=ii AND t>=timestep*(pj-1)")
                                                                  (("1"
                                                                    (flatten)
                                                                    (("1"
                                                                      (assert)
                                                                      (("1"
                                                                        (mult-by
                                                                         -1
                                                                         "timestep")
                                                                        (("1"
                                                                          (assert)
                                                                          nil
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil)
                                                                   ("2"
                                                                    (case
                                                                     "NOT pj>=ii")
                                                                    (("1"
                                                                      (hide
                                                                       2)
                                                                      (("1"
                                                                        (expand
                                                                         "pj"
                                                                         1)
                                                                        (("1"
                                                                          (expand
                                                                           "ii"
                                                                           1)
                                                                          (("1"
                                                                            (assert)
                                                                            nil
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil)
                                                                     ("2"
                                                                      (replace
                                                                       -1)
                                                                      (("2"
                                                                        (expand
                                                                         "pj"
                                                                         1)
                                                                        (("2"
                                                                          (assert)
                                                                          (("2"
                                                                            (hide-all-but
                                                                             1)
                                                                            (("2"
                                                                              (typepred
                                                                               "floor(t/timestep)")
                                                                              (("2"
                                                                                (cross-mult
                                                                                 -1)
                                                                                nil
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil)
                                                 ("2"
                                                  (inst -3 "ii")
                                                  (("2"
                                                    (assert)
                                                    nil
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil)
                                         ("2" (assert) nil nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil)
                                 ("2"
                                  (hide-all-but (-1 1))
                                  (("2"
                                    (grind :exclude "floor")
                                    nil
                                    nil))
                                  nil))
                                nil))
                              nil)
                             ("2"
                              (case "FORALL (ii:nat): ii+1<=Nsteps IMPLIES norm(man_pos_seq(s, timestep, velseq)(ii+1)) >= norm(s)")
                              (("1"
                                (skeep)
                                (("1"
                                  (inst - "i-1")
                                  (("1" (assert) nil nil))
                                  nil))
                                nil)
                               ("2"
                                (hide 2)
                                (("2"
                                  (induct "ii")
                                  (("1"
                                    (expand "man_pos_seq" 1)
                                    (("1" (propax) nil nil))
                                    nil)
                                   ("2"
                                    (skeep)
                                    (("2"
                                      (inst - "j+1")
                                      (("1" (assert) nil nil)
                                       ("2" (assert) nil nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil)
                           ("2" (skeep)
                            (("2" (expand "man_pos_seq" + 1)
                              (("2"
                                (case "velseq(i) = zero")
                                (("1"
                                  (replaces -1)
                                  (("1" (assert) nil nil))
                                  nil)
                                 ("2"
                                  (inst
                                   -
                                   "velseq(i)"
                                   "man_pos_seq(s,timestep,velseq)(i)")
                                  (("1"
                                    (flatten)
                                    (("1"
                                      (hide -2)
                                      (("1"
                                        (split -1)
                                        (("1"
                                          (expand "divergent?")
                                          (("1"
                                            (inst - "timestep")
                                            (("1"
                                              (rewrite "dist_norm")
                                              (("1"
                                                (rewrite "dist_norm")
                                                (("1"
                                                  (assert)
                                                  nil
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil)
                                         ("2" (inst?) nil nil))
                                        nil))
                                      nil))
                                    nil)
                                   ("2" (assert) nil nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil)
                     ("2" (hide 2)
                      (("2" (expand "repulsive_criteria" - 1)
                        (("2" (case "NOT s*velseq(1)>=0")
                          (("1" (ground) nil nil)
                           ("2" (hide -3)
                            (("2"
                              (case "FORALL (ii:nat): ii<=Nsteps-1 IMPLIES man_pos_seq(s, timestep, velseq)(ii+1) * velseq(ii+1) >= 0")
                              (("1"
                                (skeep)
                                (("1"
                                  (inst - "i-1")
                                  (("1" (assert) nil nil))
                                  nil))
                                nil)
                               ("2"
                                (hide 2)
                                (("2"
                                  (induct "ii")
                                  (("1"
                                    (expand "man_pos_seq")
                                    (("1" (propax) nil nil))
                                    nil)
                                   ("2"
                                    (skeep)
                                    (("2"
                                      (inst - "j+1")
                                      (("1"
                                        (assert)
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