| products/sources/formale Sprachen/PVS/ACCoRD/ |
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Quellcode-Bibliothek© Kompilation durch diese Firma[Weder Korrektheit noch Funktionsfähigkeit der Software werden zugesichert.]Datei: Proof.thy Sprache: LispOriginal von: PVS© |
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(criteria_flightplan
(hconflictever_rew 0 (hconflictever_rew-1 nil 3511624351 ("" (case "FORALL (vvv:Vect2): sq(norm(vvv)) = sqv(vvv)") (("1" (skeep) (("1" (expand "horizontal_conflict_ever_traj?") 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(("1" (inst - "pp/2" "0" "pp") (("1" (assert) (("1" (case "ff(0) = 0 AND ff(pp) = 0") (("1" (split -2) (("1" (flatten) (("1" (inst-cp - "pp/2") (("1" (replace -6) (("1" (inst -7 "pp/2") (("1" (assert) nil nil)) nil)) nil)) nil)) nil) ("2" (lemma "sqv_eq_0") (("2" (inst?) (("2" (assert) nil nil)) nil)) nil) ("3" (flatten) (("3" (assert) nil nil)) nil)) nil) ("2" (hide -1) (("2" (inst-cp - "0") (("2" (inst - "pp") (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (lemma "sqv_eq_0") (("2" (inst?) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide-all-but (-1 -2 1)) (("2" (split +) (("1" (hide -1) (("1" (skosimp*) (("1" (inst - "p!1") (("1" (rewrite "sqrt_ge" :dir rl) (("1" (rewrite "sqrt_sqv_norm") (("1" (rewrite "sqrt_sqv_norm") nil nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide -2) (("2" (skosimp*) (("2" (inst + "p!1") (("2" (rewrite "sqrt_eq" :dir rl) (("2" (rewrite "sqrt_sqv_norm") (("2" (rewrite "sqrt_sqv_norm") nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (inst -2 "newrtraj(t) - rtraj(t)" "rtraj(t)") (("1" (assert) (("1" (expand "divergent?") (("1" (skolem 5 "pp") (("1" (inst - "pp") (("1" (inst + "pp") (("1" (expand "dist") (("1" (rewrite "sq_dist_norm") (("1" (rewrite "sq_dist_norm") (("1" (assert) (("1" (assert) (("1" (hide-all-but (-1 1 5)) (("1" (grind) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (assert) nil nil)) nil)) nil)) nil) ("2" (flatten) (("2" (replace -1) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((dot_nneg_divergent formula-decl nil definitions nil) (repulsive_criterion? const-decl "bool" criteria_flightplan nil) (numfield nonempty-type-eq-decl nil number_fields nil) (- const-decl "[numfield, numfield -> numfield]" number_fields nil) (sqrt_eq formula-decl nil sqrt "reals/") (sqrt_sqv_norm formula-decl nil vectors_2D "vectors/") (sqrt_ge formula-decl nil sqrt "reals/") (NOT const-decl "[bool -> bool]" booleans nil) (sq const-decl "nonneg_real" sq "reals/") (minus_even_is_even application-judgement "even_int" integers nil) (minus_nzint_is_nzint application-judgement "nzint" integers nil) (nonzero_real nonempty-type-eq-decl nil reals nil) (sqv_eq_0 formula-decl nil vectors_2D "vectors/") (nznum nonempty-type-eq-decl nil number_fields nil) (/ const-decl "[numfield, nznum -> numfield]" number_fields nil) (posreal_div_posreal_is_posreal application-judgement "posreal" real_types nil) (quad_min_eq_intv formula-decl nil quad_minmax "reals/") (* const-decl "[numfield, numfield -> numfield]" number_fields nil) (quadratic const-decl "real" quadratic "reals/") (vy_distr_sub formula-decl nil vectors_2D "vectors/") (vx_distr_sub formula-decl nil vectors_2D "vectors/") (dot_zero_right formula-decl nil vectors_2D "vectors/") (sub_eq_args formula-decl nil vectors_2D "vectors/") (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (Nz_vect2 type-eq-decl nil vectors_2D "vectors/") (divergent? const-decl "bool" closest_approach_2D "vectors/") (= const-decl "[T, T -> boolean]" equalities nil) (scal_0 formula-decl nil vectors_2D "vectors/") (scal_1 formula-decl nil vectors_2D "vectors/") (odd_minus_even_is_odd application-judgement "odd_int" integers nil) (dist const-decl "nnreal" distance_2D "vectors/") (* const-decl "Vector" vectors_2D "vectors/") (+ const-decl "Vector" vectors_2D "vectors/") (scal_zero formula-decl nil vectors_2D "vectors/") (add_zero_left formula-decl nil vectors_2D "vectors/") (* const-decl "real" vectors_2D "vectors/") (sqv const-decl "nnreal" vectors_2D "vectors/") (norm const-decl "nnreal" vectors_2D "vectors/") (real_plus_real_is_real application-judgement "real" reals nil) (real_times_real_is_real application-judgement "real" reals nil) (sqrt_sq formula-decl nil sqrt "reals/") (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (sub_zero_right formula-decl nil vectors_2D "vectors/") (sq_dist_norm formula-decl nil distance_2D "vectors/") (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (real_minus_real_is_real application-judgement "real" reals nil) (real nonempty-type-from-decl nil reals nil) (Vector type-eq-decl nil vectors_2D "vectors/") (boolean nonempty-type-decl nil booleans nil) (/= const-decl "boolean" notequal 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) (bool nonempty-type-eq-decl nil booleans nil) (>= const-decl "bool" reals nil) (nnreal type-eq-decl nil real_types nil) (AND const-decl "[bool, bool -> bool]" booleans nil) (<= const-decl "bool" reals nil) (B formal-const-decl "nnreal" criteria_flightplan 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) (T formal-const-decl "{AB: posreal | AB > B}" criteria_flightplan nil) (Lookahead type-eq-decl nil Lookahead nil) (Vect2 type-eq-decl nil vectors_2D_def "vectors/") (Trajectory type-eq-decl nil criteria_flightplan nil) (zero const-decl "Vector" vectors_2D "vectors/") (repulsive? const-decl "bool" criteria_flightplan nil) (minus_odd_is_odd application-judgement "odd_int" integers nil)) nil)) (repulsive_criterion_coordinated 0 (repulsive_criterion_coordinated-1 nil 3511709628 ("" (skeep) (("" (expand "repulsive_criterion?") (("" (skosimp*) (("" (inst - "t!1") (("" (inst - "t!1") (("" (grind) nil nil)) nil)) nil)) nil)) nil)) nil) ((repulsive_criterion? const-decl "bool" criteria_flightplan 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) (nnreal type-eq-decl nil real_types nil) (AND const-decl "[bool, bool -> bool]" booleans nil) (<= const-decl "bool" reals nil) (B formal-const-decl "nnreal" criteria_flightplan 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) (T formal-const-decl "{AB: posreal | AB > B}" criteria_flightplan nil) (Lookahead type-eq-decl nil Lookahead nil) (real_minus_real_is_real application-judgement "real" reals nil) (minus_odd_is_odd application-judgement "odd_int" integers nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (real_plus_real_is_real application-judgement "real" reals nil) (real_times_real_is_real application-judgement "real" reals nil) (* const-decl "real" vectors_2D "vectors/") (rel_traj const-decl "Vect2" criteria_flightplan nil)) nil)) (horizontal_criterion_repulsive 0 (horizontal_criterion_repulsive-1 nil 3511692238 ("" (skeep) (("" (expand "repulsive_criterion?") (("" (expand "horizontal_criterion?") (("" (skosimp*) (("" (inst - "t!1") (("" (grind :exclude "norm") nil nil)) nil)) nil)) nil)) nil)) nil) ((repulsive_criterion? const-decl "bool" criteria_flightplan nil) (minus_odd_is_odd application-judgement "odd_int" integers nil) (real_minus_real_is_real application-judgement "real" reals nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (nnreal_times_nnreal_is_nnreal application-judgement "nnreal" real_types nil) (nonneg_real_max application-judgement "{z: nonneg_real | z >= x AND z >= y}" real_defs nil) (real_times_real_is_real application-judgement "real" reals nil) (real_plus_real_is_real application-judgement "real" reals nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (/= const-decl "boolean" notequal nil) (* const-decl "real" vectors_2D "vectors/") (sqv const-decl "nnreal" vectors_2D "vectors/") (max const-decl "{p: real | p >= m AND p >= n}" real_defs nil) (Lookahead type-eq-decl nil Lookahead nil) (T formal-const-decl "{AB: posreal | AB > B}" criteria_flightplan nil) (posreal nonempty-type-eq-decl nil real_types nil) (> const-decl "bool" reals nil) (nonneg_real nonempty-type-eq-decl nil real_types nil) (B formal-const-decl "nnreal" criteria_flightplan nil) (<= const-decl "bool" reals nil) (AND const-decl "[bool, bool -> bool]" booleans nil) (nnreal type-eq-decl nil real_types 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) (horizontal_criterion? const-decl "bool" criteria_flightplan nil)) shostak)) (horizontal_criterion_independent 0 (horizontal_criterion_independent-2 nil 3511710317 ("" (skeep) (("" (expand "horizontal_conflict_ever_traj?") (("" (skeep -2) (("" (expand "horizontal_criterion?") (("" (inst - "t") (("" (flatten) (("" (lemma "max_le") (("" (inst?) (("" (inst - "rtraj(t) * newrtraj(t)") (("" (ground) (("" (hide (-1 -2)) (("" (hide -2) (("" (lemma "cauchy_schwarz") (("" (inst - "rtraj(t)" "newrtraj(t)") (("" (case "rtraj(t) * newrtraj(t) <= norm(rtraj(t)) * norm(newrtraj(t))") (("1" (case "norm(rtraj(t))>0") (("1" (mult-by -5 "norm(rtraj(t))") (("1" (assert) nil nil)) nil) ("2" (lemma "norm_eq_0") (("2" (inst?) (("2" (assert) nil nil)) nil)) nil)) nil) ("2" (rewrite "sq_le" :dir rl) (("2" (rewrite "sq_times") (("2" (case "FORALL (vv:Vect2): sq(norm(vv)) = sqv(vv)") (("1" (inst-cp -1 "rtraj(t)") (("1" (inst - "newrtraj(t)") (("1" (assert) nil nil)) nil)) nil) ("2" (hide-all-but 1) (("2" (skeep) (("2" (rewrite "sqrt_eq" :dir rl) (("2" (rewrite "sqrt_sqv_norm") (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((horizontal_conflict_ever_traj? const-decl "bool" criteria_flightplan nil) (horizontal_criterion? const-decl "bool" criteria_flightplan nil) (nnreal_times_nnreal_is_nnreal application-judgement "nnreal" real_types nil) (Vector type-eq-decl nil vectors_2D "vectors/") (sqv const-decl "nnreal" vectors_2D "vectors/") (Vect2 type-eq-decl nil vectors_2D_def "vectors/") (Trajectory type-eq-decl nil criteria_flightplan nil) (numfield nonempty-type-eq-decl nil number_fields nil) (* const-decl "[numfield, numfield -> numfield]" number_fields nil) (norm const-decl "nnreal" vectors_2D "vectors/") (D formal-const-decl "posreal" criteria_flightplan nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (nonneg_real_max application-judgement "{z: nonneg_real | z >= x AND z >= y}" real_defs 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) (sq_le formula-decl nil sq "reals/") (= const-decl "[T, T -> boolean]" equalities nil) (sq const-decl "nonneg_real" sq "reals/") (sqrt_sqv_norm formula-decl nil vectors_2D "vectors/") (sqrt_sq formula-decl nil sqrt "reals/") (sqrt_eq formula-decl nil sqrt "reals/") (sq_times formula-decl nil sq "reals/") (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (both_sides_times_pos_lt1 formula-decl nil real_props nil) (norm_eq_0 formula-decl nil vectors_2D "vectors/") (cauchy_schwarz formula-decl nil vectors_2D "vectors/") (* const-decl "real" vectors_2D "vectors/") (max_le formula-decl nil real_defs nil) (Lookahead type-eq-decl nil Lookahead nil) (T formal-const-decl "{AB: posreal | AB > B}" criteria_flightplan nil) (posreal nonempty-type-eq-decl nil real_types nil) (> const-decl "bool" reals nil) (nonneg_real nonempty-type-eq-decl nil real_types nil) (B formal-const-decl "nnreal" criteria_flightplan nil) (<= const-decl "bool" reals nil) (AND const-decl "[bool, bool -> bool]" booleans nil) (nnreal type-eq-decl nil real_types 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)) nil) (horizontal_criterion_independent-1 nil 3511710046 ("" (skeep) (("" (expand "repulsive_criterion?") (("" (expand "horizontal_criterion?") (("" (skosimp*) (("" (inst - "t!1") (("" (grind :exclude "norm") nil)))))))))) nil) nil nil)) (horizontal_criterion_coordinated 0 (horizontal_criterion_coordinated-1 nil 3511690762 ("" (skeep) (("" (case "repulsive_criterion?(rel_traj(so, si))(rel_traj(newso, si)) AND repulsive_criterion?(rel_traj(si, so))(rel_traj(newsi, so))") (("1" (flatten) (("1" (expand "horizontal_criterion?") (("1" (skeep) (("1" (inst - "t") (("1" (inst - "t") (("1" (flatten) (("1" (assert) (("1" (lemma "max_le") (("1" (inst?) (("1" (inst - "rel_traj(so, si)(t) * rel_traj(newso, newsi)(t)") (("1" (assert) (("1" (hide 4) (("1" (lemma "repulsive_criterion_coordinated") (("1" (inst - "newsi" "newso" "si" "so") (("1" (assert) (("1" (hide (-2 -3)) (("1" (expand "repulsive_criterion?") 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(("2" (expand "horizontal_criterion?") 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(("" (expand "horizontal_conflict_ever_traj?") (("" (expand "safe_vect?") 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(("2" (assert) (("2" (rewrite "sqrt_times") (("2" (rewrite "sqrt_sqv_norm") (("2" (rewrite --> -------------------- --> maximum size reached --> -------------------- ¤ Dauer der Verarbeitung: 0.77 Sekunden (vorverarbeitet) ¤ |
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