| Quellcodebibliothek Statistik Leitseite products/Sources/formale Sprachen/PVS/ACCoRD/ (Beweissystem der NASA Version 6.0.9©) Datei vom 28.9.2014 mit Größe 332 kB |
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Quelle cd3d_si.prfSprache: Lisp |
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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) (> const-decl "bool" reals nil) (above nonempty-type-eq-decl nil int_types nil) (N formal-const-decl "above[1]" cd3d_si nil) (below type-eq-decl nil nat_types nil) (IMPLIES const-decl "[bool, bool -> bool]" booleans nil) (numfield 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application-judgement "real" reals nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (real_minus_real_is_real application-judgement "real" reals nil) (seg_lh_bottom const-decl "nnreal" cd3d_si nil) (seg_lh_top const-decl "real" cd3d_si nil)) nil)) (conflict_3D_rew_absolute_time 0 (conflict_3D_rew_absolute_time-1 nil 3481469114 ("" (skeep) (("" (lemma "conflict_3D_rew") (("" (inst?) (("" (replace -1) (("" (hide -1) (("" (ground) (("1" (skeep -1) (("1" (inst?) (("1" (assert) (("1" (expand conflict_3D?) 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(("2" (skeep -2) (("2" (inst + "t+to-flpl(j)`time") (("2" (assert) (("2" (hide -1) (("2" (grind :exclude ("velocity" "abs" "sqv" "sq")) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((conflict_3D_rew formula-decl nil cd3d_si nil) (real_plus_real_is_real application-judgement "real" reals nil) (real_minus_real_is_real application-judgement "real" reals nil) (minus_odd_is_odd application-judgement "odd_int" integers nil) (real_times_real_is_real application-judgement "real" reals nil) (conflict_3D? const-decl "bool" cd3d nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (to skolem-const-decl "real" cd3d_si nil) (flpl skolem-const-decl "FlightPlanRelevant(to)" cd3d_si nil) (j skolem-const-decl "below[N - 1]" cd3d_si nil) (<= const-decl "bool" reals nil) (seg_lh_bottom const-decl "nnreal" cd3d_si nil) (seg_lh_top const-decl "real" cd3d_si nil) (Lookahead type-eq-decl nil Lookahead nil) (t skolem-const-decl "Lookahead[seg_lh_bottom(flpl, to)(j), seg_lh_top(flpl, to)(j)]" cd3d_si nil) (NOT const-decl "[bool -> bool]" booleans nil) (Vector type-eq-decl nil vectors_2D "vectors/") (= const-decl "[T, T -> boolean]" equalities nil) (+ const-decl "Vector" vectors_2D "vectors/") (Vect2 type-eq-decl nil vectors_2D_def "vectors/") (vect2 const-decl "Vect2" vect_3D_2D "vectors/") (Vector type-eq-decl nil vectors_3D "vectors/") (- const-decl "Vector" vectors_3D "vectors/") (* const-decl "Vector" vectors_3D "vectors/") (velocity const-decl "Vect3" flightplan nil) (* const-decl "Vector" vectors_2D "vectors/") (+ const-decl "Vector" vectors_3D "vectors/") (* const-decl "[numfield, numfield -> numfield]" number_fields nil) (sqv_cont name-judgement "continuous_vr_fun" vect_cont_2D "vect_analysis/") (sq_nz_pos application-judgement "posreal" sq "reals/") (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (FlightPlanRelevant nonempty-type-eq-decl nil cd3d_si nil) (T formal-const-decl "{AB: posreal | AB > B}" cd3d_si nil) (B formal-const-decl "nnreal" cd3d_si nil) (nnreal type-eq-decl nil real_types nil) (posreal nonempty-type-eq-decl nil real_types nil) (nonneg_real nonempty-type-eq-decl nil real_types nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (AND const-decl "[bool, bool -> bool]" booleans nil) (FlightPlan nonempty-type-eq-decl nil flightplan nil) (- const-decl "[numfield, numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (IMPLIES const-decl "[bool, bool -> bool]" booleans nil) (below type-eq-decl nil nat_types nil) (N formal-const-decl "above[1]" cd3d_si nil) (above nonempty-type-eq-decl nil int_types nil) (> const-decl "bool" reals nil) (< const-decl "bool" reals 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_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) (Vect3 type-eq-decl nil vectors_3D_def "vectors/") (real nonempty-type-from-decl nil reals nil)) shostak)) (cd3d_ind?_TCC1 0 (cd3d_ind?_TCC1-1 nil 3472981403 ("" (subtype-tcc) nil nil) ((NOT const-decl "[bool -> bool]" booleans nil) (>= const-decl "bool" reals nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (< const-decl "bool" reals nil) (below type-eq-decl nil nat_types nil) (IMPLIES const-decl "[bool, bool -> bool]" booleans nil) (numfield nonempty-type-eq-decl nil 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(seg_lh_top const-decl "real" cd3d_si nil) (* const-decl "Vector" vectors_3D "vectors/") (+ const-decl "Vector" vectors_3D "vectors/") (- const-decl "Vector" vectors_3D "vectors/") (N formal-const-decl "above[1]" cd3d_si nil) (above nonempty-type-eq-decl nil int_types 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) (velocity const-decl "Vect3" flightplan nil) (real_times_real_is_real application-judgement "real" reals nil) (real_minus_real_is_real application-judgement "real" reals nil) (nzreal_div_nzreal_is_nzreal application-judgement "nzreal" real_types nil) (real_plus_real_is_real application-judgement "real" reals nil) (minus_nzreal_is_nzreal application-judgement "nzreal" real_types nil)) nil)) (cd3d_si?_TCC1 0 (cd3d_si?_TCC1-1 nil 3472981403 ("" (subtype-tcc) 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) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil)) nil)) (cd3d_ind_correct 0 (cd3d_ind_correct-1 nil 3473095354 ("" (skeep) (("" (induct "i") (("1" (flatten) (("1" (inst + "0") (("1" (assert) (("1" (expand "cd3d_ind?") (("1" (flatten) (("1" (assert) (("1" (rewrite "cd3d") nil nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (skeep) (("2" (expand "cd3d_ind?" -3) (("2" (split -3) (("1" (flatten) (("1" (inst + "1+jb") (("1" (assert) (("1" (rewrite "cd3d") nil nil)) nil)) nil)) nil) ("2" (assert) (("2" (skosimp*) (("2" (inst + "j!1") (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil) ("3" (hide 2) (("3" (skeep) (("3" (skosimp*) (("3" (assert) nil nil)) nil)) nil)) nil) ("4" (assert) nil nil) ("5" (assert) nil nil)) nil)) nil) ((real_minus_real_is_real application-judgement "real" reals nil) (<= const-decl "bool" reals nil) (seg_lh_top const-decl "real" cd3d_si nil) (seg_lh_bottom const-decl "nnreal" cd3d_si nil) (flpl skolem-const-decl "FlightPlanRelevant(to)" cd3d_si nil) (to skolem-const-decl "real" cd3d_si nil) (vo skolem-const-decl "Vect3" cd3d_si nil) (so skolem-const-decl "Vect3" cd3d_si nil) (cd3d_ind? inductive-decl "bool" cd3d_si nil) (FlightPlanRelevant nonempty-type-eq-decl nil cd3d_si nil) (T formal-const-decl "{AB: posreal | AB > B}" cd3d_si nil) (B formal-const-decl "nnreal" cd3d_si nil) (nnreal type-eq-decl nil real_types nil) (posreal nonempty-type-eq-decl nil real_types nil) (nonneg_real nonempty-type-eq-decl nil real_types nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (AND const-decl "[bool, bool -> bool]" booleans nil) (FlightPlan nonempty-type-eq-decl nil flightplan nil) (Vect3 type-eq-decl nil vectors_3D_def "vectors/") (IMPLIES const-decl "[bool, bool -> bool]" booleans nil) (below type-eq-decl nil nat_types nil) (< const-decl "bool" reals nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (below type-eq-decl nil naturalnumbers nil) (pred type-eq-decl nil defined_types nil) (D formal-const-decl "posreal" cd3d_si nil) (H formal-const-decl "posreal" cd3d_si nil) (conflict_3D? const-decl "bool" cd3d nil) (Vector type-eq-decl nil vectors_3D "vectors/") (- const-decl "Vector" vectors_3D "vectors/") (+ const-decl "Vector" vectors_3D "vectors/") (* const-decl "Vector" vectors_3D "vectors/") (velocity const-decl "Vect3" flightplan nil) (N formal-const-decl "above[1]" cd3d_si nil) (above nonempty-type-eq-decl nil int_types 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) (- const-decl "[numfield, numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-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) (below_induction formula-decl nil bounded_nat_inductions nil) (int_minus_int_is_int application-judgement "int" integers nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (>= const-decl "bool" reals nil) (nnint_plus_posint_is_posint application-judgement "posint" integers nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (cd3d formula-decl nil cd3d nil) (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil)) shostak)) (cd3d_ind_complete 0 (cd3d_ind_complete-1 nil 3473096278 ("" (skeep) (("" (induct "i") (("1" (ground) (("1" (skolem -2 "jjj") (("1" (ground) (("1" (expand "cd3d_ind?") (("1" (rewrite "cd3d" :dir rl) (("1" (expand "conflict_3D?") (("1" (skosimp*) (("1" (inst + "t!1") (("1" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (skeep) (("2" (skosimp*) (("2" (expand "cd3d_ind?" 1) (("2" (flatten) (("2" (assert) (("2" (inst + "j!1") (("2" (assert) (("2" (case "j!1 = 1+jb") (("1" (replace -1) (("1" (rewrite "cd3d" :dir rl) (("1" (expand "conflict_3D?") (("1" (skosimp*) (("1" (inst + "t!1") (("1" (assert) nil nil)) nil)) nil)) nil)) nil)) nil) ("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("3" (skosimp*) (("3" (assert) nil nil)) nil) ("4" (assert) nil nil) ("5" (assert) nil nil)) nil)) nil) ((real_minus_real_is_real application-judgement "real" reals nil) (<= const-decl "bool" reals nil) (seg_lh_top const-decl "real" cd3d_si nil) (flpl skolem-const-decl "FlightPlanRelevant(to)" cd3d_si nil) (FlightPlanRelevant nonempty-type-eq-decl nil cd3d_si nil) (to skolem-const-decl "real" cd3d_si nil) (T formal-const-decl "{AB: posreal | AB > B}" cd3d_si nil) (B formal-const-decl "nnreal" cd3d_si nil) (posreal nonempty-type-eq-decl nil real_types nil) (nonneg_real nonempty-type-eq-decl nil real_types nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (seg_lh_bottom const-decl "nnreal" cd3d_si nil) (nnreal type-eq-decl nil real_types nil) (FlightPlan nonempty-type-eq-decl nil flightplan nil) (Vect3 type-eq-decl nil vectors_3D_def "vectors/") (AND const-decl "[bool, bool -> bool]" booleans nil) (IMPLIES const-decl "[bool, bool -> bool]" booleans nil) (below type-eq-decl nil nat_types nil) (< const-decl "bool" reals nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (below type-eq-decl nil naturalnumbers nil) (pred type-eq-decl nil defined_types nil) (D formal-const-decl "posreal" cd3d_si nil) (H formal-const-decl "posreal" cd3d_si nil) (conflict_3D? const-decl "bool" cd3d nil) (Vector type-eq-decl nil vectors_3D "vectors/") (- const-decl "Vector" vectors_3D "vectors/") (+ const-decl "Vector" vectors_3D "vectors/") (* const-decl "Vector" vectors_3D "vectors/") (velocity const-decl "Vect3" flightplan nil) (cd3d_ind? inductive-decl "bool" cd3d_si nil) (N formal-const-decl "above[1]" cd3d_si nil) (above nonempty-type-eq-decl nil int_types 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) (- const-decl "[numfield, numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-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) (below_induction formula-decl nil bounded_nat_inductions nil) (int_minus_int_is_int application-judgement "int" integers nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (>= const-decl "bool" reals nil) (nnint_plus_posint_is_posint application-judgement "posint" integers nil) (real_times_real_is_real application-judgement "real" reals nil) (real_plus_real_is_real application-judgement "real" reals nil) (Lookahead type-eq-decl nil Lookahead nil) (sqv_cont name-judgement "continuous_vr_fun" vect_cont_2D "vect_analysis/") (sq_nz_pos application-judgement "posreal" sq "reals/") (cd3d formula-decl nil cd3d nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (real_le_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) (= const-decl "[T, T -> boolean]" equalities nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil)) shostak)) (cd3d_si_correct 0 (cd3d_si_correct-1 nil 3473096044 ("" (skeep) (("" (expand "cd3d_si?") (("" (lemma "cd3d_ind_correct") (("" (inst - "so" "vo" "to" "flpl" "N-2") (("1" (assert) (("1" (lemma "conflict_3D_rew") (("1" (inst - "so" "vo" "to" "flpl") (("1" (assert) nil nil)) nil)) nil)) nil) ("2" (assert) nil nil)) nil)) nil)) nil)) nil) ((cd3d_si? const-decl "bool" cd3d_si nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (int_minus_int_is_int application-judgement "int" integers nil) (N formal-const-decl "above[1]" cd3d_si nil) (above nonempty-type-eq-decl nil int_types 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) (numfield nonempty-type-eq-decl nil number_fields 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) (Vect3 type-eq-decl nil vectors_3D_def "vectors/") (nat nonempty-type-eq-decl nil naturalnumbers nil) (< const-decl "bool" reals nil) (below type-eq-decl nil nat_types nil) (IMPLIES const-decl "[bool, bool -> bool]" booleans nil) (FlightPlan nonempty-type-eq-decl nil flightplan nil) (AND const-decl "[bool, bool -> bool]" booleans nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (nonneg_real nonempty-type-eq-decl nil real_types nil) (posreal nonempty-type-eq-decl nil real_types nil) (nnreal type-eq-decl nil real_types nil) (B formal-const-decl "nnreal" cd3d_si nil) (T formal-const-decl "{AB: posreal | AB > B}" cd3d_si nil) (FlightPlanRelevant nonempty-type-eq-decl nil cd3d_si nil) (conflict_3D_rew formula-decl nil cd3d_si nil) (cd3d_ind_correct formula-decl nil cd3d_si nil)) shostak)) (cd3d_si_complete 0 (cd3d_si_complete-1 nil 3473097139 ("" (skeep) (("" (expand "cd3d_si?") (("" (lemma "cd3d_ind_complete") (("" (inst - "so" "vo" "to" "flpl" "N-2") (("1" (assert) (("1" (lemma "conflict_3D_rew") (("1" (inst - "so" "vo" "to" "flpl") (("1" (assert) nil nil)) nil)) nil)) nil) ("2" (assert) nil nil)) nil)) nil)) nil)) nil) ((int_minus_int_is_int application-judgement "int" integers nil) (cd3d_si? const-decl "bool" cd3d_si nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (N formal-const-decl "above[1]" cd3d_si nil) (above nonempty-type-eq-decl nil int_types 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) (numfield nonempty-type-eq-decl nil number_fields 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) (Vect3 type-eq-decl nil vectors_3D_def "vectors/") (nat nonempty-type-eq-decl nil naturalnumbers nil) (< const-decl "bool" reals nil) (below type-eq-decl nil nat_types nil) (IMPLIES const-decl "[bool, bool -> bool]" booleans nil) (FlightPlan nonempty-type-eq-decl nil flightplan nil) (AND const-decl "[bool, bool -> bool]" booleans nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (nonneg_real nonempty-type-eq-decl nil real_types nil) (posreal nonempty-type-eq-decl nil real_types nil) (nnreal type-eq-decl nil real_types nil) (B formal-const-decl "nnreal" cd3d_si nil) (T formal-const-decl "{AB: posreal | AB > B}" cd3d_si nil) (FlightPlanRelevant nonempty-type-eq-decl nil cd3d_si nil) (conflict_3D_rew formula-decl nil cd3d_si nil) (cd3d_ind_complete formula-decl nil cd3d_si nil)) shostak)))
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2026-05-26