| 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: Sprache: LispOriginal von: PVS© |
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(vertical_criterion
(closed_region_3D_t_def 0 (closed_region_3D_t_def-1 nil 3470394875 ("" (skeep) (("" (assert) (("" (rewrite "dot_add_left") (("" (case "(sq(D) - vect2(s) * vect2(p)) / (vect2(v) * vect2(p)) * (vect2(v) * vect2(p)) = (sq(D) - vect2(s) * vect2(p))") (("1" (replace -1) (("1" (assert) nil nil)) nil) ("2" (cross-mult 1) nil nil)) nil)) nil)) nil)) nil) ((sq_nz_pos application-judgement "posreal" sq "reals/") (real_minus_real_is_real application-judgement "real" reals nil) (real_div_nzreal_is_real application-judgement "real" reals nil) (= const-decl "[T, T -> boolean]" equalities nil) (* const-decl "[numfield, numfield -> numfield]" number_fields nil) (times_div2 formula-decl nil real_props nil) (nonzero_real nonempty-type-eq-decl nil reals nil) (dot_scal_left formula-decl nil vectors_2D "vectors/") (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/") (D formal-const-decl "posreal" vertical_criterion nil) (posreal nonempty-type-eq-decl nil real_types nil) (> const-decl "bool" reals nil) (sq const-decl "nonneg_real" sq "reals/") (nonneg_real nonempty-type-eq-decl nil real_types nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (- const-decl "[numfield, numfield -> numfield]" number_fields nil) (/ const-decl "[numfield, nznum -> numfield]" number_fields nil) (nznum nonempty-type-eq-decl nil number_fields nil) (/= const-decl "boolean" notequal nil) (numfield nonempty-type-eq-decl nil number_fields nil) (* const-decl "Vector" vectors_2D "vectors/") (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) (vect2 const-decl "Vect2" vect_3D_2D "vectors/") (Vect2 type-eq-decl nil vectors_2D_def "vectors/") (Vect3 type-eq-decl nil vectors_3D_def "vectors/") (Vector type-eq-decl nil vectors_2D "vectors/") (real nonempty-type-from-decl nil reals nil) (dot_add_left formula-decl nil vectors_2D "vectors/")) shostak)) (closed_region_3D_t_direction 0 (closed_region_3D_t_direction-1 nil 3470396743 ("" (case "forall (m,b, x1,x2: real): m > 0 AND x1 > x2 IMPLIES m*x1 + b > m*x2 + b") (("1" (label "linelem" -1) (("1" (skeep) (("1" (assert) (("1" (name "tt" "(sq(D) - 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(("1" (assert) (("1" (inst - "sq(D) - vect2(s) * vect2(p)" "vect2(v) * vect2(p)") (("1" (assert) nil nil)) nil)) nil) ("2" (assert) nil nil)) nil)) nil)) nil) ("3" (both-sides "-" "s`z*eps" 1) (("1" (assert) (("1" (rewrite "vz_distr_add") (("1" (rewrite "vect2_add") (("1" (rewrite "dot_add_left") (("1" (reveal "divisorlem") (("1" (inst - "v`z*(sq(D) - vect2(s) * vect2(p))*eps" "w`z*(sq(D) - vect2(s) * vect2(p))*eps" "H-s`z*eps" "vect2(v) * vect2(p)" "vect2(w) * vect2(p)") (("1" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (assert) nil nil)) nil) ("4" (propax) nil nil)) nil)) nil) ("2" (rewrite "vect2_add") (("2" (rewrite "dot_add_left") (("2" (typepred "dir") (("2" (expand "sign") (("2" (lift-if) (("2" (hide 4) (("2" (ground) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide-all-but 1) (("2" (skeep) (("2" (typepred "sign(c2)") (("2" (split 1) (("1" (expand "sign") (("1" (lift-if) (("1" (lift-if) (("1" (ground) nil nil)) nil)) nil)) nil) ("2" (expand "sign") (("2" (lift-if) (("2" (lift-if) (("2" (ground) (("1" (cross-mult -5) (("1" (cross-mult -6) (("1" (cross-mult 2) nil nil)) nil)) nil) ("2" (lift-if) (("2" (prop) (("1" (cross-mult -3) (("1" (cross-mult -4) (("1" (cross-mult 5) (("1" (assert) nil nil)) nil)) nil)) nil) ("2" (cross-mult -1) (("2" (cross-mult -2) (("2" (cross-mult 6) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide 2) (("2" (skeep) (("2" (typepred "sign(b)") (("2" (ground) (("1" (replace -2) (("1" (expand "sign") (("1" (lift-if) (("1" (ground) (("1" (cross-mult -2) nil nil)) nil)) nil)) nil)) nil) ("2" (replace -2) (("2" (expand "sign") (("2" (lift-if) (("2" (ground) (("2" (lemma "posreal_div_posreal_is_posreal") (("2" (inst - "a" "b") (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil) ("3" (replace -2) (("3" (expand "sign") (("3" (lift-if) (("3" (ground) (("3" (cross-mult -2) nil nil)) nil)) nil)) nil)) nil) ("4" (replace -2) (("4" (expand "sign") (("4" (lift-if) (("4" (ground) (("4" (cross-mult 3) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((posreal_div_posreal_is_posreal judgement-tcc nil real_types nil) (real_div_nzreal_is_real application-judgement "real" reals nil) (real_plus_real_is_real application-judgement "real" reals nil) (IMPLIES const-decl "[bool, bool -> bool]" booleans nil) (AND const-decl "[bool, bool -> bool]" booleans nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (sq_nz_pos application-judgement "posreal" sq "reals/") (real_minus_real_is_real application-judgement "real" reals nil) (real_times_real_is_real application-judgement "real" reals nil) (closed_region_3D const-decl "bool" vertical_criterion nil) (Vector type-eq-decl nil vectors_2D "vectors/") (* const-decl "real" vectors_2D "vectors/") (Vect3 type-eq-decl nil vectors_3D_def "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/") (dot_add_left formula-decl nil vectors_2D "vectors/") (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (minus_odd_is_odd application-judgement "odd_int" integers nil) (NOT const-decl "[bool -> bool]" booleans nil) (vect2_add formula-decl nil vect_3D_2D "vectors/") (p skolem-const-decl "Vect3" vertical_criterion nil) (s skolem-const-decl "Vect3" vertical_criterion nil) (D formal-const-decl "posreal" vertical_criterion nil) (posreal nonempty-type-eq-decl nil real_types nil) (> const-decl "bool" reals nil) (sq const-decl "nonneg_real" sq "reals/") (nonneg_real nonempty-type-eq-decl nil real_types nil) (- const-decl "[numfield, numfield -> numfield]" number_fields nil) (vz_distr_add formula-decl nil vectors_3D "vectors/") (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) (times_div1 formula-decl nil real_props nil) (times_div2 formula-decl nil real_props nil) (both_sides_minus_ge1 formula-decl nil real_props nil) (H formal-const-decl "posreal" vertical_criterion nil) (* const-decl "[numfield, numfield -> numfield]" number_fields nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (sign_mult_clos application-judgement "Sign" sign "reals/") (mult_divides1 application-judgement "(divides(n))" divides nil) (mult_divides2 application-judgement "(divides(m))" divides nil) (div_mult_pos_ge1 formula-decl nil real_props nil) (c4 skolem-const-decl "nzreal" vertical_criterion nil) (c2 skolem-const-decl "nzreal" vertical_criterion nil) (negreal nonempty-type-eq-decl nil real_types nil) (< const-decl "bool" reals nil) (nonpos_real nonempty-type-eq-decl nil real_types nil) (<= const-decl "bool" reals nil) (div_mult_neg_ge1 formula-decl nil real_props nil) (nzreal_div_nzreal_is_nzreal application-judgement "nzreal" real_types 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) (/= const-decl "boolean" notequal nil) (nzreal nonempty-type-eq-decl nil reals nil) (bool nonempty-type-eq-decl nil booleans nil) (IFF const-decl "[bool, bool -> bool]" booleans nil) (>= const-decl "bool" reals nil) (numfield nonempty-type-eq-decl nil number_fields nil) (nznum nonempty-type-eq-decl nil number_fields nil) (/ const-decl "[numfield, nznum -> numfield]" number_fields nil) (= const-decl "[T, T -> boolean]" equalities 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) (nzint nonempty-type-eq-decl nil integers nil) (OR const-decl "[bool, bool -> bool]" booleans nil) (- const-decl "[numfield -> numfield]" number_fields nil) (Sign type-eq-decl nil sign "reals/") (sign const-decl "Sign" sign "reals/")) shostak) (closed_region_3D_sum_closed-1 nil 3470137852 ("" (case "forall (a,b: nzreal): a/b >= 0 IFF sign(a) = sign(b)") (("1" (label "signlem" -1) (("1" (hide "signlem") (("1" (case "FORALL (c1, c3, k: real, c2, c4: nzreal): c1/c2 >= k AND c3/c4 >= k AND si (("1" (label "divisorlem" -1) (("1" (hide "divisorlem") (("1" (skeep) (("1" (expand "closed_region_3D") (("1" (flatten) (("1" (case "sign(vect2(v + w) * vect2(p)) = dir") (("1" (assert) (("1" (split 3) (("1" (rewrite "vect2_add") (("1" (rewrite "dot_add_left") (("1" (typepred "dir") (("1" (expand "sign") (("1" (lift-if) (("1" (ground) nil nil)) nil)) nil)) nil)) nil)) nil) ("2" (reveal "signlem") (("2" (copy -1) (("2" (inst?) 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nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((mult_divides2 application-judgement "(divides(m))" divides nil) (mult_divides1 application-judgement "(divides(n))" divides nil) (sign_mult_clos application-judgement "Sign" sign "reals/") (minus_odd_is_odd application-judgement "odd_int" integers nil) (NOT const-decl "[bool -> bool]" booleans nil) (> const-decl "bool" reals nil) (Vect2 type-eq-decl nil vectors_2D_def "vectors/") (>= const-decl "bool" reals nil) (nonneg_real nonempty-type-eq-decl nil real_types nil) (posreal nonempty-type-eq-decl nil real_types nil) (D formal-const-decl "posreal" vertical_criterion nil) (Delta const-decl "real" horizontal nil) (sq_nz_pos application-judgement "posreal" sq "reals/") (real_plus_real_is_real application-judgement "real" reals nil) (* const-decl "real" vectors_2D "vectors/") (det const-decl "real" det_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) (nnreal_times_nnreal_is_nnreal application-judgement "nnreal" real_types nil) (sqv const-decl "nnreal" vectors_2D "vectors/") (nnreal type-eq-decl nil real_types nil) (Vector type-eq-decl nil vectors_2D "vectors/") (IF const-decl "[boolean, T, T -> T]" if_def nil) (AND const-decl "[bool, bool -> bool]" booleans nil) (abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs nil) (H formal-const-decl "posreal" vertical_criterion nil) (* const-decl "[numfield, numfield -> numfield]" number_fields nil) (sign const-decl "Sign" sign "reals/") (Nz_vect2 type-eq-decl nil vectors_2D "vectors/") (Theta_D const-decl "real" horizontal nil) (- const-decl "Vector" vectors_2D "vectors/") (Theta_D_symm formula-decl nil horizontal nil) (vect2_eq formula-decl nil vect_3D_2D "vectors/") (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (closed_region_3D const-decl "bool" vertical_criterion nil) (real_div_nzreal_is_real application-judgement "real" reals nil) (* const-decl "Vector" vectors_3D "vectors/") (+ const-decl "Vector" vectors_3D "vectors/") (Delta_gt_0_nzv formula-decl nil horizontal nil) (nzint_times_nzint_is_nzint application-judgement "nzint" integers nil) (nzreal_times_nzreal_is_nzreal application-judgement "nzreal" real_types nil) (zero const-decl "Vector" vectors_2D "vectors/") (minus_real_is_real application-judgement "real" reals nil) (real_times_real_is_real application-judgement "real" reals nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (vect2 const-decl "Vect2" vect_3D_2D "vectors/") (neg_neg formula-decl nil vectors_3D "vectors/") (sign_neg_clos application-judgement "Sign" sign "reals/") (real nonempty-type-from-decl nil reals nil) (Vect3 type-eq-decl nil vectors_3D_def "vectors/") (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) (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 "boolean" notequal nil) (nzint nonempty-type-eq-decl nil integers nil) (bool nonempty-type-eq-decl nil booleans nil) (OR const-decl "[bool, bool -> bool]" booleans nil) (= const-decl "[T, T -> boolean]" equalities nil) (numfield nonempty-type-eq-decl nil number_fields nil) (- const-decl "[numfield -> numfield]" number_fields nil) (Sign type-eq-decl nil sign "reals/") (IMPLIES const-decl "[bool, bool -> bool]" booleans nil) (set type-eq-decl nil sets nil) (Criter type-eq-decl nil predicate_coordination nil) (SignedCrit type-eq-decl nil predicate_coordination nil) (vertical_criterion? const-decl 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"epsils!1*sz!1 - H!1" "epsils!1*vz!1" "0" "tln!1" "tlt!1") (("2" (assert) nil nil)) nil)) nil)) nil)) nil) ("2" (label "signlem" -1) (("2" (hide -1) (("2" (skeep) (("2" (expand "vertical_criterion?") (("2" (split -1) (("1" (flatten) (("1" (expand "conflict?") --> -------------------- --> maximum size reached --> -------------------- ¤ Dauer der Verarbeitung: 0.97 Sekunden (vorverarbeitet) ¤ |
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