| Quellcodebibliothek Statistik Leitseite products/Sources/formale Sprachen/PVS/ACCoRD/ (Beweissystem der NASA Version 6.0.9©) Datei vom 28.9.2014 mit Größe 170 kB |
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Impressum line_solutions.prfInteraktion undPortierbarkeitLisp |
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const-decl "bool" functions nil) (id const-decl "(bijective?[T, T])" identity nil) (TRUE const-decl "bool" booleans nil) (NOT const-decl "[bool -> bool]" booleans nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (sqrt const-decl "{nnz: nnreal | nnz * nnz = nnx}" sqrt "reals/") (norm_scal formula-decl nil vectors_2D "vectors/") (nonzero_abs_is_pos application-judgement "{y: posreal | y >= x}" real_defs nil) (abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs nil) (line_solution? const-decl "bool" line_solutions nil) (Sign type-eq-decl nil sign "reals/") (- const-decl "[numfield -> numfield]" number_fields nil) (OR const-decl "[bool, bool -> bool]" booleans nil) (nzint nonempty-type-eq-decl nil integers 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) (Sp_vect2 type-eq-decl nil horizontal nil) (D formal-const-decl "posreal" line_solutions nil) (sq const-decl "nonneg_real" sq "reals/") (Vect2 type-eq-decl nil vectors_2D_def "vectors/") (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (line_solution_scal formula-decl nil line_solutions nil) (line_solution_det formula-decl nil line_solutions nil) (linear_functional_is_perp_dot formula-decl nil linear_transformations_2D "vectors/") (linear_functional? 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(("1" (replace -2) (("1" (case "sq((-eps) * D * norm(v2)) = sq(D) * sqv(v2)") (("1" (replace -1) (("1" (hide -1) (("1" (lemma "sqv_perpR") (("1" (inst?) (("1" (replace -1) (("1" (hide -1) (("1" (case "sqv(v2) > 0") (("1" (mult-by 2 "sqv(v2)") (("1" (assert) nil nil)) nil) ("2" (lemma "sqv_eq_0") (("2" (inst?) (("2" (assert) (("2" (replace -1) (("2" (expand "det") (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (rewrite "sq_times") (("2" (rewrite "sq_times") (("2" (case "sq((-eps)) = 1") (("1" (replace -1) (("1" (rewrite "sq_norm") (("1" (assert) nil nil)) nil)) nil) ("2" (hide-all-but 1) (("2" (typepred "eps") (("2" (grind) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (rewrite "det_add_left") (("2" (rewrite "det_scal_left") (("2" (cross-mult -1) (("2" (replace -1 :dir rl) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (assert) nil nil)) nil)) nil) ((Sp_vect2 type-eq-decl nil horizontal nil) (sq const-decl "nonneg_real" sq "reals/") (sqv const-decl "nnreal" vectors_2D "vectors/") (det const-decl "real" det_2D "vectors/") (Vect2 type-eq-decl nil vectors_2D_def "vectors/") (norm const-decl "nnreal" vectors_2D "vectors/") (nnreal type-eq-decl nil real_types nil) (Vector type-eq-decl nil vectors_2D "vectors/") (D formal-const-decl "posreal" line_solutions 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) (>= const-decl "bool" reals nil) (Sign type-eq-decl nil sign "reals/") (OR const-decl "[bool, bool -> bool]" booleans nil) (bool nonempty-type-eq-decl nil booleans nil) (nzint nonempty-type-eq-decl nil integers 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) (- const-decl "[numfield -> numfield]" number_fields nil) (* const-decl "[numfield, numfield -> numfield]" number_fields 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) (number_field nonempty-type-from-decl nil number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (= const-decl "[T, T -> boolean]" equalities nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil) (real_div_nzreal_is_real application-judgement "real" reals nil) (nnreal_times_nnreal_is_nnreal application-judgement "nnreal" real_types nil) (+ const-decl "Vector" vectors_2D "vectors/") (* const-decl "Vector" vectors_2D "vectors/") (cauchy_schwarz formula-decl nil vectors_2D "vectors/") (sq_times formula-decl nil sq "reals/") (sq_norm formula-decl nil vectors_2D "vectors/") (NOT const-decl "[bool -> bool]" booleans nil) (minus_odd_is_odd application-judgement "odd_int" integers nil) (mult_divides1 application-judgement "(divides(n))" divides nil) (sign_mult_clos application-judgement "Sign" sign "reals/") (posreal_times_posreal_is_posreal application-judgement "posreal" real_types nil) (sign_sq_clos application-judgement "Sign" sign "reals/") (sqv_perpR formula-decl nil perpendicular_2D "vectors/") (sq_nz_pos application-judgement "posreal" sq "reals/") (real_ge_is_total_order name-judgement "(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) (v2 skolem-const-decl "Vect2" line_solutions nil) (both_sides_times_pos_ge1 formula-decl nil real_props nil) (sqv_zero formula-decl nil vectors_2D "vectors/") (perpR_eq_zero formula-decl nil perpendicular_2D "vectors/") (dot_zero_right formula-decl nil vectors_2D "vectors/") (norm_zero formula-decl nil vectors_2D "vectors/") (comp_zero_x formula-decl nil vectors_2D "vectors/") (comp_zero_y formula-decl nil vectors_2D "vectors/") (real_plus_real_is_real application-judgement "real" reals nil) (sqv_eq_0 formula-decl nil vectors_2D "vectors/") (perpR const-decl "Vect2" perpendicular_2D "vectors/") (det_perpR formula-decl nil det_2D "vectors/") (det_scal_left formula-decl nil det_2D "vectors/") (nonzero_real nonempty-type-eq-decl nil reals nil) (div_cancel3 formula-decl nil real_props nil) (det_add_left formula-decl nil det_2D "vectors/") (real_minus_real_is_real application-judgement "real" reals nil) (real_times_real_is_real application-judgement "real" reals nil) (nzreal_times_nzreal_is_nzreal application-judgement "nzreal" real_types nil) (sign_neg_clos application-judgement "Sign" sign "reals/")) nil) (line_solution_along_line_TCC1-1 nil 3472549906 ("" (skeep) (("" (postpone) nil nil)) nil) nil nil)) (line_solution_along_line 0 (line_solution_along_line-2 nil 3472550602 ("" (skeep) (("" (name "tp" "((-eps) * D * norm(v2) - det(sp, v2)) / det(v1, v2)") (("" (replace -1) (("" (assert) (("" (flatten) (("" (lemma "line_solution_det") (("" (inst - "eps" "sp + tp*v1" "v2") (("" (assert) (("" (rewrite "det_add_left") (("" (rewrite "det_scal_left") (("" (case "tp*det(v1,v2) = norm(v2) * D * (-eps) - det(sp, v2)") (("1" (replace -1) (("1" (typepred "eps") (("1" (ground) nil nil)) nil)) nil) ("2" (cross-mult -1) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((Sp_vect2 type-eq-decl nil horizontal nil) (sq const-decl "nonneg_real" sq "reals/") (sqv const-decl "nnreal" vectors_2D "vectors/") (det const-decl "real" det_2D "vectors/") (Vect2 type-eq-decl nil vectors_2D_def "vectors/") (norm const-decl "nnreal" vectors_2D "vectors/") (nnreal type-eq-decl nil real_types nil) (Vector type-eq-decl nil vectors_2D "vectors/") (D formal-const-decl "posreal" line_solutions 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) (>= const-decl "bool" reals nil) (Sign type-eq-decl nil sign "reals/") (OR const-decl "[bool, bool -> bool]" booleans nil) (bool nonempty-type-eq-decl nil booleans nil) (nzint nonempty-type-eq-decl nil integers 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) (- const-decl "[numfield -> numfield]" number_fields nil) (* const-decl "[numfield, numfield -> numfield]" number_fields 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) (number_field nonempty-type-from-decl nil number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (= const-decl "[T, T -> boolean]" equalities nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil) (real_div_nzreal_is_real application-judgement "real" reals nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (nnreal_times_nnreal_is_nnreal application-judgement "nnreal" real_types nil) (line_solution_det formula-decl nil line_solutions nil) (minus_odd_is_odd application-judgement "odd_int" integers nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (det_scal_left formula-decl nil det_2D "vectors/") (div_cancel3 formula-decl nil real_props nil) (nonzero_real nonempty-type-eq-decl nil reals nil) (NOT const-decl "[bool -> bool]" booleans nil) (real_plus_real_is_real application-judgement "real" reals nil) (det_add_left formula-decl nil det_2D "vectors/") (+ const-decl "Vector" vectors_2D "vectors/") (* const-decl "Vector" vectors_2D "vectors/") (real_minus_real_is_real application-judgement "real" reals nil) (real_times_real_is_real application-judgement "real" reals nil) (nzreal_times_nzreal_is_nzreal application-judgement "nzreal" real_types nil) (sign_neg_clos application-judgement "Sign" sign "reals/")) nil) (line_solution_along_line-1 nil 3472549914 (";;; Proof one_triangle_two_line_solutions-1 for formula rules_of_the_triangle.one_t (skeep) ((";;; Proof one_triangle_two_line_solutions-1 for formula rules_of_the_triangle.one_ (name "tp" "((-eps) * D * norm(v2) - det(sp, v2)) / det(v1, v2)") ((";;; Proof one_triangle_two_line_solutions-1 for formula rules_of_the_triangle.one_ (replace -1) ((";;; Proof one_triangle_two_line_solutions-1 for formula rules_of_the_triangle.one_ (assert) ((";;; Proof one_triangle_two_line_solutions-1 for formula rules_of_the_triangle.one_ (lemma "line_solution_det") ((";;; Proof one_triangle_two_line_solutions-1 for formula rules_of_the_triangle.one_ (inst - "eps" "sp + tp*v1" "v2") ((";;; Proof one_triangle_two_line_solutions-1 for formula rules_of_the_triangle.one_ (assert) ((";;; Proof one_triangle_two_line_solutions-1 for formula rules_of_the_triangle.one_ (split 1) (("1" (rewrite "det_add_left") (("1" (rewrite "det_scal_left") (("1" (case "tp*det(v1,v2) = norm(v2) * D * (-eps) - det(sp, v2)") (("1" (replace -1) (("1" (typepred "eps") (("1" (ground) nil))))) ("2" (cross-mult -1) (("2" (assert) nil))))))))) ("2" (postpone) nil)))))))))))))))) ";;; developed with shostak decision procedures") nil nil)))
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2026-05-26