Quelle closest_approach_3D.prf
Sprache: Lisp
(closest_approach_3Dnil 3256049050"" (skosimp*)"" (assert )"" (rewrite "sq_dist_is_dist_sq" )"" (rewrite "dist_norm" )"" (expand "norm" )"" (rewrite "sq_sqrt" )"" (expand "sqv" )"" (expand "*" )"" (expand "+" )"" (expand "-" ) (("" (assert ) nil nil )) nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )nil distance_3D nil )nil sqrt "reals/" )nil booleans nil )"bool" reals nil )nil real_types nil )"nnreal" vectors_3D nil )"Vector" vectors_3D nil )"(total_order?[real])" nil )"real" vectors_3D nil )"real" reals nil )"real" reals nil )"real" reals nil )"nnreal" vectors_3D nil )"Vector" vectors_3D nil )"[number_field -> boolean]" reals nil )nil number_fields nil )"[number -> boolean]" number_fieldsnil )nil booleans nil )nil numbers nil )"Vector" vectors_3D nil )nil vectors_3D nil )nil vectors_3D_def nil )nil reals nil )nil distance_3D nil ))nil ))nil 3255774848"" (skosimp*) (("" (grind) nil nil )) nil )"real" reals nil )"real" reals nil )"real" reals nil )"nnreal" nil )"nnreal" distance_3D nil )"nonneg_real" sq "reals/" )"Vector" vectors_3D nil )"Vector" vectors_3D nil )"real" vectors_3D nil )"Vector" vectors_3D nil ))nil 3255968102 ("" (grind) nil nil )"Vector" vectors_3D nil )"Vector" vectors_3D nil )"nonneg_real" sq "reals/" )"nnreal" distance_3D nil )"nnreal" distance_3D nil )"real" reals nil )"real" reals nil )"real" reals nil ))nil 3255967833"" (skosimp*)"" (rewrite "norm_eq_0" )"" (rewrite "sub_eq_zero" )"" (replaces -1)"" (rewrite "dist_eq_vel" )"" (rewrite "dist_eq_vel" ) nil nil )) nil ))nil ))nil ))nil ))nil )nil vectors_3D nil )nil reals nil )nil vectors_3D nil )"Vector" vectors_3D nil )nil vectors_3D_def nil )"[number_field -> boolean]" reals nil )nil number_fields nil )"[number -> boolean]" number_fieldsnil )nil booleans nil )nil numbers nil )nil closest_approach_3D nil )nil vectors_3D nil ))nil 3255962785"" (skosimp*)"" (rewrite "sq_eq_0" )"" (rewrite "norm_eq_0" )"" (assert ) (("" (postpone) nil nil )) nil )) nil ))nil ))nil )nil sq "reals/" )nil numbers nil )nil booleans nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[number_field -> boolean]" reals nil )nil reals nil )nil vectors_3D nil )nil booleans nil )"bool" reals nil )nil real_types nil )"nnreal" vectors_3D nil )"Vector" vectors_3D nil )nil vectors_3D_def nil ))nil 3256051573"" (skosimp*)"" (rewrite "dot_sq_norm" )"" (assert )"" (replace -2)"" (hide -2)"" (hide -1)"" (lemma "sq_eq_0" )"" (inst?) (("" (assert ) nil nil )) nil )) nil ))nil ))nil ))nil ))nil ))nil ))nil )nil vectors_3D nil )nil reals nil )nil vectors_3D nil )"Vector" vectors_3D nil )nil vectors_3D_def nil )nil numbers nil )nil booleans nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[number_field -> boolean]" reals nil )nil booleans nil )"bool" reals nil )nil real_types nil )"nnreal" vectors_3D nil )"nnreal" nil )nil sq "reals/" )nil vectors_3D nil )"real" reals nil ))nil 3256049208"" (skosimp*)"" (expand "time_closest" )"" (assert )"" (rewrite "dot_sq_norm" ) (("" (assert ) nil nil )) nil ))nil ))nil ))nil )"real" closest_approach_3D nil )nil vectors_3D nil )nil reals nil )nil vectors_3D nil )"Vector" vectors_3D nil )nil vectors_3D_def nil )nil vectors_3D nil )"real" reals nil )"real" reals nil )"real" reals nil ))nil 3431333345"" (skosimp*)"" (expand "time_closest" )"" (assert )"" (case "a!1 > 0" )"1" (lemma "quad_min_mono_inc" )"1" (inst - "a!1" "b!1" "c!1" "t2!1" "t1!1" )"1" (assert )"1" (assert )"1" (prop)"1" (assert )"1" (rewrite "dot_sq_norm" )"1" (lemma "sq_dist_quad" )"1" "a!1" "b!1" "c!1" "p0!1" "q0!1" "t1!1" "u!1" "v!1" "w0!1" )"1" (assert )"1" "sq_dist_quad" )"1" "a!1" "b!1" "c!1" "p0!1" "q0!1" "t2!1" "u!1" "v!1" "w0!1" )"1" assert )"1" expand "quadratic" )"1" (assert ) nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" (lemma "dot_sq_norm" )"2" (inst?) (("2" (assert ) nil nil )) nil ))nil ))nil ))nil ))nil )"2" (assert ) nil nil ))nil ))nil )"2" (assert )"2" (rewrite "dot_sq_norm" )"2" (lemma "sq_eq_0" )"2" (inst?) (("2" (assert ) nil nil )) nil )) nil ))nil ))nil ))nil ))nil ))nil ))nil )"real" closest_approach_3D nil )"bool" reals nil )nil booleans nil )nil reals nil )"[number_field -> boolean]" reals nil )nil number_fields nil )"[number -> boolean]" number_fieldsnil )nil booleans nil )nil numbers nil )"boolean" notequal nil )"real" closest_approach_3D nil )nil reals nil )nil closest_approach_3D nil )"real" reals nil )"real" quadratic "reals/" )nil vectors_3D nil )nil vectors_3D nil )"Vector" vectors_3D nil )nil vectors_3D_def nil )"(strict_total_order?[real])" real_props nil )"(total_order?[real])" nil )nil quad_minmax "reals/" )"nnreal" vectors_3D nil )nil real_types nil )"bool" reals nil )nil sq "reals/" )nil vectors_3D nil )"real" reals nil )"(total_order?[real])" nil )"(strict_total_order?[real])" real_props nil )"real" reals nil )"real" reals nil ))nil )nil 3401722700"" (skosimp*)"" (expand "time_closest" )"" (assert )"" (case "a!1 > 0" )"1" (lemma "quadratic_min_mono_inc" )"1" "a!1" "b!1" "c!1" "(LAMBDA t: sq_dist(p0!1 + t * u!1, q0!1 + t * v!1))" "t_cpa!1" "t2!1" "t1!1" )"1" (assert )"1" (prop)"1" (apply-extensionality 1 :hide? t)"1" (lemma "sq_dist_quad" )"1" "a!1" "b!1" "c!1" "p0!1" "q0!1" "x!1" "u!1" "v!1" "w0!1" )"1" (assert )"1" (expand "quadratic" )"1" (propax) nil nil )) nil ))nil ))nil ))nil )"2" (skosimp*)"2" (expand "quadratic" )"2" (lemma "sq_dist_quad" )"2" "a!1" "b!1" "c!1" "p0!1" "q0!1" "x1!1" "u!1" "v!1" "w0!1" )"2" (assert ) (("2" (assert ) nil nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" (lemma "time_closest_lem" )"2" "a!1" "b!1" "p0!1" "q0!1" "u!1" "v!1" )"2" (assert )"2" (expand "time_closest" )"2" (assert ) nil nil )) nil ))nil ))nil ))nil ))nil ))nil )"2" (assert ) nil nil ))nil ))nil )"2" (assert )"2" (rewrite "dot_sq_norm" )"2" (lemma "sq_eq_0" )"2" (inst?) (("2" (assert ) nil nil )) nil )) nil ))nil ))nil ))nil ))nil ))nil ))nil )nil vectors_3D nil )"Vector" vectors_3D nil )nil vectors_3D_def nil )"Vector" vectors_3D nil )"real" quadratic "reals/" )nil vectors_3D nil )"nnreal" vectors_3D nil )nil sq "reals/" )nil vectors_3D nil ))nil ))nil 3431334821"" (skosimp*)"" (case "norm(u!1 - v!1) = 0" )"1" (expand "is_minimum?" )"1" (skosimp*)"1" (lemma "norm_diff_eq_0" )"1" (inst -1 "p0!1" "q0!1" "t_cpa!1" "y!1" "u!1" "v!1" )"1" (assert )"1" (assert )"1" (expand "dist" )"1" (rewrite "sqrt_eq" ) nil nil )) nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" (expand "time_closest" )"2" (name "A" "(u!1-v!1)*(u!1-v!1)" )"2" (name "B" "2*(p0!1-q0!1)*(u!1-v!1)" )"2" (name "C" "(p0!1-q0!1)*(p0!1-q0!1)" )"2" (case "A > 0" )"1" (assert )"1" (lemma "quad_min" )"1" (inst -1 "A" "B" "C" )"1" (assert )"1" "(LAMBDA t: sq_dist(p0!1 + t * u!1, q0!1 + t * v!1)) = quadratic(A, B, C)" )"1" (assert )"1" (lemma "dot_sq_norm" )"1" "(u!1 - v!1)" )"1" (assert ) nil nil ))nil ))nil ))nil )"2" (apply-extensionality 1 :hide? t)"1" (lemma "sq_dist_quad" )"1" "A" "B" "C" "p0!1" "q0!1" "x!1" "u!1" "v!1" "p0!1-q0!1" )"1" assert )"1" expand "quadratic" )"1" (propax) nil nil ))nil ))nil ))nil ))nil )"2" (skosimp*)"2" expand "quadratic" )"2" "sq_dist_quad" )"2" "A" "B" "C" "p0!1" "q0!1" "x1!1" "u!1" "v!1" "p0!1-q0!1" )"2" assert )"2" (assert ) nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" (lemma "dot_sq_norm" )"2" (inst - "u!1-v!1" )"2" (lemma "sq_eq_0" )"2" (inst?) (("2" (assert ) nil nil )) nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )nil vectors_3D_def nil )"Vector" vectors_3D nil )"nnreal" vectors_3D nil )nil real_types nil )"bool" reals nil )nil booleans nil )"[number_field -> boolean]" reals nil )nil number_fields nil )"[number -> boolean]" number_fieldsnil )nil vectors_3D nil )nil reals nil )"[T, T -> boolean]" equalities nil )nil booleans nil )nil numbers nil )"Vector" vectors_3D nil )"Vector" vectors_3D nil )"nnreal" distance_3D nil )nil real_types nil )nil sqrt "reals/" )"nnreal" distance_3D nil )"(total_order?[real])" nil )nil closest_approach_3D nil )"bool" quad_minmax "reals/" )"real" vectors_3D nil )nil sq "reals/" )"real" reals nil )"real" reals nil )"real" reals nil )"(strict_total_order?[real])" real_props nil )nil vectors_3D nil )nil reals nil )"boolean" notequal nil )"real" quadratic "reals/" )nil vectors_3D nil )"(total_order?[real])" nil )nil closest_approach_3D nil )"real" reals nil )"real" closest_approach_3D nil )"real" closest_approach_3D nil )"real" closest_approach_3D nil )nil quad_minmax "reals/" )"bool" reals nil )"real" closest_approach_3D nil ))nil )nil 3421667499"" (skosimp*)"" (case "norm(u!1 - v!1) = 0" )"1" (expand "is_minimum?" )"1" (skosimp*)"1" (lemma "norm_diff_eq_0" )"1" (inst -1 "p0!1" "q0!1" "t_cpa!1" "y!1" "u!1" "v!1" )"1" (assert )"1" (assert )"1" (expand "dist" )"1" (rewrite "sqrt_eq" ) nil nil )) nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" (expand "time_closest" )"2" (name "A" "(u!1-v!1)*(u!1-v!1)" )"2" (name "B" "2*(p0!1-q0!1)*(u!1-v!1)" )"2" (name "C" "(p0!1-q0!1)*(p0!1-q0!1)" )"2" (case "A > 0" )"1" (lemma "quadratic_min" )"1" "A" "B" "C" "(LAMBDA t: sq_dist(p0!1 + t * u!1, q0!1 + t * v!1))" "t_cpa!1" )"1" (assert )"1" (prop)"1" (apply-extensionality 1 :hide? t)"1" (lemma "sq_dist_quad" )"1" "A" "B" "C" "p0!1" "q0!1" "x!1" "u!1" "v!1" "p0!1-q0!1" )"1" assert )"1" expand "quadratic" )"1" (propax) nil nil ))nil ))nil ))nil ))nil )"2" (skosimp*)"2" (expand "quadratic" )"2" "sq_dist_quad" )"2" "A" "B" "C" "p0!1" "q0!1" "x1!1" "u!1" "v!1" "p0!1-q0!1" )"2" assert )"2" (assert ) nil nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" (lemma "time_closest_lem" )"2" "A" "B" "p0!1" "q0!1" "u!1" "v!1" )"2" (assert )"2" assert )"2" expand "time_closest" )"2" (assert ) nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" (assert ) nil nil ))nil ))nil )"2" (lemma "dot_sq_norm" )"2" (inst - "u!1-v!1" )"2" (lemma "sq_eq_0" )"2" (inst?) (("2" (assert ) nil nil )) nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )nil vectors_3D_def nil )"nnreal" vectors_3D nil )nil vectors_3D nil )"Vector" vectors_3D nil )"Vector" vectors_3D nil )nil sqrt "reals/" )"real" vectors_3D nil )nil vectors_3D nil )nil sq "reals/" )nil vectors_3D nil )"real" quadratic "reals/" ))nil )nil 3255788628"" (skosimp*)"" (lemma "cpa_prep" )"" (inst?)"" (name "W0" "p0!1-q0!1" )"" "(u!1 - v!1) * (u!1 - v!1)" "2 * W0 * (u!1 - v!1)" " W0 * W0" "W0" )"" (assert ) nil nil )) nil ))nil ))nil ))nil ))nil )nil vectors_3D nil )"Vector" vectors_3D nil )"real" vectors_3D nil ))nil 3255788937"" (skosimp*)"" (lemma "time_cpa" )"" (inst?)"" (inst?)"" (expand "is_minimum?" )"" (inst -1 "t!1" )"" (expand "dist" ) (("" (rewrite "sqrt_le" ) nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )nil closest_approach_3D nil )nil numbers nil )nil booleans nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[number_field -> boolean]" reals nil )"real" closest_approach_3D nil )"(total_order?[real])" nil )nil sqrt "reals/" )nil booleans nil )"bool" reals nil )nil real_types nil )nil real_types nil )"nnreal" distance_3D nil )nil vectors_3D nil )"Vector" vectors_3D nil )"Vector" vectors_3D nil )"nnreal" distance_3D nil )"bool" quad_minmax "reals/" )nil vectors_3D_def nil )nil reals nil ))nil 3401722756"" (skosimp*)"" (assert )"" (lemma "cpa_prep_mono" )"" (inst?)"" (name "W0" "p0!1-q0!1" )"" "(u!1 - v!1) * (u!1 - v!1)" "2 * W0 * (u!1 - v!1)" " W0 * W0" "t1!1" "t2!1" "W0" )"" (assert ) nil nil )) nil ))nil ))nil ))nil ))nil ))nil )"(strict_total_order?[real])" real_props nil )"(total_order?[real])" nil )nil reals nil )nil vectors_3D_def nil )nil numbers nil )nil booleans nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[number_field -> boolean]" reals nil )"Vector" vectors_3D nil )"real" vectors_3D nil )"Vector" vectors_3D nil )"[T, T -> boolean]" equalities nil )nil vectors_3D nil )nil closest_approach_3D nil ))nil ))nil 3255958397"" (skosimp*)"" (assert )"" (flatten)"" (lemma "dist_cpa" )"" (inst -1 "p0!1" "q0!1" "t1!1" "u!1" "v!1" )"" (assert ) nil nil )) nil ))nil ))nil ))nil ))nil )"(total_order?[real])" nil )nil closest_approach_3D nil )"[number_field -> boolean]" reals nil )nil number_fields nil )"[number -> boolean]" number_fieldsnil )nil booleans nil )nil numbers nil )nil vectors_3D_def nil )nil reals nil ))nil 3401722795"" (skosimp*)"" (assert )"" (flatten)"" (lemma "dist_cpa_lt" )"" (inst?)"" (inst - "t1!1" "t2!1" )"" (assert )"" (expand "dist" )"" (lemma "sqrt_lt" )"" (inst?) (("" (assert ) nil nil )) nil )) nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"(strict_total_order?[real])" real_props nil )"(total_order?[real])" nil )nil closest_approach_3D nil )"nnreal" distance_3D nil )nil booleans nil )"bool" reals nil )nil real_types nil )nil real_types nil )"nnreal" distance_3D nil )nil vectors_3D nil )"Vector" vectors_3D nil )"Vector" vectors_3D nil )nil sqrt "reals/" )"[number_field -> boolean]" reals nil )nil number_fields nil )"[number -> boolean]" number_fieldsnil )nil booleans nil )nil numbers nil )nil vectors_3D_def nil )nil reals nil ))nil )nil 3401544437"" (skosimp*)"" (assert )"" (flatten)"" (case "t1!1 = time_closest(p0!1, q0!1, u!1, v!1)" )"1" (lemma "dist_min" )"1" (inst?)"1" (assert )"1" (assert ) (("1" (inst?) nil nil )) nil )) nil ))nil ))nil )"2" (case "norm(u!1-v!1)=0" )"1" (lemma "norm_diff_eq_0" )"1" (inst -1 "p0!1" "q0!1" "t1!1" "t2!1" "u!1" "v!1" )"1" (assert ) nil nil )) nil ))nil )"2" (rewrite "sq_dist_le" )"2" (hide 4)"2" (name "A" "(u!1 - v!1) * (u!1 - v!1)" )"2" (name "W0" "p0!1 - q0!1" )"2" (name "B" "2 * W0 * (u!1 - v!1) " )"2" (name "C" "W0*W0" )"2" (lemma "sq_dist_quad" )"2" (inst?)"2" (inst -1 "A" "B" "C" "W0" )"2" assert )"2" replace -1)"2" "2" "sq_dist_quad" )"2" "2" "A" "B" "C" "W0" )"2" assert )"2" replace -1)"2" "2" "sq_dist_quad" )"2" "2" assert )"2" "2" "A > 0" )"1" "quadratic_min_mono_inc" )"1" "A" "B" "C" "quadratic(A,B,C)" "-B / (2 * A)" "_" "_" )"1" "t2!1" "t1!1" )"1" assert )"1" expand "quadratic" )"1" assert )"1" "time_closest_lem" )"1" "1" "1" assert )nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" assert )nil nil )"3" "sq_eq_0" )"3" "3" assert )nil nil ))nil ))nil ))nil ))nil )"2" rewrite "dot_sq_norm" "2" assert )"2" "sq_eq_0" )"2" "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 ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"nnreal" vectors_3D nil )nil vectors_3D nil )nil vectors_3D nil )nil vectors_3D nil )nil sq "reals/" )"real" quadratic "reals/" )"real" vectors_3D nil )"Vector" vectors_3D nil )"Vector" vectors_3D nil ))nil )nil 3256916765"" (skosimp*)"" (assert )"" (flatten)"" (case "t2!1 = time_closest(p0!1, q0!1, u!1, v!1)" )"1" (lemma "dist_min" )"1" (inst?)"1" (assert )"1" (assert ) (("1" (inst?) nil nil )) nil )) nil ))nil ))nil )"2" (case "norm(u!1-v!1)=0" )"1" (lemma "norm_diff_eq_0" )"1" (inst -1 "p0!1" "q0!1" "t2!1" "tt!1" "u!1" "v!1" )"1" (assert ) nil nil )) nil ))nil )"2" (rewrite "sq_dist_le" )"2" (hide 4)"2" (name "A" "(u!1 - v!1) * (u!1 - v!1)" )"2" (name "W0" "p0!1 - q0!1" )"2" (name "B" "2 * W0 * (u!1 - v!1) " )"2" (name "C" "W0*W0" )"2" (lemma "sq_dist_quad" )"2" (inst?)"2" (inst -1 "A" "B" "C" "W0" )"2" assert )"2" replace -1)"2" "2" "sq_dist_quad" )"2" "2" "A" "B" "C" "W0" )"2" assert )"2" replace -1)"2" "2" "sq_dist_quad" )"2" "2" assert )"2" "2" "A > 0" )"1" "quadratic_min_mono_inc" )"1" "A" "B" "C" "quadratic(A,B,C)" "-B / (2 * A)" "_" "_" )"1" "tt!1" "t2!1" )"1" assert )"1" expand "quadratic" )"1" assert )"1" "time_closest_lem" )"1" "1" "1" assert )nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" assert )nil nil )"3" "sq_eq_0" )"3" "3" assert )nil nil ))nil ))nil ))nil ))nil )"2" rewrite "dot_sq_norm" "2" assert )"2" "sq_eq_0" )"2" "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 ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"nnreal" vectors_3D nil )nil vectors_3D nil )nil vectors_3D nil )nil vectors_3D nil )nil sq "reals/" )"real" quadratic "reals/" )"real" vectors_3D nil )"Vector" vectors_3D nil )"Vector" vectors_3D nil ))nil ))nil 3401722823"" (skosimp*)"" (assert )"" (flatten)"" (expand "dist" )"" (lemma "sqrt_eq" )"" (inst?)"" (flatten)"" (hide -1)"" (split -1)"1" (propax) nil nil )"2" (hide 2)"2" (lemma "sq_dist_quad" )"2" (name "W0" "p0!1-q0!1" )"2" (inst?)"2" "(u!1 - v!1) * (u!1 - v!1)" "2 * W0 * (u!1 - v!1)" " W0 * W0" "W0" )"2" assert )"2" replace -2)"2" "2" "sq_dist_quad" )"2" "2" "(u!1 - v!1) * (u!1 - v!1)" "2 * W0 * (u!1 - v!1)" " W0 * W0" "W0" )"2" assert )"2" replace -1)"2" "u!1 - v!1 = zero" )"1" (assert ) nil nil )"2" "norm_eq_0" )"2" "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 ))nil ))nil ))nil )"nnreal" distance_3D nil )nil numbers nil )nil booleans nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[number_field -> boolean]" reals nil )nil reals nil )nil booleans nil )"bool" reals nil )nil real_types nil )nil vectors_3D_def nil )nil real_types nil )"nnreal" distance_3D nil )nil vectors_3D nil )"Vector" vectors_3D nil )"Vector" vectors_3D nil )"[T, T -> boolean]" equalities nil )"Vector" vectors_3D nil )"real" vectors_3D nil )nil vectors_3D nil )nil vectors_3D nil )"Vector" vectors_3D nil )nil vectors_3D nil )"real" reals nil )"real" reals nil )nil closest_approach_3D nil )nil sqrt "reals/" ))nil ))nil 3406994109"" (skosimp)"" (expand "time_closest" )"" (lift-if)"" (prop)"1" (rewrite "norm_eq_0" )"1" (replaces -1) (("1" (assert ) nil nil )) nil )) nil )"2" (mult-by 2 " sq(norm(u!1 - v!1))" )"1" (assert ) nil nil ) ("2" (rewrite "sq_gt_0" ) nil nil ))nil ))nil ))nil ))nil ))nil )"real" closest_approach_3D nil )"(total_order?[real])" nil )nil vectors_3D_def nil )"Vector" vectors_3D nil )nil vectors_3D nil )nil reals nil )nil vectors_3D nil )nil sq "reals/" )"nnreal" nil )nil reals nil )nil real_props nil )"(total_order?[real])" nil )"real" reals nil )"(strict_total_order?[real])" real_props nil )"Vect3" closest_approach_3D nil )"Vect3" closest_approach_3D nil )"nnreal" vectors_3D nil )nil real_types nil )"nonneg_real" sq "reals/" )nil real_types nil )"bool" reals nil ) (> const-decl "bool" reals nil )nil booleans nil )"[number_field -> boolean]" reals nil )nil number_fields nil )"[number -> boolean]" number_fieldsnil )nil booleans nil )nil numbers nil )nil real_types nil )nil number_fields nil )"boolean" notequal nil )nil number_fields nil )"[numfield, nznum -> numfield]" number_fields nil )"[numfield -> numfield]" number_fields nil )"real" vectors_3D nil )nil real_props nil )"real" reals nil ))nil ))nil 3409339432"" (skosimp)"" (replaces -2)"" (expand "divergent?" ) (("" (grind) nil nil )) nil )) nil ))nil )"real" reals nil )"real" reals nil )"real" reals nil )"Vector" vectors_3D nil )"Vector" vectors_3D nil )"nnreal" distance_3D nil )"nnreal" distance_3D nil )"nonneg_real" sq "reals/" )"bool" closest_approach_3D nil ))nil ))nil 3406994137"" (skosimp)"" (lemma "dot_nneg_tca_npos" )"" (inst? -1)"" (assert )"" (lemma "dist_diverges" )"" (expand "divergent?" )"" (skosimp)"" (inst? -1)"" (inst -1 "0" "t!1" _)"" (inst? -1)"" (assert )"" (split -1)"1" (propax) nil nil )"2" (flatten)"2" (rewrite "norm_eq_0" )"2" (rewrite "sub_eq_zero" ) nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )nil closest_approach_3D nil )"(total_order?[real])" nil )"bool" closest_approach_3D nil )"real" closest_approach_3D nil )"Vector" vectors_3D nil )nil vectors_3D nil )nil vectors_3D nil )nil vectors_3D nil )nil vectors_3D nil )nil vectors_3D nil )"(strict_total_order?[real])" real_props nil )"(total_order?[real])" nil )nil real_types nil )"bool" reals nil )nil real_types nil )"bool" reals nil )nil booleans nil )"[number_field -> boolean]" reals nil )nil number_fields nil )"[number -> boolean]" number_fieldsnil )nil booleans nil )nil numbers nil )nil closest_approach_3D nil )nil vectors_3D_def nil )nil reals nil ))nil ))nil 3411903251"" (skosimp)"" (case "divergent?(p0!1-q0!1,zero,u!1-v!1,zero)" )"1" (hide -2)"1" (case "norm(u!1-v!1) /= 0" )"1" (flatten)"1" (name-replace "s" "p0!1-q0!1" )"1" (name-replace "w" "u!1-v!1" )"1" (expand "divergent?" )"1" (name "myt" "-(s*w)/sqv(w)" )"1" (case "myt > 0" )"1" (inst -3 "myt" )"1" (expand "dist" )"1" (rewrite "sqrt_lt" )"1" (expand "sq_dist" )"1" expand * "*" "+" )"1" "1" "1" assert )"1" expand "sq" )"1" "1" "1" "1" "1" assert )"1" "1" "1" nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" (assert ) nil nil ))nil )"2" (replaces -1 :dir rl)"2" (hide -1)"2" (expand "norm" )"2" (case "sqv(w) = 0" )"1" "1" (rewrite "sqrt_0" ) nil nil ))nil )"2" "2" (assert ) nil nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" (flatten)"2" (hide -2 2)"2" (rewrite "norm_sqv_eq_0" ) nil nil )) nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" (use "divergent_u_neq_v" )"2" (assert )"2" (flatten) (("2" (rewrite "norm_eq_0" ) nil nil ))nil ))nil ))nil ))nil ))nil )"2" (hide-all-but (-1 1))"2" (expand "divergent?" )"2" (skosimp 1)"2" (inst -1 "t!1" )"2" (assert )"2" (expand "dist" )"2" (rewrite "sqrt_lt" )"2" (rewrite "sqrt_lt" )"2" (expand "sq_dist" )"2" (assert )"2" (expand * "*" "+" "-" )"2" (assert ) nil nil )) nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"Vector" vectors_3D nil )"Vector" vectors_3D nil )nil vectors_3D nil )"bool" closest_approach_3D nil )nil booleans nil )nil booleans nil )nil vectors_3D_def nil )nil reals nil )"nnreal" vectors_3D nil )nil real_types nil )"bool" reals nil )"[number_field -> boolean]" reals nil )nil number_fields nil )"[number -> boolean]" number_fieldsnil )"boolean" notequal nil )nil numbers nil )"[T, T -> boolean]" equalities nil )nil vectors_3D nil )"bool" reals nil )"nnreal" distance_3D nil )nil vectors_3D nil )nil vectors_3D nil )nil sq "reals/" )"nnreal" nil )nil sq "reals/" )"odd_int" integers nil )nil sq "reals/" )"[numfield, numfield -> numfield]" number_fields nil )"[numfield, numfield -> numfield]" number_fields nil )nil sq "reals/" )nil vectors_3D nil )"real" reals nil )"real" reals nil )"nnreal" nil )nil real_props nil )nil real_props nil )"[bool, bool -> bool]" booleans nil )"bool" reals nil )"[numfield, numfield -> numfield]" number_fields nil )"nonneg_real" sq "reals/" )"real" reals nil )"real" reals nil )nil vectors_3D nil )nil vectors_3D nil )"(strict_total_order?[real])" real_props nil )nil sqrt "reals/" )"nnreal" distance_3D nil )"Vector" vectors_3D nil )"Vector" vectors_3D nil )nil real_types nil )nil real_types nil )"real" closest_approach_3D nil )AND const-decl "[bool, bool -> bool]" booleans nil )"(total_order?[real])" nil )"(strict_total_order?[real])" real_props nil )nil sqrt "reals/" )"Vector" closest_approach_3D nil )nil extra_real_props nil )"real" reals nil )nil number_fields nil )nil number_fields nil )"[numfield, nznum -> numfield]" number_fields nil )"[numfield -> numfield]" number_fields nil )"real" vectors_3D nil )"nnreal" vectors_3D nil )nil vectors_3D nil )nil closest_approach_3D nil ))nil ))nil 3409356106"" (skosimp)"" (split)"1" (flatten)"1" (use "divergent_u_neq_v" )"1" (assert )"1" (flatten)"1" (skeep 2)"1" (lemma "dist_diverges" )"1" "p0!1" "q0!1" "t1" "t2" "time_closest(p0!1, q0!1, u!1, v!1)" "u!1" "v!1" )"1" (beta)"1" (assert )"1" (hide 3)"1" (case "norm(u!1 - v!1) = 0" )"1" (hide-all-but (-1 2))"1" rewrite "norm_eq_0" )"1" (rewrite "sub_eq_zero" ) nil nil ))nil ))nil )"2" (assert )"2" "dot_nneg_tca_npos" )"2" "2" assert )"2" "divergent_dot_nneg" )"2" (assert ) nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" (flatten)"2" (expand "divergent?" )"2" (skosimp)"2" (inst -1 "0" "t!1" ) (("2" (assert ) nil nil )) nil ))nil ))nil ))nil ))nil ))nil )nil closest_approach_3D nil )nil vectors_3D_def nil )nil reals nil )nil closest_approach_3D nil )nil closest_approach_3D nil )"(total_order?[real])" nil )nil closest_approach_3D nil )nil vectors_3D nil )nil vectors_3D nil )"[T, T -> boolean]" equalities nil )nil vectors_3D nil )nil booleans nil )"bool" reals nil )nil real_types nil )"nnreal" vectors_3D nil )"Vector" vectors_3D nil )"(total_order?[real])" nil )"(strict_total_order?[real])" real_props nil )"real" closest_approach_3D nil )"[number_field -> boolean]" reals nil )nil number_fields nil )"[number -> boolean]" number_fieldsnil )nil booleans nil )nil numbers nil )"bool" closest_approach_3D nil )nil real_types nil )"bool" reals nil )nil real_types nil )nil vectors_3D nil )nil vectors_3D nil ))nil ))nil 3421668843"" (skosimp*)"" (expand "dot_prop?" )"" (split +)"1" (flatten)"1" (lemma "dot_nneg_divergent" )"1" (inst?) (("1" (assert ) nil nil )) nil )) nil ))nil )"2" (flatten)"2" (lemma "divergent_dot_nneg" )"2" (inst?) (("2" (assert ) nil nil )) nil )) nil ))nil ))nil ))nil ))nil )"bool" closest_approach_3D nil )nil closest_approach_3D nil )nil reals nil )nil vectors_3D_def nil )"(total_order?[real])" nil )nil closest_approach_3D nil ))nil ))nil 3402919842"" (skeep)"" (expand "*" )"" (expand "+ " )"" (lemma "quad_min_eq_intv" )"" "sq(v`x) + sq(v`y) + sq(v`z)" "2*s`x*v`x + 2*s`y*v`y + 2*s`z*v`z" "D+ sq(s`x) + sq(s`y) + sq(s`z)" "t" "t1" "t2" )"1" (split -1)"1" (expand "quadratic" )"1" (expand "sq" ) (("1" (assert ) nil nil )) nil )) nil )"2" (hide 3)"2" (hide -)"2" (expand "sq" ) (("2" (assert ) nil nil )) nil ))nil ))nil )"3" (hide 3)"3" (replace -2 -3 rl)"3" (hide -2)"3" (expand "quadratic" )"3" (expand "sq" ) (("3" (assert ) nil nil ))nil ))nil ))nil ))nil ))nil )"4" (propax) nil nil ) ("5" (propax) nil nil ))nil )"2" (expand "sq" 1) (("2" (assert ) nil nil )) nil ))nil ))nil ))nil ))nil ))nil )"Vector" vectors_3D nil )"real" vectors_3D nil )nil quad_minmax "reals/" )"(strict_total_order?[real])" real_props nil )"real" quadratic "reals/" )"(strict_total_order?[real])" real_props nil )"[numfield, numfield -> numfield]" number_fields nil )nil reals nil )nil numbers nil )nil booleans nil )"boolean" notequal nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[numfield, numfield -> numfield]" number_fields nil )nil number_fields nil )"[number_field -> boolean]" reals nil )nil reals nil )nil booleans nil )"bool" reals nil )nil real_types nil )"nonneg_real" sq "reals/" )nil vectors_3D_def nil )"Vect3" closest_approach_3D nil )"nnreal" nil )"real" reals nil )"Vector" vectors_3D nil )"real" reals nil ))nil )nil 3402657613"" (skeep)"" (lemma "quad_min_eq_intv" )"" "sq(vx) + sq(vy)" "2*sx*vx + 2*sy*vy" "D+ sq(sx) + sq(sy)" "t" "t1" "t2" )"1" (split -1)"1" (expand "quadratic" )"1" (expand "sq" ) (("1" (assert ) nil nil )) nil )) nil )"2" (hide 3)"2" (hide -)"2" (expand "sq" ) (("2" (assert ) nil nil )) nil )) nil ))nil )"3" (hide 3)"3" (replace -2 -3 rl)"3" (hide -2)"3" (expand "quadratic" )"3" (expand "sq" ) (("3" (assert ) nil nil )) nil ))nil ))nil ))nil ))nil )"4" (propax) nil nil ) ("5" (propax) nil nil ))nil )"2" (expand "sq" 1) (("2" (assert ) nil nil )) nil ))nil ))nil ))nil )"nonneg_real" sq "reals/" )"real" quadratic "reals/" )nil quad_minmax "reals/" ))nil ))nil 3402919974"" (skeep)"" (expand "*" )"" (expand "+ " )"" (lemma "quad_min_eq_is_in" )"" "sq(v`x) + sq(v`y) + sq(v`z)" "2*s`x*v`x + 2*s`y*v`y + 2*s`z*v`z" "D+ sq(s`x) + sq(s`y) + sq(s`z)" "t" "t1" "t2" )"1" (split -1)"1" (propax) nil nil )"2" (hide -)"2" (expand "sq" ) (("2" (assert ) nil nil )) nil )) nil )"3" (expand "quadratic" )"3" (expand "sq" ) (("3" (assert ) nil nil )) nil )) nil )"4" (expand "quadratic" )"4" (expand "sq" ) (("4" (assert ) nil nil )) nil )) nil )"5" (propax) nil nil ))nil )"2" (expand "sq" 1) (("2" (assert ) nil nil )) nil ))nil ))nil ))nil ))nil ))nil )"Vector" vectors_3D nil )"real" vectors_3D nil )nil quad_minmax "reals/" )"(strict_total_order?[real])" real_props nil )"(strict_total_order?[real])" real_props nil )"real" quadratic "reals/" )"[numfield, numfield -> numfield]" number_fields nil )nil reals nil )nil numbers nil )nil booleans nil )"boolean" notequal nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[numfield, numfield -> numfield]" number_fields nil )nil number_fields nil )"[number_field -> boolean]" reals nil )nil reals nil )nil booleans nil )"bool" reals nil )nil real_types nil )"nonneg_real" sq "reals/" )nil vectors_3D_def nil )"Vect3" closest_approach_3D nil )"nnreal" nil )"real" reals nil )"Vector" vectors_3D nil )"real" reals nil ))nil )nil 3402657586"" (skeep)"" (lemma "quad_min_eq_is_in" )"" "sq(vx) + sq(vy)" "2*sx*vx + 2*sy*vy" "D+ sq(sx) + sq(sy)" "t" "t1" "t2" )"1" (split -1)"1" (propax) nil nil )"2" (hide -)"2" (expand "sq" ) (("2" (assert ) nil nil )) nil )) nil )"3" (expand "quadratic" )"3" (expand "sq" ) (("3" (assert ) nil nil )) nil )) nil )"4" (expand "quadratic" )"4" (expand "sq" ) (("4" (assert ) nil nil )) nil )) nil )"5" (propax) nil nil ))nil )"2" (expand "sq" 1) (("2" (assert ) nil nil )) nil ))nil ))nil ))nil )"nonneg_real" sq "reals/" )"real" quadratic "reals/" )nil quad_minmax "reals/" ))nil ))nil 3402929953"" (skeep)"" (lemma "a_gt_0_discr_gt_0" )"" (inst?)"" (inst - "t" )"" (assert ) (("" (hide -1) (("" (grind) nil nil )) nil ))nil ))nil ))nil ))nil ))nil )nil quadratic "reals/" )"Vector" vectors_3D nil )"Vector" vectors_3D nil )"nonneg_real" sq "reals/" )"(total_order?[real])" nil )"(total_order?[real])" nil )"(strict_total_order?[real])" real_props nil )"(strict_total_order?[real])" real_props nil )"nnreal" nil )"nnreal" nil )"[numfield, numfield -> numfield]" number_fields nil )"real" vectors_3D nil )"[numfield, numfield -> numfield]" number_fields nil )nil number_fields nil )nil vectors_3D_def nil )"nnreal" vectors_3D nil )nil real_types nil )"bool" reals nil )nil booleans nil )nil vectors_3D nil )nil reals nil )"boolean" notequal nil )nil reals nil )"[number_field -> boolean]" reals nil )nil number_fields nil )"[number -> boolean]" number_fieldsnil )nil booleans nil )nil numbers nil )"real" reals nil )"real" reals nil )"real" reals nil ))nil )))
Messung V0.5 in Prozent C=100 H=100 G=100
¤ Diese beiden folgenden Angebotsgruppen bietet das Unternehmen0.43Angebot
(Wie Sie bei der Firma Beratungs- und Dienstleistungen beauftragen können 2026-04-26)
¤ *Eine klare Vorstellung vom Zielzustand
2026-05-26
