| 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: riemann_scaf.pvs Sprache: LispOriginal von: PVS© |
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(losr_iterative
(incr_trk_vect_TCC1 0 (incr_trk_vect_TCC1-1 nil 3535802573 ("" (skeep) (("" (expand "trk_only?") (("" (lemma "norms_eq_sqv") (("" (inst?) (("" (assert) (("" (hide 2) (("" (rewrite "sqv_add") (("" (case-replace "nvo*perpR(nvo) = 0") (("1" (assert) (("1" (rewrite "sqv_scal") (("1" (rewrite "sqv_scal") (("1" (rewrite "sqv_perpR") (("1" (lemma "sin2_cos2") (("1" (inst - "dir*step") (("1" (mult-by -1 "sqv(nvo)") (("1" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide 2) (("2" (grind) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((trk_only? const-decl "bool" definitions nil) (nzreal_times_nzreal_is_nzreal application-judgement "nzreal" real_types nil) (real nonempty-type-from-decl nil reals nil) (Vector type-eq-decl nil vectors_2D "vectors/") (+ const-decl "Vector" vectors_2D "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) (* const-decl "Vector" vectors_2D "vectors/") (cos const-decl "real" trig_basic "trig/") (numfield nonempty-type-eq-decl nil number_fields nil) (* const-decl "[numfield, numfield -> numfield]" number_fields 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) (- const-decl "[numfield -> numfield]" number_fields nil) (Sign type-eq-decl nil sign "reals/") (>= const-decl "bool" reals 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) (Vect2 type-eq-decl nil vectors_2D_def "vectors/") (sin const-decl "real" trig_basic "trig/") (perpR const-decl "Vect2" perpendicular_2D "vectors/") (* const-decl "real" vectors_2D "vectors/") (sqv_scal formula-decl nil vectors_2D "vectors/") (nnreal_times_nnreal_is_nnreal application-judgement "nnreal" real_types nil) (sqv_perpR formula-decl nil perpendicular_2D "vectors/") (sq const-decl "nonneg_real" sq "reals/") (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (sqv const-decl "nnreal" vectors_2D "vectors/") (nnreal type-eq-decl nil real_types nil) (both_sides_times1_imp formula-decl nil extra_real_props nil) (sin2_cos2 formula-decl nil trig_basic "trig/") (minus_real_is_real application-judgement "real" reals nil) (dot_scal_canon formula-decl nil vectors_2D "vectors/") (scal_assoc formula-decl nil vectors_2D "vectors/") (real_plus_real_is_real application-judgement "real" reals nil) (nnreal_plus_nnreal_is_nnreal application-judgement "nnreal" real_types nil) (real_times_real_is_real application-judgement "real" reals nil) (sqv_add formula-decl nil vectors_2D "vectors/") (cos_range application-judgement "trig_range" trig_basic "trig/") (sin_range application-judgement "trig_range" trig_basic "trig/") (norms_eq_sqv formula-decl nil vectors_2D "vectors/")) nil)) (losr_trk_iter_i_TCC1 0 (losr_trk_iter_i_TCC1-1 nil 3535288278 ("" (skosimp*) (("" (assert) nil nil)) nil) ((posreal_div_posreal_is_posreal application-judgement "posreal" real_types nil) (int_minus_int_is_int application-judgement "int" integers nil) (int_plus_int_is_int application-judgement "int" integers nil) (rat_max application-judgement "{s: rat | s >= q AND s >= r}" real_defs nil) (int_max application-judgement "{k: int | i <= k AND j <= k}" real_defs nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (nonneg_floor_is_nat application-judgement "nat" floor_ceil nil)) nil)) (losr_trk_iter_i_TCC2 0 (losr_trk_iter_i_TCC2-1 nil 3535288278 ("" (skosimp*) (("" (assert) nil nil)) nil) ((posreal_times_posreal_is_posreal application-judgement "posreal" real_types nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil)) nil)) (losr_trk_iter_i_TCC3 0 (losr_trk_iter_i_TCC3-1 nil 3535288278 ("" (skosimp*) (("" (typepred "nvo!1") (("" (split +) (("1" (hide-all-but (-1 -6 1)) (("1" (typepred "incr_trk_vect(nvo!1, step!1, dir!1)") (("1" (replaces -3 :dir rl) (("1" (expand "trk_only?") (("1" (assert) nil nil)) nil)) nil)) nil)) nil) ("2" (lemma "repulsive_criteria_transitive") (("2" (inst - "eps!1" "nvo!1-vi!1" "nvop!1-vi!1" "s!1" "vo!1-vi!1") (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil) ((- const-decl "Vector" vectors_2D "vectors/") (repulsive_criteria const-decl "bool" repulsive nil) (Sign type-eq-decl nil sign "reals/") (- const-decl "[numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (= const-decl "[T, T -> boolean]" equalities 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) (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) (number nonempty-type-decl nil numbers nil) (AND const-decl "[bool, bool -> bool]" booleans nil) (Nz_vect2 type-eq-decl nil vectors_2D "vectors/") (zero const-decl "Vector" vectors_2D "vectors/") (/= const-decl "boolean" notequal nil) (Vector type-eq-decl nil vectors_2D "vectors/") (trk_only? const-decl "bool" definitions nil) (Vect2 type-eq-decl nil vectors_2D_def "vectors/") (real nonempty-type-from-decl nil reals nil) (NOT const-decl "[bool -> bool]" booleans nil) (bool nonempty-type-eq-decl nil booleans nil) (boolean nonempty-type-decl nil booleans nil) (repulsive_criteria_transitive formula-decl nil repulsive nil) (posreal_times_posreal_is_posreal application-judgement "posreal" real_types nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (nz_norm_gt_0 application-judgement "posreal" vectors_2D "vectors/") (>= const-decl "bool" reals 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) (incr_trk_vect const-decl "{nvo2: Vect2 | trk_only?(nvo)(nvo2)}" losr_iterative nil)) nil)) (losr_trk_iter_i_TCC4 0 (losr_trk_iter_i_TCC4-2 nil 3535884573 ("" (skosimp*) (("" (typepred "nvo!1") (("" (hide 1) (("" (split +) (("1" (hide-all-but (-1 -4 1)) (("1" (typepred "incr_trk_vect(nvo!1, step!1, dir!1)") (("1" (replaces -3 :dir rl) (("1" (expand "trk_only?") (("1" (assert) nil nil)) nil)) nil)) nil)) nil) ("2" (lemma "repulsive_criteria_transitive") (("2" (inst - "eps!1" "nvo!1-vi!1" "nvop!1-vi!1" "s!1" "vo!1-vi!1") (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil) ((- const-decl "Vector" vectors_2D "vectors/") (repulsive_criteria const-decl "bool" repulsive nil) (Sign type-eq-decl nil sign "reals/") (- const-decl "[numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (= const-decl "[T, T -> boolean]" equalities 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) (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) (number nonempty-type-decl nil numbers nil) (AND const-decl "[bool, bool -> bool]" booleans nil) (Nz_vect2 type-eq-decl nil vectors_2D "vectors/") (zero const-decl "Vector" vectors_2D "vectors/") (/= const-decl "boolean" notequal nil) (Vector type-eq-decl nil vectors_2D "vectors/") (trk_only? const-decl "bool" definitions nil) (Vect2 type-eq-decl nil vectors_2D_def "vectors/") (real nonempty-type-from-decl nil reals nil) (NOT const-decl "[bool -> bool]" booleans nil) (bool nonempty-type-eq-decl nil booleans nil) (boolean nonempty-type-decl nil booleans nil) (incr_trk_vect const-decl "{nvo2: Vect2 | trk_only?(nvo)(nvo2)}" losr_iterative 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) (nz_norm_gt_0 application-judgement "posreal" vectors_2D "vectors/") (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (posreal_times_posreal_is_posreal application-judgement "posreal" real_types nil) (repulsive_criteria_transitive formula-decl nil repulsive nil)) nil) (losr_trk_iter_i_TCC4-1 nil 3535288278 ("" (skosimp*) (("" (hide -) (("" (assert) (("" (case "floor(maxtrk!1 / step!1) - i!1 + 1 > 0") (("1" (grind) nil nil) ("2" (hide 3) (("2" (typepred "floor(maxtrk!1 / step!1)") (("2" (name-replace "FF" "floor(maxtrk!1 / step!1)") (("2" (case "i!1 < maxtrk!1/step!1") (("1" (assert) nil nil) ("2" (hide-all-but (1 3)) (("2" (grind-reals) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) nil nil)) (losr_trk_iter_i_TCC5 0 (losr_trk_iter_i_TCC5-2 nil 3535884446 ("" (skosimp*) (("" (hide -) (("" (hide 1) (("" (assert) (("" (case "floor(maxtrk!1 / step!1) - i!1 >= 0") (("1" (grind) nil nil) ("2" (hide 3) (("2" (typepred "floor(maxtrk!1 / step!1)") (("2" (name-replace "FF" "floor(maxtrk!1 / step!1)") (("2" (case "i!1 < maxtrk!1/step!1") (("1" (assert) nil nil) ("2" (hide-all-but (1 3)) (("2" (grind-reals) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((posreal_div_posreal_is_posreal application-judgement "posreal" real_types nil) (int_minus_int_is_int application-judgement "int" integers nil) (int_plus_int_is_int application-judgement "int" integers nil) (rat_max application-judgement "{s: rat | s >= q AND s >= r}" real_defs nil) (int_max application-judgement "{k: int | i <= k AND j <= k}" real_defs nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (posreal_times_posreal_is_posreal application-judgement "posreal" real_types nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (= const-decl "[T, T -> boolean]" equalities nil) (minus_odd_is_odd application-judgement "odd_int" integers nil) (div_mult_pos_lt2 formula-decl nil real_props nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (NOT const-decl "[bool -> bool]" booleans nil) (max const-decl "{p: real | p >= m AND p >= n}" real_defs 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) (numfield nonempty-type-eq-decl nil number_fields nil) (- const-decl "[numfield, numfield -> numfield]" number_fields 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) (integer nonempty-type-from-decl nil integers nil) (AND const-decl "[bool, bool -> bool]" booleans nil) (<= const-decl "bool" reals nil) (< const-decl "bool" reals nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (floor const-decl "{i | i <= x & x < i + 1}" floor_ceil nil) (/= const-decl "boolean" notequal nil) (nznum nonempty-type-eq-decl nil number_fields nil) (/ const-decl "[numfield, nznum -> numfield]" number_fields 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) (int nonempty-type-eq-decl nil integers nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (posnat nonempty-type-eq-decl nil integers nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (nonneg_floor_is_nat application-judgement "nat" floor_ceil nil)) nil) (losr_trk_iter_i_TCC5-1 nil 3535884239 ("" (termination-tcc) nil nil) nil nil)) (losr_trk_iter_TCC1 0 (losr_trk_iter_TCC1-1 nil 3535288278 ("" (skosimp*) nil nil) nil nil)) (losr_trk_iter_TCC2 0 (losr_trk_iter_TCC2-1 nil 3535288278 ("" (skosimp* :preds? t) (("" (assert) nil nil)) nil) ((sign_neg_clos application-judgement "Sign" sign "reals/") (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (Sign3 type-eq-decl nil sign3 "reals/") (boolean nonempty-type-decl nil booleans nil) (bool nonempty-type-eq-decl nil booleans nil) (NOT const-decl "[bool -> bool]" booleans nil) (real nonempty-type-from-decl nil reals nil) (Vector type-eq-decl nil vectors_2D "vectors/") (/= const-decl "boolean" notequal nil) (zero const-decl "Vector" vectors_2D "vectors/") (Nz_vect2 type-eq-decl nil vectors_2D "vectors/") (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) (>= const-decl "bool" reals 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) (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 "[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/")) nil)) (losr_trk_iter_TCC3 0 (losr_trk_iter_TCC3-1 nil 3535288278 ("" (skosimp*) (("" (assert) nil nil)) nil) ((real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (sign_neg_clos application-judgement "Sign" sign "reals/")) nil)) (losr_trk_iter_TCC4 0 (losr_trk_iter_TCC4-1 nil 3535473716 ("" (skosimp*) (("" (typepred "losr_trk_iter_i(s!1, vo!1, vi!1, minrelgs!1, maxtrk!1, step!1, 1, dir3!1, eps!1, nvo!1)") (("" (name-replace "vv" "losr_trk_iter_i(s!1, vo!1, vi!1, minrelgs!1, maxtrk!1, step!1, 1, dir3!1, eps!1, nvo!1)") (("" (assert) (("" (flatten) (("" (assert) nil nil)) nil)) nil)) nil)) nil)) nil) ((Sign3 type-eq-decl nil sign3 "reals/") (losr_trk_iter_i def-decl "{nvo2 | nvo2 /= zero => trk_only?(vo)(nvo2) AND repulsive_criteria(s, vo - vi, eps)(nvo2 - vi)}" losr_iterative nil) (- const-decl "Vector" vectors_2D "vectors/") (repulsive_criteria const-decl "bool" repulsive nil) (trk_only? const-decl "bool" definitions nil) (AND const-decl "[bool, bool -> bool]" booleans nil) (Vect2 type-eq-decl nil vectors_2D_def "vectors/") (Sign type-eq-decl nil sign "reals/") (- const-decl "[numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (= const-decl "[T, T -> boolean]" equalities nil) (OR const-decl "[bool, bool -> bool]" booleans nil) (nzint nonempty-type-eq-decl nil integers nil) (posnat nonempty-type-eq-decl nil integers nil) (nonneg_int 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) (posreal nonempty-type-eq-decl nil real_types nil) (> const-decl "bool" reals nil) (nonneg_real nonempty-type-eq-decl nil real_types nil) (nnreal type-eq-decl nil real_types nil) (>= const-decl "bool" 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) (number nonempty-type-decl nil numbers nil) (Nz_vect2 type-eq-decl nil vectors_2D "vectors/") (zero const-decl "Vector" vectors_2D "vectors/") (/= const-decl "boolean" notequal nil) (Vector type-eq-decl nil vectors_2D "vectors/") (real nonempty-type-from-decl nil reals nil) (IMPLIES const-decl "[bool, bool -> bool]" booleans nil) (NOT const-decl "[bool -> bool]" booleans nil) (bool nonempty-type-eq-decl nil booleans nil) (boolean nonempty-type-decl nil booleans nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (sign_neg_clos application-judgement "Sign" sign "reals/")) nil)) (losr_trk_iter_TCC5 0 (losr_trk_iter_TCC5-1 nil 3535802573 ("" (skosimp*) nil nil) nil nil)) (incr_gs_vect_TCC1 0 (incr_gs_vect_TCC1-1 nil 3560175723 ("" (skeep) (("" (lemma "gs_only_normalize") (("" (inst?) (("" (assert) (("" (inst? 1) nil nil)) nil)) nil)) nil)) nil) ((gs_only_normalize formula-decl nil definitions nil) (nzreal_times_nzreal_is_nzreal application-judgement "nzreal" real_types nil) (nz_norm_gt_0 application-judgement "posreal" vectors_2D "vectors/") (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (^ const-decl "Normalized" vectors_2D "vectors/") (Normalized type-eq-decl nil vectors_2D "vectors/") (Nz_vector type-eq-decl nil vectors_2D "vectors/") (posreal nonempty-type-eq-decl nil real_types nil) (> const-decl "bool" reals nil) (nonneg_real nonempty-type-eq-decl nil real_types nil) (Sign type-eq-decl nil sign "reals/") (- const-decl "[numfield -> numfield]" number_fields nil) (= const-decl "[T, T -> boolean]" equalities 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) (* const-decl "[numfield, numfield -> numfield]" number_fields nil) (norm const-decl "nnreal" vectors_2D "vectors/") (nnreal 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) (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) (number nonempty-type-decl nil numbers nil) (Vect2 type-eq-decl nil vectors_2D_def "vectors/") (Nz_vect2 type-eq-decl nil vectors_2D "vectors/") (zero const-decl "Vector" vectors_2D "vectors/") (/= const-decl "boolean" notequal nil) (boolean nonempty-type-decl nil booleans nil) (Vector type-eq-decl nil vectors_2D "vectors/") (real nonempty-type-from-decl nil reals nil) (real_plus_real_is_real application-judgement "real" reals nil)) nil)) (losr_gs_iter_i_TCC1 0 (losr_gs_iter_i_TCC1-1 nil 3560262748 ("" (skosimp*) (("" (rewrite "max_ge") nil 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_minus_real_is_real application-judgement "real" reals nil) (real_div_nzreal_is_real application-judgement "real" reals nil) (int_plus_int_is_int application-judgement "int" integers nil) (max_ge formula-decl nil real_defs 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) (numfield nonempty-type-eq-decl nil number_fields nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (- const-decl "[numfield, numfield -> numfield]" number_fields 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) (integer nonempty-type-from-decl nil integers nil) (bool nonempty-type-eq-decl nil booleans nil) (AND const-decl "[bool, bool -> bool]" booleans nil) (<= const-decl "bool" reals nil) (< const-decl "bool" reals nil) (floor const-decl "{i | i <= x & x < i + 1}" floor_ceil nil) (IF const-decl "[boolean, T, T -> T]" if_def nil) (>= const-decl "bool" reals nil) (int nonempty-type-eq-decl nil integers nil) (/= const-decl "boolean" notequal nil) (nzint nonempty-type-eq-decl nil integers nil) (OR const-decl "[bool, bool -> bool]" booleans nil) (= const-decl "[T, T -> boolean]" equalities nil) (- const-decl "[numfield -> numfield]" number_fields nil) (Sign type-eq-decl nil sign "reals/") (nznum nonempty-type-eq-decl nil number_fields nil) (/ const-decl "[numfield, nznum -> numfield]" number_fields 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) (Vector type-eq-decl nil vectors_2D "vectors/") (nnreal type-eq-decl nil real_types nil) (norm const-decl "nnreal" vectors_2D "vectors/") (zero const-decl "Vector" vectors_2D "vectors/") (Nz_vect2 type-eq-decl nil vectors_2D "vectors/") (nonneg_int nonempty-type-eq-decl nil integers nil) (posnat nonempty-type-eq-decl nil integers nil) (nzreal_times_nzreal_is_nzreal application-judgement "nzreal" real_types nil) (nz_norm_gt_0 application-judgement "posreal" vectors_2D "vectors/") (mult_divides2 application-judgement "(divides(m))" divides nil) (mult_divides1 application-judgement "(divides(n))" divides nil) (nzint_times_nzint_is_nzint application-judgement "nzint" integers nil)) nil)) (losr_gs_iter_i_TCC2 0 (losr_gs_iter_i_TCC2-1 nil 3560262748 ("" (skosimp*) (("" (assert) (("" (typepred "nvo!1") (("" (lemma "gs_only_normalize") (("" (inst? -) (("" (assert) (("" (inst? 1) nil nil)) nil)) nil)) nil)) nil)) nil)) nil) ((real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (real_plus_real_is_real application-judgement "real" reals nil) (gs_only_normalize formula-decl nil definitions nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (boolean nonempty-type-decl nil booleans nil) (bool nonempty-type-eq-decl nil booleans nil) (NOT const-decl "[bool -> bool]" booleans nil) (real nonempty-type-from-decl nil reals nil) (Vect2 type-eq-decl nil vectors_2D_def "vectors/") (= const-decl "[T, T -> boolean]" equalities nil) (AND const-decl "[bool, 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) (Vector type-eq-decl nil vectors_2D "vectors/") (* const-decl "Vector" vectors_2D "vectors/") (numfield nonempty-type-eq-decl nil number_fields nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (>= const-decl "bool" reals nil) (nnreal type-eq-decl nil real_types nil) (norm const-decl "nnreal" vectors_2D "vectors/") (/= const-decl "boolean" notequal nil) (zero const-decl "Vector" vectors_2D "vectors/") (Nz_vect2 type-eq-decl nil vectors_2D "vectors/") (* const-decl "[numfield, numfield -> numfield]" number_fields 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/") (nonneg_int nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (posnat nonempty-type-eq-decl nil integers nil) (nonneg_real nonempty-type-eq-decl nil real_types nil) (posreal nonempty-type-eq-decl nil real_types nil) (Nz_vector type-eq-decl nil vectors_2D "vectors/") (Normalized type-eq-decl nil vectors_2D "vectors/") (^ const-decl "Normalized" vectors_2D "vectors/") (repulsive_criteria const-decl "bool" repulsive nil) (- const-decl "Vector" vectors_2D "vectors/") (nzreal_times_nzreal_is_nzreal application-judgement "nzreal" real_types nil) (nz_norm_gt_0 application-judgement "posreal" vectors_2D "vectors/") (mult_divides2 application-judgement "(divides(m))" divides nil) (mult_divides1 application-judgement "(divides(n))" divides nil) (nzint_times_nzint_is_nzint application-judgement "nzint" integers nil)) nil)) (losr_gs_iter_i_TCC3 0 (losr_gs_iter_i_TCC3-2 nil 3560263323 ("" (skosimp*) (("" (lemma "repulsive_criteria_transitive") (("" (inst - "eps!1" "nvo!1-vi!1" "nvop!1-vi!1" "s!1" "vo!1-vi!1") (("" (assert) (("" (typepred "incr_gs_vect(nvo!1, step!1, dir!1)") (("" (assert) (("" (replaces -3 :dir rl) (("" (typepred "nvo!1") (("" (lemma "gs_only_normalize") (("" (inst -1 "vo!1" "nvo!1") (("" (flatten) (("" (hide -1) (("" (split -) (("1" (lemma "gs_only_trans") (("1" (inst -1 "vo!1" "nvo!1" "nvop!1") (("1" (assert) nil nil)) nil)) nil) ("2" (inst? 1) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((repulsive_criteria_transitive formula-decl nil repulsive nil) (real_plus_real_is_real application-judgement "real" reals nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (gs_only_trans formula-decl nil definitions nil) (gs_only_normalize formula-decl nil definitions nil) (incr_gs_vect const-decl "{nvo: Vect2 | norm(vo) + dir * step > 0 IMPLIES gs_only?(vo)(nvo)}" losr_iterative nil) (NOT const-decl "[bool -> bool]" booleans nil) (gs_only? const-decl "bool" definitions nil) (IMPLIES const-decl "[bool, bool -> bool]" booleans nil) (repulsive_criteria const-decl "bool" repulsive nil) (^ const-decl "Normalized" vectors_2D "vectors/") (Normalized type-eq-decl nil vectors_2D "vectors/") (Nz_vector type-eq-decl nil vectors_2D "vectors/") (posreal nonempty-type-eq-decl nil real_types nil) (nonneg_real nonempty-type-eq-decl nil real_types nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (* const-decl "[numfield, numfield -> numfield]" number_fields nil) (Nz_vect2 type-eq-decl nil vectors_2D "vectors/") (zero const-decl "Vector" vectors_2D "vectors/") (norm const-decl "nnreal" vectors_2D "vectors/") (nnreal type-eq-decl nil real_types nil) (>= const-decl "bool" reals nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (* const-decl "Vector" vectors_2D "vectors/") (AND const-decl "[bool, bool -> bool]" booleans nil) (- const-decl "Vector" vectors_2D "vectors/") (Vector type-eq-decl nil vectors_2D "vectors/") (Vect2 type-eq-decl nil vectors_2D_def "vectors/") (Sign type-eq-decl nil sign "reals/") (- const-decl "[numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (= const-decl "[T, T -> boolean]" equalities nil) (OR const-decl "[bool, bool -> bool]" booleans nil) (bool nonempty-type-eq-decl nil booleans nil) (nzint nonempty-type-eq-decl nil integers nil) (/= const-decl "boolean" notequal 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) (nzreal_times_nzreal_is_nzreal application-judgement "nzreal" real_types nil) (nz_norm_gt_0 application-judgement "posreal" vectors_2D "vectors/") (mult_divides2 application-judgement "(divides(m))" divides nil) (mult_divides1 application-judgement "(divides(n))" divides nil) (nzint_times_nzint_is_nzint application-judgement "nzint" integers nil)) nil) (losr_gs_iter_i_TCC3-1 nil 3560262748 ("" (subtype-tcc) nil nil) nil nil)) (losr_gs_iter_i_TCC4 0 (losr_gs_iter_i_TCC4-3 nil 3560267127 ("" (skosimp*) (("" (typepred "nvo!1") (("" (hide 1) (("" (lemma "repulsive_criteria_transitive") (("" (inst - "eps!1" "nvo!1-vi!1" "nvop!1-vi!1" "s!1" "vo!1-vi!1") (("" (assert) (("" (hide (-1 -4 -6)) (("" (expand "incr_gs_vect") (("" (case "norm(nvo!1) = norm((norm(vo!1) + dir!1 * i!1 * step!1) * ^(vo!1))") (("1" (rewrite "norm_scal") (("1" (replaces -1) (("1" (replaces -1) (("1" (rewrite "normalize_scal") (("1" (rewrite "normalize_normalize") (("1" (rewrite "scal_assoc") (("1" (rewrite "sign_times_abs") (("1" (expand "sign") (("1" (assert) (("1" (expand "abs") (("1" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((- const-decl "Vector" vectors_2D "vectors/") (repulsive_criteria const-decl "bool" repulsive nil) (^ const-decl "Normalized" vectors_2D "vectors/") (Normalized type-eq-decl nil vectors_2D "vectors/") (Nz_vector type-eq-decl nil vectors_2D "vectors/") (posreal nonempty-type-eq-decl nil real_types nil) (nonneg_real nonempty-type-eq-decl nil real_types nil) (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers 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) (* const-decl "[numfield, numfield -> numfield]" number_fields nil) (Nz_vect2 type-eq-decl nil vectors_2D "vectors/") (zero const-decl "Vector" vectors_2D "vectors/") (/= const-decl "boolean" notequal nil) (norm const-decl "nnreal" vectors_2D "vectors/") (nnreal type-eq-decl nil real_types nil) (>= const-decl "bool" reals nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (* const-decl "Vector" vectors_2D "vectors/") (Vector type-eq-decl nil 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) (number nonempty-type-decl nil numbers nil) (AND const-decl "[bool, bool -> bool]" booleans nil) (= const-decl "[T, T -> boolean]" equalities nil) (Vect2 type-eq-decl nil vectors_2D_def "vectors/") (real nonempty-type-from-decl nil reals nil) (NOT const-decl "[bool -> bool]" booleans nil) (bool nonempty-type-eq-decl nil booleans nil) (boolean nonempty-type-decl nil booleans nil) (repulsive_criteria_transitive formula-decl nil repulsive nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (real_plus_real_is_real application-judgement "real" reals nil) (incr_gs_vect const-decl "{nvo: Vect2 | norm(vo) + dir * step > 0 IMPLIES gs_only?(vo)(nvo)}" losr_iterative nil) (norm_scal formula-decl nil vectors_2D "vectors/") (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (nnreal_times_nnreal_is_nnreal application-judgement "nnreal" real_types nil) (norm_normalize formula-decl nil vectors_2D "vectors/") (normalize_normalize formula-decl nil vectors_2D "vectors/") (sign_times_abs formula-decl nil sign "reals/") (real_times_real_is_real application-judgement "real" reals nil) (sign_mult_clos application-judgement "Sign" sign "reals/") (scal_assoc formula-decl nil vectors_2D "vectors/") (abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs nil) (sign const-decl "Sign" sign "reals/") (nz_nzv application-judgement "Nz_vector" vectors_2D "vectors/") (normalize_scal formula-decl nil vectors_2D "vectors/") (nzreal nonempty-type-eq-decl nil reals nil) (IMPLIES const-decl "[bool, bool -> bool]" booleans nil) (gs_only? const-decl "bool" definitions nil) (nzreal_times_nzreal_is_nzreal application-judgement "nzreal" real_types nil) (nz_norm_gt_0 application-judgement "posreal" vectors_2D "vectors/") (mult_divides2 application-judgement "(divides(m))" divides nil) (mult_divides1 application-judgement "(divides(n))" divides nil) (nzint_times_nzint_is_nzint application-judgement "nzint" integers nil)) nil) (losr_gs_iter_i_TCC4-2 nil 3560264980 ("" (skosimp*) (("" (typepred "nvo!1") (("" (hide 1) (("" (split +) (("1" (typepred "incr_gs_vect(nvo!1, step!1, dir!1)") (("1" (assert) (("1" (replaces -4 :dir rl) (("1" (hide-all-but (-1 -2 1)) (("1" (expand "gs_only?" -) (("1" (skosimp*) (("1" (replaces -) (("1" (lemma "gs_only_scal") (("1" (inst -1 "vo!1" "l!1*l!2") (("1" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (lemma "repulsive_criteria_transitive") (("2" (inst - "eps!1" "nvo!1-vi!1" "nvop!1-vi!1" "s!1" "vo!1-vi!1") (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil) ((repulsive_criteria const-decl "bool" repulsive nil) (Sign type-eq-decl nil sign "reals/") (Nz_vect2 type-eq-decl nil vectors_2D "vectors/") (zero const-decl "Vector" vectors_2D "vectors/") (Vector type-eq-decl nil vectors_2D "vectors/") (gs_only? const-decl "bool" definitions nil) (Vect2 type-eq-decl nil vectors_2D_def "vectors/") (gs_only_scal formula-decl nil definitions nil) (scal_assoc formula-decl nil vectors_2D "vectors/") (nz_nzv application-judgement "Nz_vector" vectors_2D "vectors/") (norm const-decl "nnreal" vectors_2D "vectors/") (repulsive_criteria_transitive formula-decl nil repulsive nil)) nil) (losr_gs_iter_i_TCC4-1 nil 3560262748 ("" (subtype-tcc) nil nil) nil nil)) (losr_gs_iter_i_TCC5 0 (losr_gs_iter_i_TCC5-4 nil 3560267142 ("" (skosimp*) (("" (hide -1 -2 1) (("" (typepred "nvo!1") (("" (hide -3) (("" (case "norm(nvo!1) = norm((norm(vo!1) + dir!1 * i!1 * step!1) * ^(vo!1))") (("1" (hide -2) (("1" (rewrite "norm_scal") (("1" (expand "abs") (("1" (replaces -1) (("1" (assert) (("1" (typepred "dir!1") (("1" (hide -1) (("1" (split -) (("1" (replaces -1) (("1" (assert) (("1" (case "floor((maxgs!1 - norm(vo!1)) / step!1) - i!1 >= 0") (("1" (grind) nil nil) ("2" (hide 4) (("2" (typepred "floor((maxgs!1 - norm(vo!1)) / step!1)") (("2" (name-replace "FF" "floor((maxgs!1 - norm(vo!1)) / step!1)") (("2" (case "i!1 < (maxgs!1-norm(vo!1))/step!1") (("1" (assert) nil nil) ("2" (grind-reals) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (replaces -1) (("2" (assert) (("2" (case "floor((norm(vo!1) - mings!1) / step!1) - i!1 >= 0") (("1" (grind) nil nil) ("2" (hide 4) (("2" (typepred "floor((norm(vo!1)-mings!1) / step!1)") (("2" (case "i!1 < (norm(vo!1)-mings!1)/step!1") (("1" (assert) nil nil) ("2" (grind-reals) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil) ((abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (int_minus_int_is_int application-judgement "int" integers nil) (int_plus_int_is_int application-judgement "int" integers nil) (rat_max application-judgement "{s: rat | s >= q AND s >= r}" real_defs nil) (int_max application-judgement "{k: int | i <= k AND j <= k}" real_defs nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (- const-decl "[numfield, numfield -> numfield]" number_fields nil) (integer nonempty-type-from-decl nil integers nil) (<= const-decl "bool" reals nil) (< const-decl "bool" reals nil) (floor const-decl "{i | i <= x & x < i + 1}" floor_ceil nil) (nznum nonempty-type-eq-decl nil number_fields nil) (/ const-decl "[numfield, nznum -> numfield]" number_fields nil) (max const-decl "{p: real | p >= m AND p >= n}" real_defs nil) (sqv const-decl "nnreal" vectors_2D "vectors/") (* const-decl "real" vectors_2D "vectors/") (sqrt_pos application-judgement "posreal" sqrt "reals/") (nz_sqv_gt_0 application-judgement "posreal" vectors_2D "vectors/") (real_times_real_is_real application-judgement "real" reals nil) (nnreal_plus_posreal_is_posreal application-judgement "posreal" real_types nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (div_mult_pos_lt2 formula-decl nil real_props nil) (minus_odd_is_odd application-judgement "odd_int" integers nil) (posreal_plus_nnreal_is_posreal application-judgement "posreal" real_types nil) (posreal_times_posreal_is_posreal application-judgement "posreal" real_types nil) (posint_times_posint_is_posint application-judgement "posint" integers nil) (real_div_nzreal_is_real application-judgement "real" reals nil) (norm_normalize formula-decl nil vectors_2D "vectors/") (nnreal_times_nnreal_is_nnreal application-judgement "nnreal" real_types nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (real_minus_real_is_real application-judgement "real" reals nil) (norm_scal formula-decl nil vectors_2D "vectors/") (real_plus_real_is_real application-judgement "real" reals nil) (boolean nonempty-type-decl nil booleans nil) (bool nonempty-type-eq-decl nil booleans nil) (NOT const-decl "[bool -> bool]" booleans nil) (real nonempty-type-from-decl nil reals nil) (Vect2 type-eq-decl nil vectors_2D_def "vectors/") (= const-decl "[T, T -> boolean]" equalities nil) (AND const-decl "[bool, 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) (Vector type-eq-decl nil vectors_2D "vectors/") (* const-decl "Vector" vectors_2D "vectors/") (numfield nonempty-type-eq-decl nil number_fields nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (>= const-decl "bool" reals nil) (nnreal type-eq-decl nil real_types nil) (norm const-decl "nnreal" vectors_2D "vectors/") (/= const-decl "boolean" notequal nil) (zero const-decl "Vector" vectors_2D "vectors/") (Nz_vect2 type-eq-decl nil vectors_2D "vectors/") (* const-decl "[numfield, numfield -> numfield]" number_fields 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/") (nonneg_int nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (posnat nonempty-type-eq-decl nil integers nil) (nonneg_real nonempty-type-eq-decl nil real_types nil) (posreal nonempty-type-eq-decl nil real_types nil) (Nz_vector type-eq-decl nil vectors_2D "vectors/") (Normalized type-eq-decl nil vectors_2D "vectors/") (^ const-decl "Normalized" vectors_2D "vectors/") (repulsive_criteria const-decl "bool" repulsive nil) (- const-decl "Vector" vectors_2D "vectors/") (nzreal_times_nzreal_is_nzreal application-judgement "nzreal" real_types nil) (nz_norm_gt_0 application-judgement "posreal" vectors_2D "vectors/") (mult_divides2 application-judgement "(divides(m))" divides nil) (mult_divides1 application-judgement "(divides(n))" divides nil) (nzint_times_nzint_is_nzint application-judgement "nzint" integers nil)) nil) (losr_gs_iter_i_TCC5-3 nil 3560266338 ("" (skosimp*) (("" (typepred "nvo!1") (("" (hide 1) (("" (split +) (("1" (typepred "incr_gs_vect(nvo!1, step!1, dir!1)") (("1" (assert) (("1" (replaces -4 :dir rl) (("1" (hide-all-but (-1 -2 1)) (("1" (expand "gs_only?" -) (("1" (skosimp*) (("1" (replaces -) (("1" (lemma "gs_only_scal") (("1" (inst -1 "vo!1" "l!1*l!2") (("1" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (lemma "repulsive_criteria_transitive") (("2" (inst - "eps!1" "nvo!1-vi!1" "nvop!1-vi!1" "s!1" "vo!1-vi!1") (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil) ((repulsive_criteria_transitive formula-decl nil repulsive nil) (norm const-decl "nnreal" vectors_2D "vectors/") (nz_nzv application-judgement "Nz_vector" vectors_2D "vectors/") (scal_assoc formula-decl nil vectors_2D "vectors/") (gs_only_scal formula-decl nil definitions nil) (Vect2 type-eq-decl nil vectors_2D_def "vectors/") (gs_only? const-decl "bool" definitions nil) (Vector type-eq-decl nil vectors_2D "vectors/") (zero const-decl "Vector" vectors_2D "vectors/") (Nz_vect2 type-eq-decl nil vectors_2D "vectors/") (Sign type-eq-decl nil sign "reals/") (repulsive_criteria const-decl "bool" repulsive nil)) nil) (losr_gs_iter_i_TCC5-2 nil 3560265196 ("" (skosimp*) (("" (hide -) (("" (hide 1) (("" (case "floor((maxgs!1-mings!1) / step!1) - i!1 + 1 > 0") (("1" (grind) nil nil) ("2" (hide 4) (("2" (typepred "floor((maxgs!1 - mings!1) / step!1)") (("2" (name-replace "FF" "floor((maxgs!1 - mings!1) / step!1)") (("2" (case "i!1 < (maxgs!1 - mings!1) / step!1") (("1" (assert) nil nil) ("2" (typepred "maxgs!1") (("2" (typepred "mings!1") (("2" (grind-reals) (("2" (case "maxgs!1 > mings!1") (("1" (grind-reals) (("1" (postpone) nil nil)) nil) ("2" (postpone) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) nil nil) (losr_gs_iter_i_TCC5-1 nil 3560262748 ("" (termination-tcc) nil nil) nil nil)) (losr_gs_iter_i_TCC6 0 (losr_gs_iter_i_TCC6-3 nil 3560267166 ("" (skosimp* :preds? t) (("" (case "gs_only?(vo!1)(nvo!1)") (("1" (replaces -10) (("1" (rewrite "gs_only_zero_right") nil nil)) nil) ("2" (lemma "gs_only_normalize") (("2" (inst?) (("2" (assert) (("2" (inst?) nil nil)) nil)) nil)) nil)) nil)) nil) ((gs_only? const-decl "bool" definitions nil) (gs_only_zero_right formula-decl nil definitions nil) (real_ge_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) (real_plus_real_is_real application-judgement "real" reals nil) (gs_only_normalize formula-decl nil definitions nil) (nzreal_times_nzreal_is_nzreal application-judgement "nzreal" real_types nil) (nz_norm_gt_0 application-judgement "posreal" vectors_2D "vectors/") (mult_divides2 application-judgement "(divides(m))" divides nil) (mult_divides1 application-judgement "(divides(n))" divides nil) (nzint_times_nzint_is_nzint application-judgement "nzint" integers nil) (boolean nonempty-type-decl nil booleans nil) (bool nonempty-type-eq-decl nil booleans nil) (NOT const-decl "[bool -> bool]" booleans nil) (real nonempty-type-from-decl nil reals nil) (Vector type-eq-decl nil vectors_2D "vectors/") (/= const-decl "boolean" notequal nil) (zero const-decl "Vector" vectors_2D "vectors/") (Nz_vect2 type-eq-decl nil vectors_2D "vectors/") (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) (>= const-decl "bool" reals 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) (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) (nonneg_int nonempty-type-eq-decl nil integers nil) (posnat 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 "[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/") (Vect2 type-eq-decl nil vectors_2D_def "vectors/") (AND const-decl "[bool, bool -> bool]" booleans nil) (* const-decl "Vector" vectors_2D "vectors/") (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (nnreal type-eq-decl nil real_types nil) (norm const-decl "nnreal" vectors_2D "vectors/") (* const-decl "[numfield, numfield -> numfield]" number_fields nil) (Nz_vector type-eq-decl nil vectors_2D "vectors/") (Normalized type-eq-decl nil vectors_2D "vectors/") (^ const-decl "Normalized" vectors_2D "vectors/") (repulsive_criteria const-decl "bool" repulsive nil) (- const-decl "Vector" vectors_2D "vectors/")) nil) (losr_gs_iter_i_TCC6-2 nil 3560266318 ("" (skosimp*) (("" (hide -) (("" (hide 1) (("" (case "floor((maxgs!1-mings!1) / step!1) - i!1 + 1 > 0") (("1" (grind) nil) ("2" (hide 4) (("2" (typepred "floor((maxgs!1 - mings!1) / step!1)") (("2" (name-replace "FF" "floor((maxgs!1 - mings!1) / step!1)") (("2" (case "i!1 < (maxgs!1 - mings!1) / step!1") (("1" (assert) nil) ("2" (typepred "maxgs!1") (("2" (typepred "mings!1") (("2" (grind-reals) (("2" (case "maxgs!1 > mings!1") (("1" (grind-reals) (("1" (postpone) nil))) ("2" (postpone) nil)))))))))))))))))))))))) nil) nil nil) (losr_gs_iter_i_TCC6-1 nil 3560262748 ("" (skosimp* :preds? t) (("" (replaces -5) (("" (rewrite "gs_only_zero_right") nil nil)) nil)) nil) ((gs_only_zero_right formula-decl nil definitions nil) (Vector type-eq-decl nil vectors_2D "vectors/") (zero const-decl "Vector" vectors_2D "vectors/") (Nz_vect2 type-eq-decl nil vectors_2D "vectors/") (Sign type-eq-decl nil sign "reals/") (Vect2 type-eq-decl nil vectors_2D_def "vectors/") (gs_only? const-decl "bool" definitions nil) (repulsive_criteria const-decl "bool" repulsive nil)) nil)) (losr_gs_iter_TCC1 0 (losr_gs_iter_TCC1-1 nil 3560452362 ("" (skosimp*) nil nil) nil nil)) (losr_gs_iter_TCC2 0 (losr_gs_iter_TCC2-1 nil 3560452362 ("" (skosimp* :preds? t) (("" (assert) nil nil)) nil) ((sign_neg_clos application-judgement "Sign" sign "reals/") (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (Sign3 type-eq-decl nil sign3 "reals/") (boolean nonempty-type-decl nil booleans nil) (bool nonempty-type-eq-decl nil booleans nil) (NOT const-decl "[bool -> bool]" booleans nil) (real nonempty-type-from-decl nil reals nil) (Vector type-eq-decl nil vectors_2D "vectors/") (/= const-decl "boolean" notequal nil) (zero const-decl "Vector" vectors_2D "vectors/") (Nz_vect2 type-eq-decl nil vectors_2D "vectors/") (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) (>= const-decl "bool" reals 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) (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 "[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/")) nil)) (losr_gs_iter_TCC3 0 (losr_gs_iter_TCC3-1 nil 3560452362 ("" (skosimp*) (("" (assert) (("" (expand "incr_gs_vect") (("" (assert) (("" (expand "losr_gs_iter_dir") (("" (lift-if) (("" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil) ((real_plus_real_is_real application-judgement "real" reals nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (sign_neg_clos application-judgement "Sign" sign "reals/") (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) (posreal_plus_nnreal_is_posreal application-judgement "posreal" real_types nil) (losr_gs_iter_dir const-decl "Sign3" losr_iterative nil) (minus_odd_is_odd application-judgement "odd_int" integers nil) (posreal_times_posreal_is_posreal application-judgement "posreal" real_types nil) (incr_gs_vect const-decl "{nvo: Vect2 | norm(vo) + dir * step > 0 IMPLIES gs_only?(vo)(nvo)}" losr_iterative nil) (real_times_real_is_real application-judgement "real" reals nil) (nz_norm_gt_0 application-judgement "posreal" vectors_2D "vectors/")) nil)) (losr_gs_iter_TCC4 0 (losr_gs_iter_TCC4-1 nil 3560452362 ("" (skosimp*) (("" (typepred "losr_gs_iter_i(s!1, vo!1, vi!1, minrelgs!1, mings!1, maxgs!1, step!1, 1, dir3!1, eps!1, nvo!1)") (("" (name-replace "LGS" "losr_gs_iter_i(s!1, vo!1, vi!1, minrelgs!1, mings!1, maxgs!1, step!1, 1, dir3!1, eps!1, nvo!1)") (("" (assert) (("" (flatten) (("" (assert) nil nil)) nil)) nil)) nil)) nil)) nil) ((Sign3 type-eq-decl nil sign3 "reals/") (losr_gs_iter_i def-decl "{nvo2 | nvo2 /= zero => gs_only?(vo)(nvo2) AND repulsive_criteria(s, vo - vi, eps)(nvo2 - vi)}" losr_iterative nil) (gs_only? const-decl "bool" definitions nil) (- const-decl "Vector" vectors_2D "vectors/") (repulsive_criteria const-decl "bool" repulsive nil) (^ const-decl "Normalized" vectors_2D "vectors/") (Normalized type-eq-decl nil vectors_2D "vectors/") (Nz_vector type-eq-decl nil vectors_2D "vectors/") (* const-decl "[numfield, numfield -> numfield]" number_fields nil) (norm const-decl "nnreal" vectors_2D "vectors/") (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (* const-decl "Vector" vectors_2D "vectors/") (AND const-decl "[bool, bool -> bool]" booleans nil) (Vect2 type-eq-decl nil vectors_2D_def "vectors/") (Sign type-eq-decl nil sign "reals/") (- const-decl "[numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (= const-decl "[T, T -> boolean]" equalities nil) (OR const-decl "[bool, bool -> bool]" booleans nil) (nzint nonempty-type-eq-decl nil integers nil) (posnat nonempty-type-eq-decl nil integers nil) (nonneg_int 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) (posreal nonempty-type-eq-decl nil real_types nil) (> const-decl "bool" reals nil) (nonneg_real nonempty-type-eq-decl nil real_types nil) (nnreal type-eq-decl nil real_types nil) (>= const-decl "bool" 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) (number nonempty-type-decl nil numbers nil) (Nz_vect2 type-eq-decl nil vectors_2D "vectors/") (zero const-decl "Vector" vectors_2D "vectors/") (/= const-decl "boolean" notequal nil) (Vector type-eq-decl nil vectors_2D "vectors/") (real nonempty-type-from-decl nil reals nil) (IMPLIES const-decl "[bool, bool -> bool]" booleans nil) (NOT const-decl "[bool -> bool]" booleans nil) (bool nonempty-type-eq-decl nil booleans nil) (boolean nonempty-type-decl nil booleans nil) (nzreal_times_nzreal_is_nzreal application-judgement "nzreal" real_types nil) (mult_divides2 application-judgement "(divides(m))" divides nil) (mult_divides1 application-judgement "(divides(n))" divides nil) (nzint_times_nzint_is_nzint application-judgement "nzint" integers nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (sign_neg_clos application-judgement "Sign" sign "reals/") (real_times_real_is_real application-judgement "real" reals nil) (nz_norm_gt_0 application-judgement "posreal" vectors_2D "vectors/")) nil)) (losr_gs_iter_TCC5 0 (losr_gs_iter_TCC5-1 nil 3560452362 ("" (skosimp*) nil nil) ((nz_norm_gt_0 application-judgement "posreal" vectors_2D "vectors/") (real_times_real_is_real application-judgement "real" reals nil)) nil))) ¤ Dauer der Verarbeitung: 0.93 Sekunden (vorverarbeitet) ¤ |
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