| products/sources/formale sprachen/PVS/vect_analysis/ |
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Quellcode-Bibliothek© Kompilation durch diese Firma[Weder Korrektheit noch Funktionsfähigkeit der Software werden zugesichert.]Datei: csequence_flatten.prf Sprache: LispOriginal von: PVS© |
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(limit_vect2_vect2
(cv_unique 0 (cv_unique-3 nil 3445169897 ("" (grind :exclude ("abs" "norm" "-" "sigma") :if-match nil) (("" (case "norm(l1!1 - l2!1) = 0") (("1" (lemma "norm_eq_0") (("1" (inst?) (("1" (assert) (("1" (lemma "add_move_right") (("1" (inst?) (("1" (inst -1 "zero") (("1" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (name "eps" "norm(l1!1 - l2!1)") (("2" (replace -1) (("2" (inst -3 "eps/2") (("1" (inst -2 "eps/2") (("1" (skosimp*) (("1" (case " EXISTS (x: Vect2): norm(x - a!1) < delta!1 AND norm(x - a!1) < delta!2") (("1" (skosimp*) (("1" (inst?) (("1" (inst?) (("1" (lemma "norm_triangle") (("1" (inst - "l1!1" "f!1(x!1)" "l2!1") (("1" (case-replace "norm(l1!1 - l2!1) > 0") (("1" (assert) (("1" (lemma "norm_sym") (("1" (inst - "l1!1" "f!1(x!1)") (("1" (assert) nil nil)) nil)) nil)) nil) ("2" (lemma "norm_eq_0") (("2" (inst?) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (name "DEL" "min(delta!1,delta!2)") (("2" (inst + "a!1") (("2" (assert) nil nil)) nil)) nil)) nil)) nil) ("2" (assert) nil nil)) nil) ("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil) ((Vect2 type-eq-decl nil vectors_2D_def "vectors/") (- 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) (bool nonempty-type-eq-decl nil booleans 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) (Vector type-eq-decl nil vectors_2D "vectors/") (real nonempty-type-from-decl nil reals nil) (= const-decl "[T, T -> boolean]" equalities nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil) (add_move_right formula-decl nil vectors_2D "vectors/") (zero const-decl "Vector" vectors_2D "vectors/") (add_zero_left formula-decl nil vectors_2D "vectors/") (norm_eq_0 formula-decl nil vectors_2D "vectors/") (AND const-decl "[bool, bool -> bool]" booleans nil) (< const-decl "bool" reals nil) (norm_triangle formula-decl nil vectors_2D "vectors/") (norm_sym formula-decl nil vectors_2D "vectors/") (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (nnreal_plus_nnreal_is_nnreal application-judgement "nnreal" real_types nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (norm_zero formula-decl nil vectors_2D "vectors/") (sub_eq_args formula-decl nil vectors_2D "vectors/") (min const-decl "{p: real | p <= m AND p <= n}" real_defs nil) (<= const-decl "bool" reals nil) (posreal_min application-judgement "{z: posreal | z <= x AND z <= y}" real_defs nil) (nonneg_real nonempty-type-eq-decl nil real_types nil) (posreal nonempty-type-eq-decl nil real_types nil) (eps skolem-const-decl "nnreal" limit_vect2_vect2 nil) (/ const-decl "[numfield, nznum -> numfield]" number_fields nil) (nznum nonempty-type-eq-decl nil number_fields nil) (/= const-decl "boolean" notequal nil) (numfield nonempty-type-eq-decl nil number_fields nil) (> const-decl "bool" reals nil) (nnreal_div_posreal_is_nnreal application-judgement "nnreal" real_types nil) (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (convergence const-decl "bool" limit_vect2_vect2 nil)) nil) (cv_unique-2 nil 3445169733 ("" (grind :exclude ("abs" "norm" "-" "sigma") :if-match nil) (("" (case "norm(l1!1 - l2!1) = 0") (("1" (lemma "norm_eq_0") (("1" (inst?) 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(("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (name "DEL" "min(delta!1,delta!2)") (("2" (postpone) nil nil)) nil)) nil)) nil) ("2" (postpone) nil nil)) nil) ("2" (postpone) nil nil)) nil)) nil)) nil)) nil)) nil) nil nil) (cv_unique-1 nil 3299406886 ("" (grind :exclude ("abs" "norm" "-") :if-match nil) (("" (rewrite "abs_diff_0") (("" (name "eps" "abs(l1!1 - l2!1)") (("" (replace -1) (("" (inst -4 "eps/2") (("1" (inst -5 "eps/2") (("1" (assert) (("1" (skosimp*) (("1" (case " EXISTS (x: Vect2): a!1 /= x AND norm(x - a!1) < delta!1 AND norm(x - a!1) < delta!2") (("1" (skosimp*) (("1" (inst?) (("1" (inst?) (("1" (assert) (("1" (case "0 < norm(x!1 - a!1)") (("1" (assert) (("1" (lemma "triangle2") (("1" (inst - "eps/2" "eps/2" "l1!1" "f!1(x!1)" "l2!1") (("1" (assert) nil nil)) nil)) nil)) nil) ("2" (lemma "norm_eq_0") (("2" (inst?) (("2" (assert) (("2" (replace -1 * lr) (("2" (assert) (("2" (rewrite "sub_eq_zero") nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide -4 -5) (("2" (name "DEL" "min(delta!1,delta!2)") (("2" (inst + "(a!1`x + DEL/2, a!1`y)") (("2" (grind) nil nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (assert) nil nil)) nil) ("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil) ((abs_diff_0 formula-decl nil abs_lems "reals/") (* const-decl "real" vectors_2D "vectors/") (sqv const-decl "nnreal" vectors_2D "vectors/") (sqrt_square formula-decl nil sqrt "reals/") (triangle2 formula-decl nil abs_lems "reals/") (sub_eq_zero formula-decl nil vectors_2D "vectors/") (norm_zero formula-decl nil vectors_2D "vectors/") (norm_eq_0 formula-decl nil vectors_2D "vectors/") (norm const-decl "nnreal" vectors_2D "vectors/") (Vector type-eq-decl nil vectors_2D "vectors/") (Vect2 type-eq-decl nil vectors_2D_def "vectors/")) nil)) (cv_in_domain 0 (cv_in_domain-4 nil 3445170107 ("" (grind :exclude ("abs" "norm" "-") :if-match nil) (("" (case "norm(l!1 - f!1(x!1)) = 0") (("1" (lemma "norm_eq_0") (("1" (inst?) 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(("1" (assert) (("1" (rewrite "norm_sym") (("1" (assert) nil nil)) nil)) nil)) nil)) nil) ("2" (assert) nil nil)) nil)) nil)) nil) ((Vect2 type-eq-decl nil vectors_2D_def "vectors/") (- 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) (bool nonempty-type-eq-decl nil booleans 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) (Vector type-eq-decl nil vectors_2D "vectors/") (real nonempty-type-from-decl nil reals nil) (= const-decl "[T, T -> boolean]" equalities nil) (boolean nonempty-type-decl nil booleans nil) (number nonempty-type-decl nil numbers nil) (sub_eq_zero formula-decl nil vectors_2D "vectors/") (norm_eq_0 formula-decl nil vectors_2D "vectors/") (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (sub_eq_args formula-decl nil vectors_2D "vectors/") (norm_zero formula-decl nil vectors_2D "vectors/") (norm_sym formula-decl nil vectors_2D "vectors/") (posreal nonempty-type-eq-decl nil real_types nil) (nonneg_real nonempty-type-eq-decl nil real_types nil) (> const-decl "bool" reals nil) (l!1 skolem-const-decl "Vect2" limit_vect2_vect2 nil) (f!1 skolem-const-decl "[Vect2 -> Vect2]" limit_vect2_vect2 nil) (x!1 skolem-const-decl "Vect2" limit_vect2_vect2 nil) (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (convergence const-decl "bool" limit_vect2_vect2 nil)) nil) (cv_in_domain-3 nil 3445170048 (";;; Proof cv_sum-1 for formula limit_real_vect2.cv_sum" (skeep) ((";;; Proof cv_sum-1 for formula limit_real_vect2.cv_sum" (grind :exclude ("abs" "norm" "+" "-") :if-match nil) ((";;; Proof cv_sum-1 for formula limit_real_vect2.cv_sum" (inst - "epsilon!1/4") ((";;; Proof cv_sum-1 for formula limit_real_vect2.cv_sum" (inst - "epsilon!1/4") ((";;; Proof cv_sum-1 for formula limit_real_vect2.cv_sum" (skosimp*) ((";;; Proof cv_sum-1 for formula limit_real_vect2.cv_sum" (inst 1 "min(delta!1, delta!2)") ((";;; Proof cv_sum-1 for formula limit_real_vect2.cv_sum" (skosimp*) ((";;; Proof cv_sum-1 for formula limit_real_vect2.cv_sum" (inst?) ((";;; Proof cv_sum-1 for formula limit_real_vect2.cv_sum" (inst?) ((";;; Proof cv_sum-1 for formula limit_real_vect2.cv_sum" (assert) ((";;; Proof cv_sum-1 for formula limit_real_vect2.cv_sum" (lemma "norm_add_le") ((";;; Proof cv_sum-1 for formula limit_real_vect2.cv_sum" (inst - "f1(x!1) - l1" "f2(x!1)-l2") ((";;; Proof cv_sum-1 for formula limit_real_vect2.cv_sum" (case-replace "norm(f1(x!1) - l1 + (f2(x!1) - l2)) = norm((f1 + f2)(x!1) - (l1 + l2))") (("1" (assert) nil) ("2" (hide-all-but 1) (("2" (grind :exclude "norm") nil)))))))))))))))))))))))))))) ";;; developed with shostak decision procedures") nil nil) (cv_in_domain-2 nil 3445169975 ("" (grind :exclude ("abs" "norm" "-") :if-match nil) (("" (case "norm(l!1 - f!1(x!1)) = 0") (("1" (lemma "norm_eq_0") (("1" (inst?) (("1" (assert) (("1" (rewrite "sub_eq_zero") nil nil)) nil)) nil)) nil) ("2" (inst - "norm(l!1 - f!1(x!1))") (("1" (skosimp*) (("1" (inst?) (("1" (assert) (("1" (rewrite "norm_sym") (("1" (assert) nil nil)) nil)) nil)) nil)) nil) ("2" (assert) nil nil)) nil)) nil)) nil) ((norm_sym formula-decl nil vectors_2D "vectors/") (norm_zero formula-decl nil vectors_2D "vectors/") (sub_eq_args formula-decl nil vectors_2D "vectors/") (norm_eq_0 formula-decl nil vectors_2D "vectors/") (sub_eq_zero formula-decl nil vectors_2D "vectors/") (Vector type-eq-decl nil vectors_2D "vectors/") (norm const-decl "nnreal" vectors_2D "vectors/") (Vect2 type-eq-decl nil vectors_2D_def "vectors/")) nil) (cv_in_domain-1 nil 3299406886 ("" (grind :exclude ("abs" "norm" "-") :if-match nil) (("" (rewrite "abs_diff_0") (("" (inst - "abs(l!1 - f!1(x!1))") (("" (skosimp*) (("" (inst?) (("" (assert) (("" (rewrite "abs_diff_commute" -) (("" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((Vect2 type-eq-decl nil vectors_2D_def "vectors/") (abs_diff_0 formula-decl nil abs_lems "reals/") (sub_eq_args formula-decl nil vectors_2D "vectors/") (norm_zero formula-decl nil vectors_2D "vectors/") (abs_diff_commute formula-decl nil abs_lems "reals/")) nil)) (cv_sum 0 (cv_sum-2 nil 3445170168 ("" (skeep) (("" (grind :exclude ("abs" "norm" "+" "-") :if-match nil) (("" (inst - "epsilon!1/4") (("" (inst - "epsilon!1/4") (("" (skosimp*) (("" (inst 1 "min(delta!1, delta!2)") (("" (skosimp*) (("" (inst?) (("" (inst?) (("" (assert) (("" (lemma "norm_add_le") (("" (inst - "f1(x!1) - l1" "f2(x!1)-l2") (("" (case-replace "norm(f1(x!1) - l1 + (f2(x!1) - l2)) = norm((f1 + f2)(x!1) - (l1 + l2))") (("1" (assert) nil nil) ("2" (hide-all-but 1) (("2" (grind :exclude "norm") nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((convergence const-decl "bool" limit_vect2_vect2 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) (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) (number nonempty-type-decl nil numbers 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) (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (posreal_min application-judgement "{z: posreal | z <= x AND z <= y}" real_defs nil) (min const-decl "{p: real | p <= m AND p <= n}" real_defs nil) (<= const-decl "bool" reals nil) (AND const-decl "[bool, bool -> bool]" booleans nil) (Vect2 type-eq-decl nil vectors_2D_def "vectors/") (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (- const-decl "Vector" vectors_2D "vectors/") (Vector type-eq-decl nil vectors_2D "vectors/") (real_plus_real_is_real application-judgement "real" reals nil) (real_minus_real_is_real application-judgement "real" reals nil) (nnreal_plus_nnreal_is_nnreal application-judgement "nnreal" real_types nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (= const-decl "[T, T -> boolean]" equalities nil) (nnreal type-eq-decl nil real_types nil) (norm const-decl "nnreal" vectors_2D "vectors/") (+ const-decl "Vector" vectors_2D "vectors/") (+ const-decl "[Vect2 -> Vect2]" limit_vect2_vect2 nil) (norm_add_le formula-decl nil vectors_2D "vectors/") (numfield nonempty-type-eq-decl nil number_fields nil) (/= const-decl "boolean" notequal nil) (nznum nonempty-type-eq-decl nil number_fields nil) (/ const-decl "[numfield, nznum -> numfield]" number_fields nil) (posreal_div_posreal_is_posreal application-judgement "posreal" real_types nil)) nil) (cv_sum-1 nil 3299406886 ("" (grind :exclude ("abs" "norm" "-") :if-match nil) (("" (inst - "epsilon!1/2") (("" (inst - "epsilon!1/2") (("" (skosimp*) (("" (inst 1 "min(delta!1, delta!2)") (("" (skosimp*) (("" (inst?) (("" (inst?) (("" (assert) (("" (lemma "triangle" ("x" "f1!1(x!1) - l1!1" "y" "f2!1(x!1) - l2!1")) (("" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((Vect2 type-eq-decl nil vectors_2D_def "vectors/") (+ const-decl "[Vect2 -> real]" vect2_fun_ops "vectors/")) nil)) (cv_neg 0 (cv_neg-2 nil 3445170197 ("" (skeep) (("" (grind :exclude ("abs" "norm" "-") :if-match nil) (("" (inst - "epsilon!1") (("" (skolem!) (("" (inst + "delta!1") (("" (skosimp) (("" (inst?) (("" (assert) (("" (case-replace "norm((-f)(x!1) - -l) = norm(f(x!1) -l)") (("" (assert) (("" (hide-all-but 1) (("" (lemma "norm_neg") (("" (inst - "f(x!1) - l") (("" (grind :exclude "norm") nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((convergence const-decl "bool" limit_vect2_vect2 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) (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) (number nonempty-type-decl nil numbers 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) (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (norm_neg formula-decl nil vectors_2D "vectors/") (real_minus_real_is_real application-judgement "real" reals nil) (minus_real_is_real application-judgement "real" reals nil) (= const-decl "[T, T -> boolean]" equalities nil) (Vector type-eq-decl nil vectors_2D "vectors/") (nnreal type-eq-decl nil real_types nil) (norm const-decl "nnreal" vectors_2D "vectors/") (- const-decl "Vector" vectors_2D "vectors/") (- const-decl "[Vect2 -> Vect2]" limit_vect2_vect2 nil) (- const-decl "Vector" vectors_2D "vectors/") (Vect2 type-eq-decl nil vectors_2D_def "vectors/")) nil) (cv_neg-1 nil 3299406886 ("" (grind :exclude ("abs" "norm" "-") :if-match nil) (("" (inst - "epsilon!1") (("" (skolem!) (("" (inst + "delta!1") (("" (skosimp) (("" (inst?) (("" (assert) (("" (expand "-") (("" (lemma "abs_neg") (("" (inst - "f!1(x!1) - l!1") (("" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((Vect2 type-eq-decl nil vectors_2D_def "vectors/") (abs_neg formula-decl nil abs_lems "reals/")) nil)) (cv_diff 0 (cv_diff-2 nil 3445170225 ("" (skosimp*) (("" (case-replace "f1!1 - f2!1 = f1!1 + (-f2!1)") (("1" (lemma "cv_sum") (("1" (inst?) (("1" (inst - "(-f2!1)" "-l2!1") (("1" (assert) (("1" (hide 2) (("1" (lemma "cv_neg") (("1" (inst?) (("1" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide-all-but 1) (("2" (grind) (("2" (apply-extensionality 1 :hide? t) nil nil)) nil)) nil)) nil)) nil) ((real nonempty-type-from-decl nil reals nil) (Vect2 type-eq-decl nil vectors_2D_def "vectors/") (boolean nonempty-type-decl nil booleans nil) (= const-decl "[T, T -> boolean]" equalities nil) (- const-decl "[Vect2 -> Vect2]" limit_vect2_vect2 nil) (+ const-decl "[Vect2 -> Vect2]" limit_vect2_vect2 nil) (- const-decl "[Vect2 -> Vect2]" limit_vect2_vect2 nil) (add_neg_sub formula-decl nil vectors_2D "vectors/") (cv_neg formula-decl nil limit_vect2_vect2 nil) (Vector type-eq-decl nil vectors_2D "vectors/") (- const-decl "Vector" vectors_2D "vectors/") (cv_sum formula-decl nil limit_vect2_vect2 nil) (- const-decl "Vector" vectors_2D "vectors/") (+ const-decl "Vector" vectors_2D "vectors/") (real_plus_real_is_real application-judgement "real" reals nil) (minus_real_is_real application-judgement "real" reals nil) (real_minus_real_is_real application-judgement "real" reals nil)) nil) (cv_diff-1 nil 3299406886 ("" (skosimp*) (("" (rewrite "diff_function") (("" (lemma "cv_sum") (("" (inst?) (("" (inst - "(-f2!1)" "-l2!1") (("" (assert) (("" (hide 2) (("" (lemma "cv_neg") (("" (inst?) (("" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((diff_function formula-decl nil vect2_fun_ops "vectors/") (Vect2 type-eq-decl nil vectors_2D_def "vectors/")) nil)) (cv_const 0 (cv_const-1 nil 3299406886 ("" (expand "convergence") (("" (skosimp*) (("" (expand "const_fun") (("" (assert) nil nil)) nil)) nil)) nil) ((norm_zero formula-decl nil vectors_2D "vectors/") (sub_eq_args formula-decl nil vectors_2D "vectors/") (const_fun const-decl "[Vect2 -> Vect2]" limit_vect2_vect2 nil) (convergence const-decl "bool" limit_vect2_vect2 nil)) nil)) (lim_TCC1 0 (lim_TCC1-1 nil 3445162370 ("" (skeep) (("" (typepred "x0") (("" (expand "nonempty?") (("" (expand "empty?") (("" (expand "convergent?") (("" (skosimp*) (("" (expand "member") (("" (inst?) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((convergent? const-decl "bool" limit_vect2_vect2 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) (empty? const-decl "bool" sets nil) (member const-decl "bool" sets nil) (nonempty? const-decl "bool" sets nil)) nil)) (lim_fun_lemma 0 (lim_fun_lemma-1 nil 3299406886 ("" (skolem!) (("" (name-replace "ll" "lim(f!1, x0!1)" :hide? nil) (("" (expand "lim" -) (("" (typepred "x0!1") (("" (expand "convergent?") 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(("" (use "lim_fun_lemma") (("" (ground) (("" (use "cv_unique" ("l2" "lim(f!1, x0!1)")) (("" (assert) nil nil)) nil)) nil)) nil)) nil) ((lim_fun_lemma formula-decl nil limit_vect2_vect2 nil) (convergent? const-decl "bool" limit_vect2_vect2 nil) (bool nonempty-type-eq-decl nil booleans nil) (boolean nonempty-type-decl nil booleans nil) (Vect2 type-eq-decl nil vectors_2D_def "vectors/") (real nonempty-type-from-decl nil reals nil) (cv_unique formula-decl nil limit_vect2_vect2 nil) (lim const-decl "Vect2" limit_vect2_vect2 nil)) nil)) (convergence_equiv 0 (convergence_equiv-1 nil 3299406886 ("" (skolem!) (("" (prop) (("1" (expand "convergent?") (("1" (inst?) nil nil)) nil) ("2" (rewrite "lim_fun_def") (("2" (expand "convergent?") (("2" (inst?) nil nil)) nil)) nil) ("3" (rewrite "lim_fun_def") nil nil)) nil)) nil) ((Vect2 type-eq-decl nil vectors_2D_def "vectors/") (real nonempty-type-from-decl nil reals nil) (convergent? const-decl "bool" limit_vect2_vect2 nil) (bool nonempty-type-eq-decl nil booleans nil) (boolean nonempty-type-decl nil booleans nil) (lim_fun_def formula-decl nil limit_vect2_vect2 nil)) nil)) (convergent_in_domain 0 (convergent_in_domain-1 nil 3299406886 ("" (grind :exclude "convergence") (("" (forward-chain "cv_in_domain") (("" (assert) nil nil)) nil)) nil) ((cv_in_domain formula-decl nil limit_vect2_vect2 nil) (Vect2 type-eq-decl nil vectors_2D_def "vectors/") (real nonempty-type-from-decl nil reals nil) (convergent? const-decl "bool" limit_vect2_vect2 nil)) nil)) (lim_in_domain 0 (lim_in_domain-1 nil 3299406886 ("" (skosimp) (("" (rewrite "lim_fun_def") (("" (rewrite "convergent_in_domain") nil nil)) nil)) nil) ((lim_fun_def formula-decl nil limit_vect2_vect2 nil) (real nonempty-type-from-decl nil reals nil) (Vect2 type-eq-decl nil vectors_2D_def "vectors/") (boolean nonempty-type-decl nil booleans nil) (bool nonempty-type-eq-decl nil booleans nil) (convergent? const-decl "bool" limit_vect2_vect2 nil) (convergent_in_domain formula-decl nil limit_vect2_vect2 nil)) nil)) (sum_fun_convergent 0 (sum_fun_convergent-1 nil 3299406886 ("" (expand "convergent?") (("" (skosimp*) (("" (inst 1 "l!1 + l!2") (("" (rewrite "cv_sum") nil nil)) nil)) nil)) nil) ((cv_sum formula-decl nil limit_vect2_vect2 nil) (+ const-decl "Vector" vectors_2D "vectors/") (Vector type-eq-decl nil vectors_2D "vectors/") (Vect2 type-eq-decl nil vectors_2D_def "vectors/") (real nonempty-type-from-decl nil reals nil) (convergent? const-decl "bool" limit_vect2_vect2 nil)) nil)) (neg_fun_convergent 0 (neg_fun_convergent-1 nil 3299406886 ("" (expand "convergent?") (("" (skosimp*) (("" (forward-chain "cv_neg") (("" (inst?) nil nil)) nil)) nil)) nil) ((- const-decl "Vector" vectors_2D "vectors/") (Vector type-eq-decl nil vectors_2D "vectors/") (Vect2 type-eq-decl nil vectors_2D_def "vectors/") (real nonempty-type-from-decl nil reals nil) (cv_neg formula-decl nil limit_vect2_vect2 nil) (convergent? const-decl "bool" limit_vect2_vect2 nil)) nil)) (diff_fun_convergent 0 (diff_fun_convergent-1 nil 3299406886 ("" (expand "convergent?") (("" (skosimp*) (("" (inst 1 "l!1 - l!2") (("" (rewrite "cv_diff") nil nil)) nil)) nil)) nil) ((cv_diff formula-decl nil limit_vect2_vect2 nil) (- const-decl "Vector" vectors_2D "vectors/") (Vector type-eq-decl nil vectors_2D "vectors/") (Vect2 type-eq-decl nil vectors_2D_def "vectors/") (real nonempty-type-from-decl nil reals nil) (convergent? const-decl "bool" limit_vect2_vect2 nil)) nil)) (const_fun_convergent 0 (const_fun_convergent-1 nil 3299406886 ("" (expand "convergent?") (("" (skolem!) (("" (inst?) (("" (rewrite "cv_const") nil nil)) nil)) nil)) nil) ((cv_const formula-decl nil limit_vect2_vect2 nil) (Vect2 type-eq-decl nil vectors_2D_def "vectors/") (real nonempty-type-from-decl nil reals nil) (convergent? const-decl "bool" limit_vect2_vect2 nil)) nil)) (lim_sum_fun_TCC1 0 (lim_sum_fun_TCC1-1 nil 3299406886 ("" (skosimp) (("" (rewrite "sum_fun_convergent") nil nil)) nil) ((sum_fun_convergent formula-decl nil limit_vect2_vect2 nil) (real nonempty-type-from-decl nil reals nil) (Vect2 type-eq-decl nil vectors_2D_def "vectors/")) nil)) (lim_sum_fun 0 (lim_sum_fun-1 nil 3299406886 ("" (auto-rewrite "lim_fun_lemma" "lim_fun_def" "sum_fun_convergent" ("cv_sum")) (("" (skosimp) (("" (assert) nil nil)) nil)) nil) ((lim_fun_lemma formula-decl nil limit_vect2_vect2 nil) (cv_sum formula-decl nil limit_vect2_vect2 nil) (lim_fun_def formula-decl nil limit_vect2_vect2 nil)) nil)) (lim_neg_fun_TCC1 0 (lim_neg_fun_TCC1-1 nil 3299406886 ("" (lemma "neg_fun_convergent") (("" (propax) nil nil)) nil) ((neg_fun_convergent formula-decl nil limit_vect2_vect2 nil)) nil)) (lim_neg_fun 0 (lim_neg_fun-1 nil 3299406886 ("" (auto-rewrite "lim_fun_lemma" "lim_fun_def" "neg_fun_convergent" ("cv_neg")) (("" (skosimp) (("" (assert) nil nil)) nil)) nil) ((lim_fun_lemma formula-decl nil limit_vect2_vect2 nil) (cv_neg formula-decl nil limit_vect2_vect2 nil) (lim_fun_def formula-decl nil limit_vect2_vect2 nil)) nil)) (lim_diff_fun_TCC1 0 (lim_diff_fun_TCC1-1 nil 3299406886 ("" (skosimp) (("" (rewrite "diff_fun_convergent") nil nil)) nil) ((diff_fun_convergent formula-decl nil limit_vect2_vect2 nil) (real nonempty-type-from-decl nil reals nil) (Vect2 type-eq-decl nil vectors_2D_def "vectors/")) nil)) (lim_diff_fun 0 (lim_diff_fun-1 nil 3299406886 ("" (auto-rewrite "lim_fun_lemma" "lim_fun_def" "diff_fun_convergent" ("cv_diff")) (("" (skosimp) (("" (assert) nil nil)) nil)) nil) ((lim_fun_lemma formula-decl nil limit_vect2_vect2 nil) (cv_diff formula-decl nil limit_vect2_vect2 nil) (lim_fun_def formula-decl nil limit_vect2_vect2 nil)) nil)) (lim_const_fun_TCC1 0 (lim_const_fun_TCC1-1 nil 3299406886 ("" (lemma "const_fun_convergent") (("" (propax) nil nil)) nil) ((const_fun_convergent formula-decl nil limit_vect2_vect2 nil)) nil)) (lim_const_fun 0 (lim_const_fun-1 nil 3299406886 ("" (auto-rewrite "lim_fun_lemma" "lim_fun_def" "const_fun_convergent" ("cv_const")) (("" (skosimp) (("" (assert) nil nil)) nil)) nil) ((cv_const formula-decl nil limit_vect2_vect2 nil) (lim_fun_def formula-decl nil limit_vect2_vect2 nil)) nil))) ¤ Dauer der Verarbeitung: 0.54 Sekunden (vorverarbeitet) ¤ |
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