| products/sources/formale sprachen/PVS/exact_real_arith/ |
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Quellcode-Bibliothek© Kompilation durch diese Firma[Weder Korrektheit noch Funktionsfähigkeit der Software werden zugesichert.]Datei: powerseries.prf Sprache: LispOriginal von: PVS© |
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(prelude_aux
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(("2" (expand "total_order?") (("2" (expand "strict_order?") (("2" (expand "partial_order?") (("2" (expand "preorder?") (("2" (expand "transitive?") 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const-decl "bool" orders nil) (partial_order? const-decl "bool" orders nil) (transitive? const-decl "bool" relations nil) (x!1 skolem-const-decl "real" prelude_aux nil) (z!1 skolem-const-decl "real" prelude_aux nil) (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (nnint_times_nnint_is_nnint application-judgement "nonneg_int" integers nil) (even_times_int_is_even application-judgement "even_int" integers nil) (mult_divides1 application-judgement "(divides(n))" divides nil) (negreal_times_negreal_is_posreal judgement-tcc nil real_types nil) (dichotomous? const-decl "bool" orders nil) (antisymmetric? const-decl "bool" relations nil) (reflexive? const-decl "bool" relations nil) (trichotomous? const-decl "bool" orders nil) (irreflexive? const-decl "bool" relations nil) (AND const-decl "[bool, bool -> bool]" booleans nil) (both_sides_times_neg_lt1 formula-decl nil real_props nil) (preorder? const-decl "bool" orders nil) (strict_order? const-decl "bool" orders nil) (strict_total_order? const-decl "bool" orders nil) (total_le formula-decl nil real_props nil)) nil)) (both_sides_times_nonneg_le1 0 (both_sides_times_nonneg_le1-1 nil 3250061827 ("" (skosimp*) (("" (case "0 < nnz!1") (("1" (lemma "both_sides_times_pos_le1" ("x" "x!1" "y" "y!1" "pz" "nnz!1")) (("1" (bash) nil nil) ("2" (assert) nil nil)) nil) ("2" (case "nnz!1=0") (("1" (replace -1) (("1" (assert) nil nil)) nil) ("2" (assert) nil nil)) nil)) nil)) nil) ((nnreal type-eq-decl nil real_types nil) (>= const-decl "bool" reals nil) (< const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans 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) (real_lt_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) (real_times_real_is_real application-judgement "real" reals nil) (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (both_sides_times_pos_le1 formula-decl nil real_props 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) (= const-decl "[T, T -> boolean]" equalities nil)) nil)) (both_sides_times_nonpos_le1 0 (both_sides_times_nonpos_le1-1 nil 3250061827 ("" (skosimp*) (("" (case "0 > npz!1") (("1" (lemma "both_sides_times_neg_le1" ("y" "y!1" "x" "x!1" "nz" "npz!1")) (("1" (bash) nil nil) ("2" (assert) nil nil)) nil) ("2" (case "npz!1=0") (("1" (replace -1) (("1" (assert) nil nil)) nil) ("2" (assert) nil nil)) nil)) nil)) nil) ((npreal type-eq-decl nil real_types nil) (<= const-decl "bool" reals nil) (> const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans 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) (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) (real_times_real_is_real application-judgement "real" reals nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (both_sides_times_neg_le1 formula-decl nil real_props nil) (nonpos_real nonempty-type-eq-decl nil real_types nil) (< const-decl "bool" reals nil) (negreal nonempty-type-eq-decl nil real_types nil) (= const-decl "[T, T -> boolean]" equalities nil)) nil)) (abs_nonneg 0 (abs_nonneg-1 nil 3250061827 ("" (grind) nil nil) ((abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs nil)) nil)) (abs_nonpos 0 (abs_nonpos-1 nil 3250061827 ("" (grind) nil nil) ((boolean nonempty-type-decl nil booleans nil) (bool nonempty-type-eq-decl nil booleans nil) (NOT const-decl "[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) (real nonempty-type-from-decl nil reals nil) (<= const-decl "bool" reals nil) (npreal type-eq-decl nil real_types nil) (real_lt_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) (abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs nil)) nil)) (odd_even 0 (odd_even-1 nil 3250061827 ("" (skolem!) 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(("" (rewrite "odd_even") (("" (bash) nil nil)) nil)) nil) ((odd_even formula-decl nil prelude_aux 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) (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)) nil)) (expt_product_aux_TCC1 0 (expt_product_aux_TCC1-1 nil 3250061827 ("" (subtype-tcc) nil nil) nil nil)) (expt_product_aux_TCC2 0 (expt_product_aux_TCC2-1 nil 3250061827 ("" (subtype-tcc) nil nil) nil nil)) (expt_product_aux 0 (expt_product_aux-1 nil 3250061827 ("" (induct "n") (("1" (grind) nil nil) ("2" (skosimp*) (("2" (inst - "n0x!1" "n0y!1") (("2" (lemma "expt_plus" ("i" "j!1" "j" "1")) (("2" (inst-cp - "n0x!1") (("2" (inst-cp - "n0y!1") (("2" (inst - "n0x!1 *n0y!1") (("2" (grind) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((expt_plus formula-decl nil exponentiation nil) (int_minus_int_is_int application-judgement "int" integers nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (nzreal_div_nzreal_is_nzreal application-judgement "nzreal" real_types nil) (nzreal_expt application-judgement "nzreal" exponentiation nil) (nnint_plus_posint_is_posint application-judgement "posint" integers nil) (nzreal_exp application-judgement "nzreal" exponentiation nil) (expt def-decl "real" exponentiation nil) (nat_induction formula-decl nil naturalnumbers nil) (* const-decl "[numfield, numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (^ const-decl "real" exponentiation nil) (OR const-decl "[bool, bool -> bool]" booleans nil) (= const-decl "[T, T -> boolean]" equalities nil) (nzreal nonempty-type-eq-decl nil reals nil) (/= const-decl "boolean" notequal nil) (pred type-eq-decl nil defined_types nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans 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)) nil)) 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(expt_division_aux_TCC1 0 (expt_division_aux_TCC1-1 nil 3251301322 ("" (grind) nil nil) nil shostak)) (expt_division_aux 0 (expt_division_aux-1 nil 3251299141 ("" (skosimp) (("" (rewrite "div_expt") nil nil)) nil) ((div_expt formula-decl nil exponentiation 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) (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) (bool nonempty-type-eq-decl nil booleans nil) (>= const-decl "bool" reals nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (/= const-decl "boolean" notequal nil) (nzreal 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(("1" (flatten) (("1" (skolem!) (("1" (lemma "expt_plus" ("n0x" "-1" "i" "j!1" "j" "j!1")) (("1" (lemma "expt_product" ("n0x" "-1" "n0y" "-1" "i" "j!1")) (("1" (lemma "expt_1i" ("i" "j!1")) (("1" (bash) nil nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (expand "odd?") (("2" (flatten) (("2" (skolem!) 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(int_plus_int_is_int application-judgement "int" integers nil) (expt_pos formula-decl nil exponentiation nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (exp_of2_exists_aux formula-decl nil prelude_aux nil) (rat_minus_rat_is_rat application-judgement "rat" rationals nil) (real_lt_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) (minus_int_is_int application-judgement "int" integers nil) (/ const-decl "[numfield, nznum -> numfield]" number_fields nil) (nznum nonempty-type-eq-decl nil number_fields nil) (both_sides_minus_lt2 formula-decl nil real_props nil) (posrat_div_posrat_is_posrat application-judgement "posrat" rationals nil) (nzreal nonempty-type-eq-decl nil reals nil) (expt_inverse formula-decl nil exponentiation nil) (lt_equiv_le_plus_one formula-decl nil prelude_aux nil) (expt_x0 formula-decl nil exponentiation nil) (nnint_plus_posint_is_posint application-judgement "posint" integers nil) (even_plus_odd_is_odd application-judgement "odd_int" integers nil) (both_sides_expt_gt1_lt formula-decl nil exponentiation nil) (NOT const-decl "[bool -> bool]" booleans nil) (^ const-decl "real" exponentiation nil) (/= const-decl "boolean" notequal nil) (OR const-decl "[bool, bool -> bool]" booleans nil) (both_sides_div_pos_lt2 formula-decl nil real_props nil) (posrat_exp application-judgement "posrat" exponentiation nil) (nnrat_exp application-judgement "nnrat" exponentiation nil)) shostak)) (exp_of_exists2 0 (exp_of_exists2-1 nil 3251283119 ("" (skosimp*) (("" (lemma "exp_of_exists" ("b" "2" "py" "1/lt1y!1")) (("" (skosimp*) (("" (lemma "expt_pos" ("px" "2" "i" "i!1+1")) (("" (lemma "both_sides_div_pos_lt2" ("pz" "1" "px" "lt1y!1" "py" "2^-(i!1+1)")) (("" (lemma "expt_inverse" ("n0x" "2" "i" "-(i!1+1)")) (("" (assert) (("" (replace -1 -2 rl) (("" (replace -5 -2) (("" (assert) (("" (lemma "exp_of2_exists" ("lt1x" "lt1x!1")) (("" 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(- const-decl "[numfield -> numfield]" number_fields nil) (^ const-decl "real" exponentiation nil) (OR const-decl "[bool, bool -> bool]" booleans nil) (both_sides_div_pos_lt2 formula-decl nil real_props nil) (posrat_exp application-judgement "posrat" exponentiation nil) (nnrat_exp application-judgement "nnrat" exponentiation nil) (minus_int_is_int application-judgement "int" integers nil)) shostak)) (floor_sqrt_val 0 (floor_sqrt_val-1 nil 3250061827 ("" (skosimp*) (("" (lemma "floor_def" ("x" "sqrt(n!1)")) (("" (flatten -1) (("" (typepred "sqrt(n!1)") (("" (lemma "nonneg_floor_is_nat" ("x" "sqrt(n!1)")) (("" (expand ">=") (("" (rewrite "sq_rew") (("" (rewrite "sq_rew") (("" (rewrite "sq_rew") (("" (lemma "sqrt_le" ("nny" "sq(m!1)" "nnz" "n!1")) (("" (lemma "sqrt_lt" ("nnz" "sq(1+m!1)" "nny" "n!1")) (("" (replace -1 1 rl) (("" (replace -2 1 rl) (("" (rewrite "sqrt_sq") (("" (rewrite "sqrt_sq") (("" (split 1) (("1" (flatten) (("1" (lemma "trich_lt" ("x" "floor(sqrt(n!1))" "y" "m!1")) 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(sqrt_lt formula-decl nil sqrt "reals/") (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (sq_nz_pos application-judgement "posreal" sq "reals/") (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (sq_sqrt formula-decl nil sqrt "reals/") (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (nnint_plus_posint_is_posint application-judgement "posint" integers nil) (nonneg_floor_is_nat application-judgement "nat" floor_ceil nil) (sq_rew formula-decl nil sq "reals/") (nonneg_floor_is_nat judgement-tcc nil floor_ceil nil)) nil)) (ceiling_sqrt_0 0 (ceiling_sqrt_0-1 nil 3287291927 ("" (rewrite "sqrt_0") (("" (grind) nil nil)) nil) ((nonneg_ceiling_is_nat application-judgement "nat" floor_ceil nil) (sqrt_0 formula-decl nil sqrt "reals/")) shostak)) (ceiling_sqrt_val 0 (ceiling_sqrt_val-1 nil 3287290302 ("" (skosimp*) (("" (rewrite "sq_rew") (("" (rewrite "sq_rew") (("" (lemma "ceiling_def" ("x" "sqrt(pn!1)")) (("" (flatten -1) (("" (typepred "pn!1") (("" (lemma "sqrt_le" ("nny" "1" "nnz" "pn!1")) (("" (rewrite "sqrt_1") (("" (assert) (("" (name-replace "M" "ceiling(sqrt(pn!1))") (("" --> -------------------- --> maximum size reached --> -------------------- ¤ Dauer der Verarbeitung: 0.63 Sekunden (vorverarbeitet) ¤ |
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