| Quellcodebibliothek Statistik Leitseite products/sources/formale Sprachen/PVS/float/ (Beweissystem der NASA Version 6.0.9©) Datei vom 28.9.2014 mit Größe 50 kB |
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Quelle IEEE_854.prf Sprache: unbekannt |
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(IEEE_854
(Significand_size_TCC1 0 (Significand_size_TCC1-1 nil 3321206276 ("" (tcc :defs !) nil nil) ((/= const-decl "boolean" notequal nil)) nil)) (Exponent_balance_TCC1 0 (Exponent_balance_TCC1-1 nil 3321206276 ("" (tcc :defs !) nil nil) ((/= const-decl "boolean" notequal nil)) nil)) (Exponent_balance_TCC2 0 (Exponent_balance_TCC2-1 nil 3321206276 ("" (tcc :defs !) nil nil) ((expt def-decl "real" exponentiation nil) (^ const-decl "real" exponentiation nil) (/= const-decl "boolean" notequal nil) (minus_int_is_int application-judgement "int" integers nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (posrat_div_posrat_is_posrat application-judgement "posrat" rationals nil) (posnat_expt application-judgement "posnat" exponentiation nil) (int_plus_int_is_int application-judgement "int" integers nil) (posrat_exp application-judgement "posrat" exponentiation nil) (nnrat_exp application-judgement "nnrat" exponentiation nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil)) nil)) (Exponent_balance 0 (Exponent_balance-1 nil 3321206276 ("" (lemma "E_balance") (("" (lemma "expt_x1") (("" (inst?) (("" (lemma "expt_x0") (("" (inst?) (("" (ground) (("" (lemma "expt_plus") (("" (inst - "1" "E_max+E_min" "b") (("" (assert) (("" (typepred "b") (("" (case "forall (i:above(1)): 4<=i*i") (("1" (inst?) (("1" (assert) nil))) ("2" (induct "i" 1 "above_induction[1]") (("1" (assert) nil) ("2" (skosimp*) (("2" (assert) nil)))))))))))))))))))))))))) nil) ((expt_x1 formula-decl nil exponentiation nil) (expt_x0 formula-decl nil exponentiation nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (nnrat_exp application-judgement "nnrat" exponentiation nil) (posint_exp application-judgement "posint" exponentiation nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (posrat_exp application-judgement "posrat" exponentiation nil) (nzreal nonempty-type-eq-decl nil reals nil) (/= const-decl "boolean" notequal nil) (E_min formal-const-decl "integer" IEEE_854 nil) (E_max formal-const-decl "integer" IEEE_854 nil) (integer nonempty-type-from-decl nil integers nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (NOT const-decl "[bool -> bool]" booleans nil) (pred type-eq-decl nil defined_types nil) (above_induction formula-decl nil bounded_int_inductions nil) (even_times_int_is_even application-judgement "even_int" integers nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (odd_plus_odd_is_even application-judgement "even_int" integers nil) (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (^ const-decl "real" exponentiation nil) (>= const-decl "bool" reals nil) (OR const-decl "[bool, bool -> bool]" booleans nil) (* const-decl "[numfield, numfield -> numfield]" number_fields nil) (<= const-decl "bool" reals nil) (mult_divides1 application-judgement "(divides(n))" divides nil) (posint_times_posint_is_posint application-judgement "posint" integers nil) (posrat_times_posrat_is_posrat application-judgement "posrat" rationals nil) (expt_plus formula-decl nil exponentiation nil) (b formal-const-decl "above(1)" IEEE_854 nil) (above nonempty-type-eq-decl nil integers 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) (int_plus_int_is_int application-judgement "int" integers nil) (E_balance formula-decl nil IEEE_854 nil)) nil)) (E_max_gt_E_min 0 (E_max_gt_E_min-1 nil 3321206276 ("" (lemma "Exponent_range") (("" (grind-reals) (("" (cross-mult -1) nil nil)) nil)) nil) ((real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (rat_div_nzrat_is_rat application-judgement "rat" rationals nil) (int_minus_int_is_int application-judgement "int" integers 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) (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) (above nonempty-type-eq-decl nil integers nil) (p formal-const-decl "above(1)" IEEE_854 nil) (numfield nonempty-type-eq-decl nil number_fields nil) (- const-decl "[numfield, numfield -> numfield]" number_fields nil) (integer nonempty-type-from-decl nil integers nil) (E_max formal-const-decl "integer" IEEE_854 nil) (E_min formal-const-decl "integer" IEEE_854 nil) (mult_divides2 application-judgement "(divides(m))" divides nil) (mult_divides1 application-judgement "(divides(n))" divides nil) (posint_times_posint_is_posint application-judgement "posint" integers nil) (div_mult_pos_gt1 formula-decl nil extra_real_props nil) (Exponent_range formula-decl nil IEEE_854 nil)) nil)) (HUG_example 0 (HUG_example-1 nil 3321206276 ("" (ground) nil nil) ((real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (posint_times_posint_is_posint application-judgement "posint" integers nil) (mult_divides1 application-judgement "(divides(n))" divides nil) (mult_divides2 application-judgement "(divides(m))" divides nil) (int_minus_int_is_int application-judgement "int" integers nil)) nil)) (ex754_2 0 (ex754_2-1 nil 3321206276 ("" (assert) nil nil) ((real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (nzrat_div_nzrat_is_nzrat application-judgement "nzrat" rationals nil) (odd_minus_even_is_odd application-judgement "odd_int" integers nil) (minus_nzint_is_nzint application-judgement "nzint" integers nil) (minus_even_is_even application-judgement "even_int" integers nil)) nil)) (ex754_3 0 (ex754_3-1 nil 3321206276 ("" (grind) nil nil) ((real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (posint_exp application-judgement "posint" exponentiation nil) (posnat_expt application-judgement "posnat" exponentiation nil) (posrat_div_posrat_is_posrat application-judgement "posrat" rationals nil) (posint_times_posint_is_posint application-judgement "posint" integers nil) (even_times_int_is_even application-judgement "even_int" integers nil) (mult_divides1 application-judgement "(divides(n))" divides nil) (mult_divides2 application-judgement "(divides(m))" divides nil) (^ const-decl "real" exponentiation nil) (expt def-decl "real" exponentiation nil)) nil)) (E_min_neg 0 (E_min_neg-1 nil 3321206276 ("" (lemma "E_balance") (("" (lemma "Exponent_range") (("" (ground) (("1" (cross-mult -3) nil nil) ("2" (cross-mult -2) nil nil)) nil)) nil)) nil) ((Exponent_range formula-decl nil IEEE_854 nil) (div_mult_pos_gt1 formula-decl nil extra_real_props nil) (posint_times_posint_is_posint application-judgement "posint" integers nil) (mult_divides1 application-judgement "(divides(n))" divides nil) (mult_divides2 application-judgement "(divides(m))" divides nil) (E_min formal-const-decl "integer" IEEE_854 nil) (E_max formal-const-decl "integer" IEEE_854 nil) (integer nonempty-type-from-decl nil integers nil) (- const-decl "[numfield, numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (p formal-const-decl "above(1)" IEEE_854 nil) (above 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) (>= 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) (int_minus_int_is_int application-judgement "int" integers nil) (rat_div_nzrat_is_rat application-judgement "rat" rationals nil) (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (int_plus_int_is_int application-judgement "int" integers nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (E_balance formula-decl nil IEEE_854 nil)) nil)) (E_max_pos 0 (E_max_pos-1 nil 3321206276 ("" (lemma "E_balance") (("" (lemma "Exponent_range") (("" (ground) (("1" (cross-mult -3) nil nil) ("2" (cross-mult -2) nil nil)) nil)) nil)) nil) ((Exponent_range formula-decl nil IEEE_854 nil) (div_mult_pos_gt1 formula-decl nil extra_real_props nil) (posint_times_posint_is_posint application-judgement "posint" integers nil) (mult_divides1 application-judgement "(divides(n))" divides nil) (mult_divides2 application-judgement "(divides(m))" divides nil) (E_min formal-const-decl "integer" IEEE_854 nil) (E_max formal-const-decl "integer" IEEE_854 nil) (integer nonempty-type-from-decl nil integers nil) (- const-decl "[numfield, numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (p formal-const-decl "above(1)" IEEE_854 nil) (above 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) (>= 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) (int_minus_int_is_int application-judgement "int" integers nil) (rat_div_nzrat_is_rat application-judgement "rat" rationals nil) (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (int_plus_int_is_int application-judgement "int" integers nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (E_balance formula-decl nil IEEE_854 nil)) nil)) (IMP_IEEE_854_defs_TCC1 0 (IMPORTING1_TCC1-1 nil 3321206276 ("" (rewrite "E_max_gt_E_min") nil nil) ((E_max_gt_E_min formula-decl nil IEEE_854 nil)) nil))) [ 0.20Quellennavigators Projekt ] |
2026-03-28