| products/Sources/formale Sprachen/VDM/VDMSL/looseSL/ |
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Quellcode-Bibliothek© Kompilation durch diese Firma[Weder Korrektheit noch Funktionsfähigkeit der Software werden zugesichert.]Datei: sigma_nat.prf Sprache: LispOriginal von: PVS© |
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(sigma_nat
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real_props nil)) nil)) (int_is_T_high 0 (int_is_T_high-1 nil 3352138082 ("" (skosimp*) (("" (inst-cp + 0) (("" (inst + "x!1") (("1" (assert) nil nil) ("2" (assert) nil nil)) nil)) nil)) 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) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil)) nil)) (nat_is_T_low 0 (nat_is_T_low-1 nil 3352138082 ("" (judgement-tcc) nil nil) nil nil)) (sigma_shift_TCC1 0 (sigma_shift_TCC1-1 nil 3403006081 ("" (skosimp*) (("" (assert) nil nil)) nil) ((int_plus_int_is_int application-judgement "int" integers nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil)) nil)) (sigma_shift 0 (sigma_shift-1 nil 3308675684 ("" (skosimp*) (("" (rewrite "sigma_shift_T") nil nil)) nil) ((nnint_plus_nnint_is_nnint application-judgement "nonneg_int" integers nil) (int_plus_int_is_int application-judgement "int" integers nil) (sigma_shift_T formula-decl nil sigma nil) (OR const-decl "[bool, bool -> bool]" booleans nil) (<= const-decl "bool" reals nil) (T_high type-eq-decl nil sigma nil) (T_low type-eq-decl nil sigma 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 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(sigma_shift_neg-1 nil 3308675684 ("" (skosimp*) (("" (lemma "sigma_shift_T2") (("" (inst?) (("" (inst - "high!1" "low!1" "0 - m!1") (("" (assert) (("" (prop) (("1" (replace -1 :hide? t) (("1" (rewrite "sigma_eq") (("1" (skosimp*) (("1" (assert) nil nil)) nil)) nil)) nil) ("2" (case "high!1 (("1" (expand "sigma") (("1" (assert) nil nil)) nil) ("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) 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) (sigma_shift_T2 formula-decl nil sigma nil) (int_minus_int_is_int application-judgement "int" integers nil) (OR const-decl "[bool, bool -> bool]" booleans nil) (<= const-decl "bool" reals nil) (T_high type-eq-decl nil sigma nil) (T_low type-eq-decl nil sigma nil) (numfield nonempty-type-eq-decl nil number_fields nil) (- const-decl "[numfield, numfield -> numfield]" number_fields nil) (IMPLIES const-decl "[bool, bool -> bool]" booleans nil) (NOT const-decl "[bool -> bool]" booleans nil) (< const-decl "bool" reals nil) (IF const-decl "[boolean, T, T -> T]" if_def nil) (sigma_eq formula-decl nil sigma nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (minus_odd_is_odd application-judgement "odd_int" integers nil) (sigma def-decl "real" sigma 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) (int_plus_int_is_int application-judgement "int" integers nil)) nil)) (sigma_shift_ng2 0 (sigma_shift_ng2-1 nil 3308675684 ("" (skosimp*) (("" (lemma "sigma_shift_T2") (("" (inst?) (("" (inst - "high!1" "low!1" "0-m!1") (("" (assert) (("" (prop) (("1" (replace -1 :hide? t) (("1" (rewrite "sigma_eq") (("1" (expand "~") (("1" (assert) (("1" (skosimp*) (("1" (assert) (("1" (lift-if) (("1" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (case "high!1 (("1" (expand "sigma") (("1" (assert) nil nil)) nil) ("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) 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) 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(int_plus_int_is_int application-judgement "int" integers nil)) nil)) (sigma_shift_i_TCC1 0 (sigma_shift_i_TCC1-1 nil 3410183793 ("" (subtype-tcc) 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) (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 "bool" reals nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (int_plus_int_is_int application-judgement "int" integers nil) (real_le_is_total_order name-judgement 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(real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil)) nil)) (sigma_shift_i_TCC3 0 (sigma_shift_i_TCC3-1 nil 3410183793 ("" (subtype-tcc) 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) (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 "bool" reals nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (real_le_is_total_order name-judgement "(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)) nil)) (sigma_shift_i 0 (sigma_shift_i-1 nil 3410183811 ("" (skosimp*) (("" (rewrite "sigma_shift_T2") (("1" (rewrite "sigma_restrict_eq") (("1" (hide 2) (("1" (expand "restrict") (("1" (propax) nil nil)) nil)) nil) ("2" (skosimp*) (("2" (assert) nil nil)) nil)) nil) ("2" (case "low!1 <= high!1") (("1" (assert) nil nil) ("2" (grind) nil nil)) nil)) nil)) nil) ((sigma_shift_T2 formula-decl nil sigma nil) (OR const-decl "[bool, bool -> bool]" booleans nil) (<= const-decl "bool" reals nil) (T_high type-eq-decl nil sigma nil) (T_low type-eq-decl nil sigma 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) (int_plus_int_is_int application-judgement "int" integers nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (restrict const-decl "[T -> real]" sigma nil) (< const-decl "bool" reals nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (IF const-decl "[boolean, T, T -> T]" if_def nil) (sigma_restrict_eq formula-decl nil sigma nil) (NOT const-decl "[bool -> bool]" booleans nil) (IMPLIES const-decl "[bool, bool -> bool]" booleans nil) (sigma def-decl "real" sigma nil) (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil)) nil)) (sigma_shift_to_zero_TCC1 0 (sigma_shift_to_zero_TCC1-1 nil 3594380184 ("" (subtype-tcc) nil nil) nil nil)) (sigma_shift_to_zero_TCC2 0 (sigma_shift_to_zero_TCC2-1 nil 3594380184 ("" (subtype-tcc) 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 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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)) nil)) (sigma_split_ge_TCC1 0 (sigma_split_ge_TCC1-1 nil 3352162210 ("" (skosimp*) (("" (inst + 0) (("" (assert) nil nil)) nil)) 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 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