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Datei: sigma_vector.prf Sprache: Lisp

Original von: PVS^©

(sigma_vector (connected_domain 0 (connected_domain-1 nil 3521046835 ("" (skosimp) (("" (grind) (("" (grind) (("" (postpone) nil nil)) nil)) nil)) nil) nil shostak)) (low_TCC1 0 (tcc "tcc" 3489915882 ("" (skosimp) (("" (lemma "connected_domain") (("" (inst -1 "x!1" "y!1" "z!1") (("" (assert) nil nil)) nil)) nil)) nil) ((connected_domain formula-decl nil sigma_vector nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (integer nonempty-type-from-decl nil integers nil) (T formal-subtype-decl nil sigma_vector nil) (T_pred const-decl "[int -> boolean]" sigma_vector 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)) shostak) (low_TCC1-1 nil 3489915779 ("" (assuming-tcc) nil nil) nil nil)) (oh_TCC1 0 (oh_TCC1-1 nil 3518275428 ("" (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) (= const-decl "[T, T -> boolean]" equalities nil) (posnat nonempty-type-eq-decl nil integers nil) (Vector type-eq-decl nil vectors "vectors/") (Maping type-eq-decl nil linear_map nil) (AND const-decl "[bool, bool -> bool]" 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) (>= const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (n formal-const-decl "posnat" sigma_vector nil) (Map type-eq-decl nil linear_map nil) (T_pred const-decl "[int -> boolean]" sigma_vector nil) (T formal-subtype-decl nil sigma_vector nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (real_lt_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)) nil)) (oh_TCC2 0 (oh_TCC2-1 nil 3518275428 ("" (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) (= const-decl "[T, T -> boolean]" equalities nil) (posnat nonempty-type-eq-decl nil integers nil) (Vector type-eq-decl nil vectors "vectors/") (Maping type-eq-decl nil linear_map nil) (AND const-decl "[bool, bool -> bool]" 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) (>= const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (n formal-const-decl "posnat" sigma_vector nil) (Map type-eq-decl nil linear_map nil) (T_pred const-decl "[int -> boolean]" sigma_vector nil) (T formal-subtype-decl nil sigma_vector nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (real_lt_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)) nil)) (SigmaV_last_TCC1 0 (thm "fin" 3546879131 ("" (skosimp) (("" (typepred "high!1") (("" (case " T_pred(high!1)") (("1" (inst 2 "high!1") (("1" (assert) nil nil)) nil) ("2" (case "(EXISTS (j: T): high!1 <= j)") (("1" (skosimp) (("1" (grind) nil nil)) nil) ("2" (assert) nil nil)) nil)) nil)) nil)) nil) ((T_high type-eq-decl nil sigma "reals/") (<= const-decl "bool" reals nil) (T formal-subtype-decl nil sigma_vector nil) (T_pred const-decl "[int -> boolean]" sigma_vector 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) (number nonempty-type-decl nil numbers nil) (OR 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) (high!1 skolem-const-decl "T_high[T]" sigma_vector 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_le_is_total_order name-judgement "(total_order?[real])" real_props nil)) shostak) (SigmaV_last_TCC1-1 nil 3546878969 ("" (subtype-tcc) nil nil) ((T_high type-eq-decl nil sigma "reals/")) nil)) (SigmaV_last_TCC2 0 (thm "fin" 3546879358 ("" (skosimp) (("" (typepred "high!1") (("" (typepred "low!1") (("" (grind) (("1" (lemma "connected_domain") (("1" (inst -1 "low!1" "j!1" "high!1") (("1" (assert) nil nil)) nil)) nil) ("2" (lemma "connected_domain") (("2" (typepred "low!1") (("2" (inst -2 "j!1" "j!2" "high!1") (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((T_high type-eq-decl nil sigma "reals/") (<= const-decl "bool" reals nil) (T formal-subtype-decl nil sigma_vector nil) (T_pred const-decl "[int -> boolean]" sigma_vector 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) (number nonempty-type-decl nil numbers nil) (OR 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) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (integer nonempty-type-from-decl nil integers nil) (connected_domain formula-decl nil sigma_vector nil) (T_low type-eq-decl nil sigma "reals/")) shostak) (SigmaV_last_TCC2-1 nil 3546878969 ("" (subtype-tcc) nil nil) ((T_high type-eq-decl nil sigma "reals/") (T_low type-eq-decl nil sigma "reals/")) nil)) (SigmaV_last 0 (SigmaV_last-1 nil 3546883946 ("" (skosimp) (("" (expand "SigmaV") (("" (apply-extensionality) (("1" (hide 2) (("1" (expand "+") (("1" (lemma "sigma_last[T]") (("1" (inst -1 "LAMBDA (j: T): F!1(j)(x!1)" "high!1" "low!1") (("1" (assert) nil nil)) nil)) nil)) nil)) nil) ("2" (skosimp) (("2" (typepred "high!1") (("2" (case " T_pred(high!1)") (("1" (inst 2 "high!1") (("1" (assert) nil nil)) nil) ("2" (case " (EXISTS (j: T): high!1 <= j)") (("1" (skosimp) (("1" (inst 3 "j!1") (("1" (assert) nil nil)) nil)) nil) ("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((SigmaV const-decl "Vector[n]" sigma_vector nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (NOT const-decl "[bool -> bool]" booleans nil) (sigma_last formula-decl nil sigma "reals/") (real_plus_real_is_real application-judgement "real" reals nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (int_minus_int_is_int application-judgement "int" integers nil) (high!1 skolem-const-decl "T_high[T]" sigma_vector nil) (T_high type-eq-decl nil sigma "reals/") (<= const-decl "bool" reals nil) (T formal-subtype-decl nil sigma_vector nil) (- const-decl "[numfield, numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (T_pred const-decl "[int -> boolean]" sigma_vector nil) (OR const-decl "[bool, bool -> bool]" booleans nil) (T_low type-eq-decl nil sigma "reals/") (sigma def-decl "real" sigma "reals/") (Index type-eq-decl nil vectors "vectors/") (Vector type-eq-decl nil vectors "vectors/") (+ const-decl "real" vectors "vectors/") (below type-eq-decl nil nat_types nil) (n formal-const-decl "posnat" sigma_vector 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 "bool" reals 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)) shostak)) (SigmaV_scal 0 (thm "finished" 3546764749 ("" (skosimp) (("" (case "p!1>m!1") (("1" (expand "SigmaV") (("1" (expand "sigma") (("1" (replace -1) (("1" (expand "*") (("1" (propax) nil nil)) nil)) nil)) nil)) nil) ("2" (case "p!1=m!1") (("1" (hide 1) (("1" (replace -1) (("1" (expand "SigmaV") (("1" (expand "sigma") (("1" (expand "sigma") (("1" (apply-extensionality) (("1" (hide 2) (("1" (expand "*") (("1" (expand "*") (("1" (propax) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (case "p!1) (("1" (hide 1 2) (("1" (expand "SigmaV") (("1" (lemma "sigma_scal[T]") (("1" (apply-extensionality) (("1" (hide 2) (("1" (inst -1 "LAMBDA (j: T): F!1(j)(x!1)" "a!1" "m!1" "p!1") (("1" (case " sigma(p!1, m!1, LAMBDA (i: T): a!1 * F!1(i)(x!1))= sigma(p!1, m!1, LAMBDA (j: T): (a!1 * F!1)(j)(x!1))") (("1" (replace -1 -2) (("1" (replace -2 1) (("1" (hide -1 -2) (("1" (expand "*") (("1" (propax) nil nil)) nil)) nil)) nil)) nil) ("2" (hide -1 2) (("2" (expand "*") (("2" (expand "*") (("2" (propax) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (assert) nil nil)) nil)) nil)) nil)) nil) ((T formal-subtype-decl nil sigma_vector nil) (T_pred const-decl "[int -> boolean]" sigma_vector 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 "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) (sigma def-decl "real" sigma "reals/") (* const-decl "Vector" vectors "vectors/") (SigmaV const-decl "Vector[n]" sigma_vector nil) (T_high type-eq-decl nil sigma "reals/") (T_low type-eq-decl nil sigma "reals/") (<= const-decl "bool" reals nil) (OR const-decl "[bool, bool -> bool]" booleans nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (* const-decl "[numfield, numfield -> numfield]" number_fields nil) (real_times_real_is_real application-judgement "real" reals nil) (sigma_scal formula-decl nil sigma "reals/") (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (Index type-eq-decl nil vectors "vectors/") (Vector type-eq-decl nil vectors "vectors/") (* const-decl "[real, [T -> Vector[n]] -> [T -> Vector[n]]]" sigma_vector nil) (numfield nonempty-type-eq-decl nil number_fields nil) (below type-eq-decl nil nat_types nil) (n formal-const-decl "posnat" sigma_vector nil) (posnat nonempty-type-eq-decl nil integers nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (< const-decl "bool" reals nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (>= const-decl "bool" reals nil) (= const-decl "[T, T -> boolean]" equalities nil)) shostak) (SigmaV_scal-1 nil 3546675674 ("" (skosimp) (("" (case "p!1>m!1") (("1" (expand "SigmaV") (("1" (expand "sigma") (("1" (replace -1) (("1" (expand "*") (("1" (propax) nil nil)) nil)) nil)) nil)) nil) ("2" (case "p!1=m!1") (("1" (hide 1) (("1" (replace -1) (("1" (expand "SigmaV") (("1" (expand "sigma") (("1" (expand "sigma") (("1" (apply-extensionality) (("1" (hide 2) (("1" (expand "*") (("1" (expand "*") (("1" (propax) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (case "p!1) (("1" (hide 1 2) (("1" (expand "SigmaV") (("1" (lemma "sigma_scal[T]") (("1" (apply-extensionality) (("1" (hide 2) (("1" (inst -1 "LAMBDA (j: T): F!1(j)(x!1)" "a!1" "m!1" "p!1") (("1" (case " sigma(p!1, m!1, LAMBDA (i: T): a!1 * F!1(i)(x!1))= sigma(p!1, m!1, LAMBDA (j: T): (a!1 * F!1)(j)(x!1))") (("1" (replace -1 -2) (("1" (replace -2 1) (("1" (hide -1 -2) (("1" (postpone) nil nil)) nil)) nil)) nil) ("2" (hide -1 2) (("2" (expand "*") (("2" (expand "*") (("2" (propax) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (assert) nil nil)) nil)) nil)) nil)) nil) ((Vector type-eq-decl nil vectors "vectors/") (Index type-eq-decl nil vectors "vectors/") (sigma_scal formula-decl nil sigma "reals/") (T_low type-eq-decl nil sigma "reals/") (T_high type-eq-decl nil sigma "reals/") (* const-decl "Vector" vectors "vectors/") (sigma def-decl "real" sigma "reals/")) shostak)))

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