| products/Sources/formale Sprachen/PVS/reals/ |
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Quellcode-Bibliothek© Kompilation durch diese Firma[Weder Korrektheit noch Funktionsfähigkeit der Software werden zugesichert.]Datei: product_fseq_posnat.prf Sprache: LispOriginal von: PVS© |
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(product_fseq_posnat
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(("2" (flatten) (("2" (name-replace "II" "product(0, n!1 - 1, fs!1`seq)") (("2" (name-replace "JJ" "product(1 + n!1, length(fs!1) - 1, fs!1`seq)") (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((below type-eq-decl nil naturalnumbers nil) (fseq type-eq-decl nil fseqs "structures/") (barray type-eq-decl nil fseqs "structures/") (posnat nonempty-type-eq-decl nil integers nil) (> const-decl "bool" reals nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (>= const-decl "bool" reals 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) (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_times_real_is_real application-judgement "real" reals nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (even_minus_odd_is_odd application-judgement "odd_int" integers nil) (product_middle formula-decl nil product nil) (product const-decl "posnat" product_fseq_posnat nil) (T_low type-eq-decl nil product nil) (T_high type-eq-decl nil product nil) (<= const-decl "bool" reals nil) (OR const-decl "[bool, bool -> bool]" booleans 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) (prod_posnat judgement-tcc nil product nil) (prod_nat judgement-tcc nil product nil) (posrat_times_posrat_is_posrat application-judgement "posrat" rationals nil) (posrat_div_posrat_is_posrat application-judgement "posrat" rationals nil) (both_sides_times_pos_ge1 formula-decl nil real_props nil) (nonneg_real nonempty-type-eq-decl nil real_types nil) (posreal nonempty-type-eq-decl nil real_types nil) (/= const-decl "boolean" notequal nil) (nznum nonempty-type-eq-decl nil number_fields nil) (/ const-decl "[numfield, nznum -> numfield]" number_fields nil) (* const-decl "[numfield, numfield -> numfield]" number_fields nil) (product def-decl "real" product nil) (bijective? const-decl "bool" functions nil) (id const-decl "(bijective?[T, T])" identity nil) (TRUE const-decl "bool" booleans 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) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (prod_nnr application-judgement "nnreal" product_nat nil) (prod_nat application-judgement "nat" product_nat nil) (prod_pr application-judgement "posreal" product_nat nil) (prod_posnat application-judgement "posnat" product_nat nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (product_last formula-decl nil product nil) (int_minus_int_is_int application-judgement "int" integers nil) (= const-decl "[T, T -> boolean]" equalities nil) (numfield nonempty-type-eq-decl nil number_fields nil) (- const-decl "[numfield, numfield -> numfield]" number_fields nil)) nil) (product_fseq_ge-2 nil 3410529222 (";;; Proof product_ge-1 for formula product_seq.product_ge" (skosimp*) ((";;; Proof product_ge-1 for formula product_seq.product_ge" (lemma "product_mult") ((";;; Proof product_ge-1 for formula product_seq.product_ge" (inst -1 "fs!1^^(0,n!1)" "fs!1^^(n!1+1,length(fs!1)-1)") ((";;; Proof product_ge-1 for formula product_seq.product_ge" (case-replace "fs!1 ^^ (0, n!1) o fs!1 ^^ (n!1 + 1, length(fs!1) - 1) = fs!1") (("1" (hide -1) (("1" (hide -1) (("1" (expand "product") (("1" (lemma "product_middle") (("1" (inst?) 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(("2" (inst - "(LAMBDA (n: nat): IF n < fs`length THEN fs`seq(n) ELSE nn ENDIF)") (("2" (split -1) (("1" (assert) (("1" (expand "product" 2 2) (("1" (assert) nil nil)) nil)) nil) ("2" (hide 3) (("2" (skosimp*) (("2" (lift-if) (("2" (ground) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) nil nil)) (product_fseq1 0 (product_fseq1-1 nil 3410609736 ("" (grind) nil 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) (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) (default const-decl "T" fseqs "structures/") (fseq1 const-decl "fseq" fseqs "structures/") (nat nonempty-type-eq-decl nil naturalnumbers nil) (product def-decl "real" product nil) (product const-decl "posnat" product_fseq_posnat nil)) shostak))) ¤ Dauer der Verarbeitung: 0.52 Sekunden (vorverarbeitet) ¤ |
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