| products/Sources/formale Sprachen/PVS/Bernstein/ |
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Quellcode-Bibliothek© Kompilation durch diese Firma[Weder Korrektheit noch Funktionsfähigkeit der Software werden zugesichert.]Datei: linear_functions.prf Sprache: LispOriginal von: PVS© |
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(multi_bernstein
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"(total_order?[real])" real_props nil) (ge_realorder name-judgement "RealOrder" util nil)) nil)) (bsproduct_eval_TCC3 0 (bsproduct_eval_TCC3-1 nil 3509275056 ("" (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) (>= const-decl "bool" 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) (nat nonempty-type-eq-decl nil naturalnumbers nil) (int_minus_int_is_int application-judgement "int" integers nil) (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (gt_realorder name-judgement "RealOrder" util nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (ge_realorder name-judgement "RealOrder" util nil)) nil)) (multibs_eval_rec_TCC1 0 (multibs_eval_rec_TCC1-1 nil 3498990086 ("" (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) (>= const-decl "bool" 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) (nat nonempty-type-eq-decl nil naturalnumbers nil) (int_minus_int_is_int application-judgement "int" integers nil) (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (gt_realorder name-judgement "RealOrder" util nil) (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (le_realorder name-judgement "RealOrder" util nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (ge_realorder name-judgement "RealOrder" util nil)) nil)) (multibs_eval_rec_TCC2 0 (multibs_eval_rec_TCC2-1 nil 3498990086 ("" (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) (>= const-decl "bool" 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) (nat nonempty-type-eq-decl nil naturalnumbers nil) (int_minus_int_is_int application-judgement "int" integers nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (ge_realorder name-judgement "RealOrder" util nil)) nil)) (multibs_eval_rec_TCC3 0 (multibs_eval_rec_TCC3-1 nil 3498990086 ("" (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 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(("1" (assert) nil nil)) nil) ("2" (hide 3) (("2" (induct "rr") (("1" (skeep) (("1" (expand "multibs_eval_rec") (("1" (hide -1) (("1" (lemma "sigma_scal") (("1" (inst - "(LAMBDA (d: nat): multibs_eval_rec(bspoly, bsdegmono, cf, 1 + vv, 1, 0) (cgm WITH [(0) := d])(X))" "(bspoly(0)(1 + vv)(x!1) * Bern(x!1, bsdegmono(1 + vv))(X(1 + vv)))" "bsdegmono(0)" "0") (("1" (replace -1 :dir rl) (("1" (hide -1) (("1" (rewrite "sigma_restrict_eq") (("1" (decompose-equality) (("1" (expand "restrict") (("1" (lift-if) (("1" (ground) (("1" (hide 3) (("1" (expand "multibs_eval_rec") (("1" (expand "multibs_eval_mono") (("1" (expand "sigma") (("1" (expand "sigma") (("1" (expand "product" + 3) (("1" (expand "product" + 3) (("1" (case "NOT product(0, vv, LAMBDA (k: nat): IF cgm WITH [(0) := x!2](k) <= bsdegmono(k) THEN Bern(cgm WITH [(0) := x!2](k), bsdegmono(k))(X(k)) ELSE 1 ENDIF) = product(0, vv, LAMBDA (k: nat): IF cgm WITH [(1 + vv) := x!1, (0) := x!2](k) <= bsdegmono(k) THEN Bern(cgm WITH [(1 + vv) := x!1, (0) := x!2](k), bsdegmono(k)) (X(k)) ELSE 1 ENDIF)") (("1" (hide 3) (("1" (rewrite "product_restrict_eq") (("1" (hide 2) (("1" (decompose-equality) (("1" (expand "restrict") (("1" (lift-if) (("1" (ground) nil nil)) nil)) nil) ("2" (skosimp*) (("2" (assert) nil nil)) nil) ("3" (skosimp*) (("3" (assert) nil nil)) nil)) nil)) nil)) nil)) nil) ("2" (replace -1 :dir rl) (("2" (hide -1) (("2" (case "product(0, vv, LAMBDA (j: nat): bspoly(0)(j)(cgm WITH [(0) := x!2](j)))=product(0, vv, LAMBDA (j: nat): bspoly(0)(j)(cgm WITH [(1 + vv) := x!1, (0) := x!2](j)))") (("1" (assert) nil nil) ("2" (hide 3) (("2" (rewrite "product_restrict_eq") (("2" (hide 2) (("2" (decompose-equality) (("2" (expand "restrict") (("2" (lift-if) (("2" (ground) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("3" (skosimp*) (("3" (assert) nil nil)) nil) ("4" (skosimp*) (("4" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (skolem 1 "rr") (("2" (flatten) (("2" (skeep) (("2" (assert) (("2" (expand "multibs_eval_rec" +) (("2" (lemma "sigma_scal") (("2" (inst?) 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nil) ("4" (skosimp*) (("4" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((real_times_real_is_real application-judgement "real" reals nil) (sigma def-decl "real" sigma "reals/") (multibs_eval_rec def-decl "real" multi_bernstein nil) (CoeffMono type-eq-decl nil util nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (bsproduct_eval const-decl "real" multi_bernstein 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 "[numfield, numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (= const-decl "[T, T -> boolean]" equalities nil) (Coeff type-eq-decl nil util nil) (MultiBernstein type-eq-decl nil util nil) (Polyproduct type-eq-decl nil util nil) (Polynomial type-eq-decl nil util nil) (DegreeMono type-eq-decl nil util nil) (Vars type-eq-decl nil util nil) (nat 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