| 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: cc_plugin.mlpack Sprache: UnknownOriginal von: PVS© |
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(multi_bernstein
(IMP_sigma_bijection_TCC1 0 (IMP_sigma_bijection_TCC1-1 nil 3618684915 ("" (assuming-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) (integer nonempty-type-from-decl nil integers nil) (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)) (bsproduct_eval_TCC1 0 (bsproduct_eval_TCC1-1 nil 3498406967 ("" (subtype-tcc) nil nil) nil nil)) (bsproduct_eval_TCC2 0 (bsproduct_eval_TCC2-1 nil 3498406967 ("" (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) (real_ge_is_total_order name-judgement "(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 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_TCC4 0 (multibs_eval_rec_TCC4-1 nil 3498990086 ("" (termination-tcc) nil nil) nil nil)) (multibs_eval_1_term 0 (multibs_eval_1_term-1 nil 3499083500 ("" (expand "multibs_eval") (("" (expand "sigma") (("" (expand "sigma") (("" (case "FORALL (X: Vars, bsdegmono: DegreeMono, bspoly: MultiBernstein, cf: Coeff, mvars: nat): cf(0) * bsproduct_eval(bspoly(0), bsdegmono, mvars+1)(X) = multibs_eval_rec(bspoly, bsdegmono, cf, mvars+1, 1, mvars+1) (LAMBDA (i: nat): 0)(X)") (("1" (skeep) (("1" (inst?) (("1" (assert) nil nil)) nil)) nil) ("2" (hide 2) (("2" (induct "mvars") (("1" (skeep) (("1" (assert) (("1" (expand "bsproduct_eval") (("1" (expand "product") (("1" (expand "product") (("1" (expand "multibs_eval_rec") (("1" (rewrite "sigma_scal" :dir rl) (("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 "product") (("1" (expand "product") (("1" (expand "multibs_eval_mono") (("1" (expand "sigma") (("1" (expand "sigma") (("1" (expand "product") (("1" (expand "product") (("1" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (skosimp*) (("2" (assert) nil nil)) nil)) nil) ("2" (skosimp*) (("2" (assert) nil nil)) nil)) nil) ("2" (skosimp*) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (skolem 1 "vv") (("2" (flatten) (("2" (skeep) (("2" (assert) (("2" (expand "bsproduct_eval" +) (("2" (expand "product" + 1) (("2" (lemma "sigma_scal") (("2" (inst - "LAMBDA (j: nat): IF j > bsdegmono(1 + vv) THEN 0 ELSE bspoly(0)(1 + vv)(j) * Bern(j, bsdegmono(1 + vv))(X(1 + vv)) ENDIF" "cf(0) * product(0, vv, LAMBDA (i: nat): sigma(0, bsdegmono(i), LAMBDA (j: nat): IF j > bsdegmono(i) THEN 0 ELSE bspoly(0)(i)(j) * Bern(j, bsdegmono(i))(X(i)) ENDIF))" "bsdegmono(1+vv)" "0") (("1" (assert) (("1" (replace -1 :dir rl) (("1" (hide -1) (("1" (expand "multibs_eval_rec" +) (("1" (rewrite "sigma_restrict_eq") (("1" (decompose-equality) (("1" (expand "restrict") (("1" (lift-if) (("1" (ground) (("1" (hide 3) (("1" (expand "bsproduct_eval") (("1" (inst?) (("1" (inst - "cf") (("1" (mult-by -1 "bspoly(0)(1 + vv)(x!1) * Bern(x!1, bsdegmono(1 + vv))(X(1 + vv))") (("1" (replace -1) (("1" (hide -1) (("1" (case "FORALL (rr:nat,cgm:CoeffMono): rr<=vv IMPLIES multibs_eval_rec(bspoly, bsdegmono, cf, 1 + vv, 1, 1 + rr) (cgm)(X) * (bspoly(0)(1 + vv)(x!1) * Bern(x!1, bsdegmono(1 + vv))(X(1 + vv))) = multibs_eval_rec(bspoly, bsdegmono, cf, 2 + vv, 1, 1 + rr) (cgm WITH [(1 + vv) := x!1])(X)") (("1" (inst?) (("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?) (("2" (inst - "(bspoly(0)(1 + vv)(x!1) * Bern(x!1, bsdegmono(1 + vv))(X(1 + vv)))") (("2" (replace -1 :dir rl) (("2" (hide -1) (("2" (rewrite "sigma_restrict_eq") (("2" (hide 2) (("2" (decompose-equality) (("2" (expand "restrict") (("2" (lift-if) (("2" (ground) (("2" (inst - "cgm WITH [(1 + rr) := x!2]") (("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) ("2" (skosimp*) (("2" (assert) nil nil)) nil) ("3" (skosimp*) (("3" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (skosimp*) (("2" (assert) nil nil)) nil) ("3" (skosimp*) (("3" (assert) nil nil)) nil) ("4" (skosimp*) (("4" (assert) nil nil)) nil)) nil) ("2" (skosimp*) (("2" (assert) nil nil)) nil) ("3" (skosimp*) (("3" (assert) nil nil)) nil) ("4" (skosimp*) (("4" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (skosimp*) (("2" (assert) 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) ((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 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) (nnint_plus_posint_is_posint application-judgement "posint" integers nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (ge_realorder name-judgement "RealOrder" util nil) (int_minus_int_is_int application-judgement "int" integers nil) (- const-decl "[numfield, numfield -> numfield]" number_fields nil) (int_plus_int_is_int application-judgement "int" integers nil) (pred type-eq-decl nil defined_types nil) (nat_induction formula-decl nil naturalnumbers nil) (even_plus_odd_is_odd application-judgement "odd_int" integers nil) (product def-decl "real" product "reals/") (sigma_restrict_eq formula-decl nil sigma "reals/") (gt_realorder name-judgement "RealOrder" util nil) (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (multibs_eval_mono const-decl "real" multi_bernstein nil) (restrict const-decl "[T -> real]" sigma "reals/") (bsdegmono skolem-const-decl "DegreeMono" multi_bernstein nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (lt_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) (sigma_scal formula-decl nil sigma "reals/") (IF const-decl "[boolean, T, T -> T]" if_def nil) (above nonempty-type-eq-decl nil integers nil) (Bern const-decl "real" bernstein_polynomials "reals/") (OR const-decl "[bool, bool -> bool]" booleans nil) (<= const-decl "bool" reals nil) (T_high type-eq-decl nil sigma "reals/") (T_low type-eq-decl nil sigma "reals/") (NOT const-decl "[bool -> bool]" booleans nil) (IMPLIES const-decl "[bool, bool -> bool]" booleans nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (bsdegmono skolem-const-decl "DegreeMono" multi_bernstein nil) (vv skolem-const-decl "nat" multi_bernstein nil) (T_high type-eq-decl nil product "reals/") (T_low type-eq-decl nil product "reals/") (both_sides_times1_imp formula-decl nil extra_real_props nil) (restrict const-decl "[T -> real]" product "reals/") (x!1 skolem-const-decl "nat" multi_bernstein nil) (x!2 skolem-const-decl "nat" multi_bernstein nil) (cgm skolem-const-decl "CoeffMono" multi_bernstein nil) (product_restrict_eq formula-decl nil product "reals/") (multibs_eval const-decl "real" multi_bernstein nil)) nil)) (multibs_eval_equiv 0 (multibs_eval_equiv-3 nil 3499083601 ("" (case "FORALL (X: Vars, bsdegmono: DegreeMono, bspoly: MultiBernstein, cf: Coeff, nvars, terms: posnat,cfn:nat,ct:nat,lb:nat,pz:nat): lb<=pz AND cfn+lb<=ct AND ct< multibs_eval(bspoly, bsdegmono, cfnew, nvars, terms)(X) = multibs_eval_rec(bspoly, bsdegmono, cfnew, nvars, terms, nvars) (LAMBDA (i: nat): 0)(X)") (("1" (skeep) (("1" (inst - "X" "bsdegmono" "bspoly" "cf" "nvars" "terms" "0" "terms-1" "terms-1" "terms-1") (("1" (assert) (("1" (case "multibs_eval(bspoly, bsdegmono, LAMBDA (i: nat): IF i <= terms - 1 THEN cf(i) ELSE 0 ENDIF, nvars, terms) (X) = multibs_eval(bspoly, bsdegmono, cf, nvars, terms)(X) AND multibs_eval_rec(bspoly, b LAMBDA (i: nat): IF i <= terms - 1 THEN cf(i) ELSE 0 ENDIF, nvars, terms, nvars) (LAMBDA (i: nat): 0)(X) = multibs_eval_rec(bspoly, bsdegmono, cf, nvars, terms, nvars) (LAMBDA (i: nat): 0)(X)") (("1" (assert) (("1" (flatten) (("1" 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