(integral_boundednil 3282561874"" (lemma "connected_domain" ) (("" (propax) nil nil )) nil )nil integral_bounded nil )) shostak))nil 3282561874"" (lemma "not_one_element" ) (("" (propax) nil nil )) nil )nil integral_bounded nil )) shostak))nil 3282561874"" (skosimp*) (("" (assert ) nil nil )) nil )"(strict_total_order?[real])" real_props nil ))nil 3282561874"" (skosimp*) (("" (assert ) nil nil )) nil )"posint" nil )"(strict_total_order?[real])" real_props nil ))nil 3477651374"" (skosimp*)"" case "(FORALL (eps: posreal): AND xx <= EP(j+1))") "1" (assert )"1" (inst - "1000" )"1" (skosimp*)"1" (inst + "EP!1" )"1" (skosimp*)"1" (inst - "j!1" )"1" (expand "bounded_on?" )"1" "1000 / abs(EP!1`seq(1 + j!1) - EP!1`seq(j!1)) + abs(f!1(EP!1`seq(j!1)))" )"1" (skosimp*)"1" (inst?)"1" (assert )"1" (lemma "abs_diff" )"1" "f!1(x!1)" "f!1(EP!1`seq(j!1))" )"1" (assert ) nil nil ))nil ))nil ))nil ))nil ))nil )"2" (typepred "EP!1" )"2" (inst - "j!1" ) (("2" (assert ) nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" (hide 2)"2" (skosimp*)"2" (assert )"2" (lemma "Lemma_1[T]" )"2" (inst?)"2" (assert )"2" (inst -1 "eps!1" )"2" (skosimp*)"2" "EP" "eq_partition(a!1,b!1,floor((b!1-a!1)/delta!1) + 2)" )"1" (inst + "EP" )"1" (skosimp*)"1" (case "T_pred(xx!1)" )"1" case "abs(EP`seq(1 + j!1) - EP`seq(j!1)) > 0" )"1" "1" "1" "SecJ" "(EP`seq(1 + j!1) - EP`seq(j!1))" )"1" "F_DIF" "(f!1((EP)(j!1)) - f!1(xx!1))" )"1" assert )"1" rewrite "abs_mult" "1" "EP`seq(1 + j!1) * f!1(xx!1) - EP`seq(j!1) * f!1(xx!1) + ") "1" "1" "abs_neg" )"1" "SecJ * F_DIF" )"1" replace -1)"1" "1" "EP" "EP" "gxis(a!1,b!1,EP,j!1,true,xx!1)" "gxis(a!1,b!1,EP,j!1,false,xx!1)" )"1" "1" expand "Rie_sum" )"1" assert )"1" assert )"1" rewrite "sigma_minus[below[length(EP)-1]]" )"1" "(LAMBDA (i: below(length(EP) - 1)): LAMBDA (i: below(length(EP) - 1)):IF i = j!1 THEN") "1" assert )"1" "1" "EP`seq(1 + j!1) * f!1(EP`seq(j!1)) - ") "1" "1" case "j!1 < length(EP) - 2" )"1" "sigma_below[length(EP)-1].sigma_split_ge" )"1" "_" "length(EP) - 2" "0" "j!1" )"1" assert )"1" "1" assert )"1" replace "1" "1" "sigma(1 + j!1, length(EP) - 2, LAMBDA (i: below(length(EP) - 1)):IF i = j!1 THEN SecJ * F_DIF ELSE 0 ENDIF)) = 0") "1" "1" rewrite "sigma_last_ge" )"1" assert )"1" case "sigma(0, j!1 - 1, LAMBDA (i: below(length(EP) - 1)):IF i = j!1 THEN SecJ * F_DIF ELSE 0 ENDIF)) = 0") "1" assert )nil nil )"2" "sigma_restrict_eq[below(length(EP)-1)]" )"2" "2" "(LAMBDA (i: below(length(EP) - 1)): 0)" )"2" expand "restrict" )"2" replace "2" "2" "sigma_const[below(length(EP)-1)]" )"2" "2" assert )nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"3" "3" assert )nil nil ))nil ))nil ))nil ))nil ))nil )"2" "2" "sigma_restrict_eq[below(length(EP)-1)]" )"1" "1" "(LAMBDA (i: below(length(EP) - 1)): 0)" )"1" expand "restrict" )"1" replace "1" "1" "sigma_const[below(length(EP)-1)]" )"1" "1" assert )nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" "2" "2" assert )nil nil ))nil ))nil ))nil ))nil )"3" "3" assert )nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" case "j!1 = length(EP) - 2" )"1" rewrite "sigma_last_ge" )"1" "sigma(0, length(EP) - 3, LAMBDA (i: below(length(EP) - 1)):IF i = j!1 THEN SecJ * F_DIF ELSE 0 ENDIF)) = 0") "1" assert )nil nil )"2" "sigma_restrict_eq[below(length(EP)-1)]" )"1" "1" "(LAMBDA (i: below(length(EP) - 1)): 0)" )"1" expand "restrict" )"1" assert )"1" "sigma_const[below(length(EP)-1)]" )"1" "1" assert )nil nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" "2" assert )nil nil ))nil ))nil )"3" "3" assert )nil nil ))nil ))nil ))nil )"2" assert )nil nil ))nil ))nil ))nil )"2" assert )nil nil ))nil ))nil ))nil )"2" "2" "2" expand "gxis" )"2" "2" nil nil ))nil ))nil ))nil ))nil ))nil )"2" "2" expand "gxis" )"2" assert )nil nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" "N_from_delta" )"2" "2" assert )nil nil ))nil ))nil )"3" "N_from_delta" )"3" "3" assert )nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" (assert ) nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" "2" "EP" )"2" "j!1" )"2" (assert ) nil nil ))nil ))nil ))nil ))nil )"2" "2" "connected_domain" )"2" expand "connected?" )"2" "2" "2" (assert ) nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" (hide 2)"2" (case "(b!1 - a!1) / delta!1 > 0" )"1" (assert ) nil nil )"2" (cross-mult 1) nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"3" (hide 2)"3" (skosimp*)"3" (typepred "EP!1" )"3" (inst - "j!1" ) (("3" (assert ) nil nil )) nil )) nil ))nil ))nil )"4" (hide 2)"4" (skosimp*)"4" (lemma "connected_domain" )"4" (expand "connected?" )"4" (inst - "_" "_" "xx!1" )"4" (inst?)"4" (inst?) (("4" (assert ) nil nil )) nil )) nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"[numfield, nznum -> numfield]" number_fields nil )nil number_fields nil )"boolean" notequal nil )"{n: nonneg_real | n >= m AND n >= -m}" real_defsnil )"[numfield -> numfield]" number_fields nil )"[below[length(fs)] -> T]" finite_sequencesnil )nil finite_sequences nil )"[bool, bool -> bool]" booleans nil )nil integral_def nil )"[numfield, numfield -> numfield]" number_fields nil )nil naturalnumbers nil )"bool" reals nil )nil integers nil )"[rational -> boolean]" integers nil )nil rationals nil )"[real -> boolean]" rationals nil )"[numfield, numfield -> numfield]" number_fields nil )nil number_fields nil )"[T, T -> boolean]" equalities nil )nil finite_sequences nil )nil intervals_real "reals/" )"bool" reals nil )AND const-decl "[bool, bool -> bool]" booleans nil )nil integral_bounded nil )"[real -> boolean]" integral_bounded nil )nil nat_types nil )nil naturalnumbers nil )nil real_types nil )"bool" reals nil )nil real_types nil )"bool" reals nil )nil booleans nil )nil reals nil )"[number_field -> boolean]" reals nil )nil number_fields nil )"[number -> boolean]" number_fieldsnil )nil booleans nil )nil numbers nil )"nzreal" nil )"posint" nil )"real" reals nil )NOT const-decl "[bool -> bool]" booleans nil )"(total_order?[real])" nil )"real" reals nil )"posint" nil )"T" integral_bounded nil )"T" integral_bounded nil )"partition[T](a!1, b!1)" integral_boundednil )"below(length(EP!1) - 1)" integral_boundednil )"odd_int" integers nil )nil abs_lems "reals/" )"(total_order?[real])" nil )"(strict_total_order?[real])" real_props nil )"int" integers nil )"bool" integral_bounded nil )"(strict_total_order?[real])" real_props nil )nil integral_prep nil )nil extra_real_props nil )nil real_props nil )"below(length(EP) - 1)" integral_boundednil )"{fs: finite_sequence[{x | a!1 <= x AND x <= b!1}] | AND AND AND " integral_bounded nil) "nnreal" nil )"[numfield, numfield -> numfield]" number_fields nil )"real" reals nil )nil abs_lems "reals/" )"bool" booleans nil )"bool" booleans nil )"(xis?(a, b, P))" integral_prep nil )"bool" integral_def nil )nil integral_def nil )"real" integral_def nil )IF const-decl "[boolean, T, T -> T]" if_def nil )nil sigma_below "reals/" )nil sigma "reals/" )"nat" sigma_below "reals/" )nil sigma "reals/" )"even_int" integersnil )"(divides(n))" divides nil )"(divides(m))" divides nil )"[T -> real]" sigma "reals/" )nil sigma_below "reals/" )"odd_int" integersnil )"real" sigma "reals/" )nil sigma_below "reals/" )nil sigma "reals/" )OR const-decl "[bool, bool -> bool]" booleans nil )nil sigma "reals/" )nil sigma "reals/" )"real" reals nil )nil real_props nil )nil integral_bounded nil )"bool" deriv_domain_def nil )"{i | i <= x & x < i + 1}" floor_ceil nil )nil integers nil )"partition(a, b)" integral_def nil )nil integers nil )"real" reals nil )"int" integers nil ))nil )nil 3282561219"" (skosimp*)"" case "(FORALL (eps: posreal): AND xx <= EP(j+1))") "1" (assert )"1" (inst - "1000" )"1" (skosimp*)"1" (inst + "EP!1" )"1" (skosimp*)"1" (inst - "j!1" )"1" (expand "bounded_on?" )"1" "1000 / abs(EP!1`seq(1 + j!1) - EP!1`seq(j!1)) + abs(f!1(EP!1`seq(j!1)))" )"1" (skosimp*)"1" (inst?)"1" (assert )"1" (lemma "abs_diff" )"1" "f!1(x!1)" "f!1(EP!1`seq(j!1))" )"1" (assert ) nil nil ))nil ))nil ))nil ))nil ))nil )"2" (typepred "EP!1" )"2" (inst - "j!1" ) (("2" (assert ) nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" (hide 2)"2" (skosimp*)"2" (assert )"2" (lemma "Lemma_1[T]" )"2" (inst?)"2" (assert )"2" (inst -1 "eps!1" )"2" (skosimp*)"2" "EP" "eq_partition(a!1,b!1,floor((b!1-a!1)/delta!1) + 2)" )"1" (inst + "EP" )"1" (skosimp*)"1" (case "T_pred(xx!1)" )"1" case "abs(EP`seq(1 + j!1) - EP`seq(j!1)) > 0" )"1" "1" "1" "SecJ" "(EP`seq(1 + j!1) - EP`seq(j!1))" )"1" "F_DIF" "(f!1((EP)(j!1)) - f!1(xx!1))" )"1" assert )"1" rewrite "abs_mult" "1" "EP`seq(1 + j!1) * f!1(xx!1) - EP`seq(j!1) * f!1(xx!1) + ") "1" "1" "abs_neg" )"1" "SecJ * F_DIF" )"1" replace -1)"1" "1" "EP" "EP" "gxis(a!1,b!1,EP,j!1,true,xx!1)" "gxis(a!1,b!1,EP,j!1,false,xx!1)" )"1" "1" expand "Rie_sum" )"1" assert )"1" assert )"1" rewrite "sigma_minus[below[length(EP)-1]]" )"1" "(LAMBDA (i: below(length(EP) - 1)): quality 87%
¤ Dauer der Verarbeitung: 0.33 Sekunden
(vorverarbeitet)
¤ *© Formatika GbR, Deutschland
