SSL restriction_integral.prf
Interaktion und
(restriction_integralnil 3432062629"" (lemma "sub_domain" )"" (skosimp)"" (inst - "a!1" ) (("" (skosimp) (("" (assert ) nil nil )) nil ))nil ))nil ))nil )nil restriction_integral nil )"[real -> boolean]" restriction_integral nil )nil reals nil )"[number_field -> boolean]" reals nil )nil number_fields nil )"[number -> boolean]" number_fieldsnil )nil booleans nil )nil numbers nil )nil restriction_integral nil ))nil ))nil 3432062629"" (expand "connected?" )"" (skosimp)"" (lemma "connected_domain_T2" ("x" "x!1" "y" "y!1" ))"" (inst - "z!1" ) (("" (assert ) nil nil )) nil )) nil ))nil ))nil )"(total_order?[real])" nil )nil restriction_integral nil )nil numbers nil )nil booleans nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[number_field -> boolean]" reals nil )nil reals nil )"[real -> boolean]" restriction_integral nil )nil restriction_integral nil )"bool" deriv_domain_def "analysis/" ))nil ))nil 3432062629"" (expand "not_one_element?" )"" (lemma "not_one_element_T2" ) (("" (propax) nil nil )) nil ))nil )nil restriction_integral nil )"bool" deriv_domain_def "analysis/" ))nil ))nil 3432062629"" (expand "connected?" )"" (lemma "connected_domain_T1" ) (("" (propax) nil nil )) nil ))nil )nil restriction_integral nil )"bool" deriv_domain_def "analysis/" ))nil ))nil 3432062629"" (lemma "not_one_element_T1" )"" (expand "not_one_element?" ) (("" (propax) nil nil )) nil )) nil )"bool" deriv_domain_def "analysis/" )nil restriction_integral nil ))nil ))nil 3432063069"" (auto-rewrite "xis_lem" )"" case "FORALL (a, b: T1, f: [T2 -> real]): a<b=> ") "1" (skosimp)"1" (expand "Integrable?" )"1" (case-replace "a!1=b!1" )"1" (assert ) nil nil )"2" (case-replace "a!1<b!1" )"1" (inst - "a!1" "b!1" "f!1" ) (("1" (assert ) nil nil ))nil )"2" (inst - "b!1" "a!1" "f!1" ) (("2" (assert ) nil nil ))nil ))nil ))nil ))nil ))nil )"2" (hide 2)"2" (skosimp)"2" (split)"1" (flatten)"1" (expand "integrable?" )"1" (skosimp)"1" (inst + "S!1" )"1" (expand "integral?" )"1" (skosimp)"1" (inst - "epsi!1" )"1" (skosimp)"1" (inst + "delta!1" )"1" "1" "P!1" )"1" "1" "1" "R!1" )"1" "R!1" )"1" "1" expand "Riemann_sum?" )"1" "1" "xis!1" )"1" replace -1)"1" "1" expand "Rie_sum" )"1" expand "finseq_appl" )"1" expand "restrict" )"1" nil nil ))nil ))nil ))nil ))nil ))nil )"2" "2" "1" "1" "xis!1(x1!1)" )"1" assert )"1" "sub_domain" "x" "xis!1(x1!1)" ))"1" "1" assert )nil nil ))nil ))nil ))nil ))nil ))nil )"2" "xis!1" )"2" expand "xis?" )"2" expand "finseq_appl" )"2" nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" "2" expand "width" )"2" (propax) nil nil ))nil ))nil ))nil )"2" "2" "1" "1" "P!1`seq(x1!1)" )"1" assert )"1" "sub_domain" "x" "P!1`seq(x1!1)" ))"1" "1" assert )nil nil ))nil ))nil ))nil ))nil ))nil )"2" "2" "P!1" )"2" "ii!1" )nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" (flatten)"2" (expand "integrable?" )"2" (skosimp)"2" (inst + "S!1" )"2" (expand "integral?" )"2" (skosimp)"2" (inst - "epsi!1" )"2" (skosimp)"2" (inst + "delta!1" )"2" "2" "P!1" )"1" "1" "1" "R!1" )"1" "1" "R!1" )"1" expand "Riemann_sum?" )"1" "1" "xis!1" )"1" replace -1)"1" "1" expand "Rie_sum" )"1" expand "restrict" )"1" expand "finseq_appl" )"1" nil nil ))nil ))nil ))nil ))nil ))nil )"2" "1" "1" "xis!1(x1!1)" )"1" assert )"1" "connected_domain_T1" "x" "a!1" "y" "b!1" "z" "xis!1(x1!1)" ))"1" assert )nil nil ))nil ))nil ))nil ))nil )"2" "xis!1" )"2" expand "xis?" )"2" expand "finseq_appl" )"2" nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" "2" expand "width" )"2" (propax) nil nil ))nil ))nil ))nil )"2" "2" "1" "1" "P!1`seq(x1!1)" )"1" assert )"1" "connected_domain_T1" "x" "a!1" "y" "b!1" "z" "P!1`seq(x1!1)" ))"1" (assert ) nil nil ))nil ))nil ))nil ))nil )"2" "2" "P!1" )"2" "ii!1" )nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"3" (hide 2)"3" (skosimp*)"3" (lemma "sub_domain" ("x" "x!1" ))"3" (skolem!) (("3" (assert ) nil nil )) nil )) nil ))nil ))nil )"4" (skosimp)"4" (lemma "sub_domain" ("x" "b!1" ))"4" (skolem!) (("4" (assert ) nil nil )) nil )) nil ))nil )"5" (hide 2)"5" (skosimp)"5" (lemma "sub_domain" ("x" "a!1" ))"5" (skolem!) (("5" (assert ) nil nil )) nil )) nil ))nil ))nil ))nil ))nil )"R" restrict nil )"bool" integral_def "analysis/" )"[bool, bool -> bool]" booleans nil )"bool" reals nil )"[bool, bool -> bool]" booleans nil )nil booleans nil )nil restriction_integral nil )"[real -> boolean]" restriction_integral nil )nil restriction_integral nil )"[real -> boolean]" restriction_integral nil )nil reals nil )"[number_field -> boolean]" reals nil )nil number_fields nil )"[number -> boolean]" number_fieldsnil )nil booleans nil )nil numbers nil )"bool" integral_def "analysis/" )"(strict_total_order?[real])" real_props nil )"[T, T -> boolean]" equalities nil )"partition[T2](a!1, b!1)" nil )"(xis?(a!1, b!1, P!1))" nil )nil restriction_integral nil )"(Riemann_sum?(a!1, b!1, P!1, f!1))" nil )"real" reals nil )"bool" integral_def "analysis/" )nil real_types nil )"bool" reals nil )nil real_types nil )"bool" reals nil )"int" integers nil )"(strict_total_order?[real])" real_props nil )"partition[T1](a!1, b!1)" nil )nil integral_def "analysis/" )"[numfield, numfield -> numfield]" number_fields nil )nil naturalnumbers nil )"[numfield, numfield -> numfield]" number_fields nil )nil number_fields nil )nil finite_sequences nil )nil intervals_real "reals/" )"T1" restriction_integral nil )"T1" restriction_integral nil )"bool" reals nil )nil nat_types nil )nil naturalnumbers nil )nil integers nil )"[rational -> boolean]" integers nil )nil rationals nil )"[real -> boolean]" rationals nil )AND const-decl "[bool, bool -> bool]" booleans nil )"posreal" integral_def "analysis/" )NOT const-decl "[bool -> bool]" booleans nil )"bool" integral_def "analysis/" )"(xis?(a!1, b!1, P!1))" nil )"[below[length(fs)] -> T]" finite_sequencesnil )"real" integral_def "analysis/" )"real" reals nil )nil restriction_integral nil )"(total_order?[real])" nil )"(Riemann_sum?(a!1, b!1, P!1, restrict[T2, T1, real](f!1)))" nil )"[T2 -> real]" restriction_integral nil )"bool" integral_def "analysis/" ))nil 3432062629"" (skosimp)"" (hide -1)"" (typepred "b!1" )"" (lemma "sub_domain" ("x" "b!1" ))"" (skosimp) (("" (assert ) nil nil )) nil )) nil ))nil ))nil ))nil )nil restriction_integral nil )nil booleans nil )nil booleans nil )NOT const-decl "[bool -> bool]" booleans nil )nil numbers nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[number_field -> boolean]" reals nil )nil reals nil )"[real -> boolean]" restriction_integral nil )nil restriction_integral nil ))nil ))nil 3432062629"" (skosimp)"" (skosimp)"" (lemma "sub_domain" ("x" "x!1" ))"" (skosimp) (("" (assert ) nil nil )) nil )) nil ))nil ))nil )nil restriction_integral nil )nil numbers nil )nil booleans nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[number_field -> boolean]" reals nil )nil reals nil )"[real -> boolean]" restriction_integral nil )nil restriction_integral nil ))nil ))nil 3432189764"" (skosimp)"" (lemma "restrict_Integrable" ("a" "a!1" "b" "b!1" "f" "f!1" ))"" (assert ) nil nil )) nil ))nil )nil restriction_integral nil )"[real -> boolean]" restriction_integral nil )nil restriction_integral nil )"[real -> boolean]" restriction_integral nil )nil reals nil )"[number_field -> boolean]" reals nil )nil number_fields nil )"[number -> boolean]" number_fieldsnil )nil booleans nil )nil numbers nil )nil restriction_integral nil ))nil ))nil 3432064068"" case "forall a,b,f: a<b&integrable?[T2](a, b, f) & integrable?[T1](a,b,restrict[T2,T1,real](f))=> ") "1" (skosimp)"1" "restrict_Integrable" ("a" "a!1" "b" "b!1" "f" "f!1" ))"1" (assert )"1" (expand "Integrable?" )"1" (expand "Integral" )"1" (case-replace "a!1=b!1" )"1" (assert )"1" (case-replace "a!1<b!1" )"1" (assert )"1" (inst - "a!1" "b!1" "f!1" )"1" (assert ) nil nil )) nil ))nil )"2" (assert )"2" (inst - "b!1" "a!1" "f!1" )"2" (assert ) nil nil )) nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" (hide 2)"2" (skosimp*)"2" (typepred "integral[T2](a!1, b!1, f!1)" )"2" "integral[T1](a!1, b!1, restrict[T2, T1, real](f!1))" )"1" (expand "integral?" )"1" (name-replace "LHS" "integral[T2](a!1, b!1, f!1)" )"1" "RHS" "integral[T1](a!1, b!1, restrict[T2, T1, real](f!1))" )"1" (typepred "abs(LHS-RHS)" )"1" (hide -2 -3)"1" (expand ">=" -1)"1" (expand "<=" -1)"1" (split -1)"1" (name "EPS" "abs(LHS-RHS)" )"1" replace -1)"1" "EPS/2" )"1" "EPS/2" )"1" "1" "DELTA" "min(delta!1,delta!2)" )"1" "N" "floor((b!1-a!1)/DELTA)+2" )"1" "width_eq_part[T1]" "a" "a!1" "b" "b!1" "N" "N" ))"1" "width_eq_part[T2]" "a" "a!1" "b" "b!1" "N" "N" ))"1" assert )"1" case "(b!1-a!1)/(N-1)<DELTA" )"1" case "DELTA <= delta!1 & DELTA<=delta!2" )"1" "1" "eq_partition[T1](a!1, b!1, N)" )"1" "eq_partition[T2](a!1, b!1, N)" )"1" replace "1" replace "1" assert )"1" "1" "1" "1" "Riemann?_Rie[T2]" "a" "a!1" "b" "b!1" "f" "f!1" ))"1" "Riemann?_Rie[T1]" "a" "a!1" "b" "b!1" "f" "restrict[T2, T1, real](f!1)" ))"1" assert )"1" "eq_partition[T1](a!1, b!1, N)" "gen_xis[T1](a!1,b!1,eq_partition[T1](a!1, b!1, N))" )"1" "eq_partition[T1](a!1, b!1, N)" "_" )"1" case "N>=1" )"1" "R1" "Rie_sum(a!1, b!1, eq_partition[T1](a!1, b!1, N), ") "1" replace "1" "R1" )"1" "gen_xis[T1](a!1, b!1, eq_partition[T1](a!1, b!1, N))" )"1" "R2" "Rie_sum[T2](a!1, b!1, eq_partition[T1](a!1, b!1, N), ") "1" replace "1" case "eq_partition[T1](a!1, b!1, N)=eq_partition[T2](a!1, b!1, N)" )"1" "R2" )"1" "R1=R2" )"1" "1" nil nil ))nil )"2" "2" "2" expand "R1" )"2" expand "R2" )"2" "FF" "gen_xis[T1](a!1, b!1, eq_partition[T1](a!1, b!1, N))" )"2" expand "Rie_sum" )"2" expand "finseq_appl" )"2" expand "restrict" )"2" nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" assert )nil nil ))nil )"2" expand "eq_partition" )"2" nil nil ))nil ))nil ))nil ))nil )"2" "2" "gen_xis[T1](a!1, b!1, eq_partition[T1](a!1, b!1, N))" )"2" expand "xis?" )"2" "1" "1" expand "finseq_appl" )"1" "x1!1" )"1" "1" "parts_order_le[T1]" "P" "eq_partition[T1](a!1, b!1, N)" "a" "a!1" "b" "b!1" ))"1" "0" "x1!1" )"1" assert )"1" "1" "sub_domain" "x" "gen_xis[T1](a!1, b!1, eq_partition[T1](a!1, b!1, N))(x1!1)" ))"1" "1" assert )nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" "2" expand "finseq_appl" )"2" "ii!1" )nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" "2" "posreal_div_posreal_is_posreal" "px" "b!1-a!1" "py" "DELTA" ))"2" "nonneg_floor_is_nat" )"2" "(b!1 - a!1) / DELTA" )"1" assert )nil nil )"2" assert )nil nil ))nil ))nil ))nil ))nil ))nil )"2" "2" "1" "1" "eq_partition[T1](a!1, b!1, N)`seq(x1!1)" )"1" assert )"1" "sub_domain" "x" "eq_partition[T1](a!1, b!1, N)`seq(x1!1)" ))"1" "1" assert )nil nil ))nil ))nil ))nil ))nil ))nil )"2" "eq_partition[T1](a!1, b!1, N)" )"2" nil nil ))nil ))nil ))nil ))nil )"2" "not_one_element_T1" )"2" "2" "posreal_div_posreal_is_posreal" "px" "b!1-a!1" "py" "DELTA" ))"2" "nonneg_floor_is_nat" "x" "(b!1 - a!1) / DELTA" ))"1" assert )nil nil )"2" assert )nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" assert )nil nil ))nil )"2" assert )nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" "2" nil nil ))nil ))nil )"2" "2" "posreal_div_posreal_is_posreal" "px" "b!1-a!1" "py" "DELTA" ))"2" "floor((b!1 - a!1) / DELTA)" )"2" rewrite "div_mult_pos_lt1" "2" rewrite "div_mult_pos_lt1" "2" rewrite "div_mult_pos_le2" "2" assert )nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" assert )"2" "floor((b!1 - a!1) / DELTA)" )"2" "posreal_div_posreal_is_posreal" "px" "b!1-a!1" "py" "DELTA" ))"2" assert )nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" (assert ) nil nil ))nil )"2" (assert ) nil nil ))nil ))nil ))nil )"2" (expand "abs" )"2" "2" (grind) nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" (lemma "not_one_element_T1" )"2" (skosimp)"2" (lemma "sub_domain" ("x" "x!1" ))"2" (skosimp) (("2" (assert ) nil nil )) nil )) nil ))nil ))nil ))nil ))nil ))nil ))nil )"3" (skosimp)"3" (lemma "not_one_element_T1" )"3" (skosimp)"3" (lemma "sub_domain" ("x" "x!1" ))"3" (skolem!) (("3" (assert ) nil nil )) nil )) nil ))nil ))nil ))nil )"4" (skosimp)"4" (lemma "connected_domain_T1" )"4" (lemma "sub_domain" ("x" "b!1" ))"4" (skolem!) (("4" (assert ) nil nil )) nil )) nil ))nil ))nil )"5" (skosimp)"5" (hide-all-but 1)"5" (lemma "sub_domain" ("x" "a!1" ))"5" (skosimp) (("5" (assert ) nil nil )) nil )) nil ))nil ))nil )"6" (skosimp)"6" (lemma "sub_domain" ("x" "b!1" ))"6" (skosimp)"6" (assert )"6" (skosimp*)"6" (lemma "sub_domain" ("x" "x!1" ))"6" (skolem!) (("6" (assert ) nil nil )) nil )) nil ))nil ))nil ))nil ))nil ))nil )"7" (skosimp)"7" (lemma "sub_domain" ("x" "a!1" ))"7" (skosimp)"7" (assert )"7" (lemma "sub_domain" ("x" "b!1" ))"7" (skolem!) (("7" (assert ) nil nil )) nil )) nil ))nil ))nil ))nil ))nil )"8" (skosimp)"8" (lemma "not_one_element_T1" )"8" (lemma "sub_domain" ("x" "a!1" ))"8" (skolem!) (("8" (assert ) nil nil )) nil )) nil ))nil ))nil ))nil )nil restriction_integral nil )NOT const-decl "[bool -> bool]" booleans nil )"real" reals nil )"bool" reals nil )"(strict_total_order?[real])" real_props nil )"nnreal" nil )"bool" reals nil )"boolean" notequal nil )nil number_fields nil )"[numfield, nznum -> numfield]" number_fields nil )"T1" restriction_integral nil )"T1" restriction_integral nil )"[T2 -> real]" restriction_integral nil )"{S: real | integral?(a!1, b!1, f!1, S)}" nil )"{S: real | integral?(a!1, b!1, restrict[T2, T1, real](f!1), S)}" nil )"{n: nonneg_real | n >= LHS - RHS AND n >= -(LHS - RHS)}" nil )nil real_types nil )"real" reals nil )"int" integers nil )"[numfield, numfield -> numfield]" number_fields nil )"[real -> boolean]" rationals nil )nil rationals nil )"[rational -> boolean]" integers nil )nil integers nil )"{i | i <= x & x < i + 1}" floor_ceil nil )nil integers nil )"int" restriction_integral nil )"(xis?(a, b, P))" integral_def "analysis/" )"bool" integral_def "analysis/" )"real" restriction_integral nil )"[below[length(fs)] -> T]" finite_sequencesnil )"real" reals nil )"(total_order?[real])" nil )nil restriction_integral nil )"posint" nil )nil integral_def "analysis/" )"real" restriction_integral nil )"bool" integral_def "analysis/" )"real" integral_def "analysis/" )nil real_types nil )"posreal" restriction_integral nil )"posreal" restriction_integral nil )"{z: posreal | z <= delta!1 AND z <= delta!2}" nil )nil floor_ceil nil )nil restriction_integral nil )nil integral_def "analysis/" )"(total_order?[real])" nil )nil naturalnumbers nil )nil nat_types nil )nil intervals_real "reals/" )nil finite_sequences nil )nil naturalnumbers nil )nil integral_def "analysis/" )"partition(a, b)" integral_def"analysis/" )nil real_props nil )nil real_props nil )"real" reals nil )"int" integers nil )nil integers nil )nil integral_def "analysis/" )min const-decl "{p: real | p <= m AND p <= n}" real_defs nil )"{z: posreal | z <= x AND z <= y}" real_defs nil )"bool" reals nil )nil real_types nil )nil number_fields nil )"[numfield -> numfield]" number_fields nil )"{n: nonneg_real | n >= m AND n >= -m}" real_defsnil )"[numfield, numfield -> numfield]" number_fields nil )"odd_int" integers nil )"real" integral_def "analysis/" )"(strict_total_order?[real])" real_props nil )"real" reals nil )"bool" integral_def "analysis/" )nil restriction_integral nil )nil numbers nil )nil booleans nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[number_field -> boolean]" reals nil )nil reals nil )"[real -> boolean]" restriction_integral nil )nil restriction_integral nil )"[real -> boolean]" restriction_integral nil )nil restriction_integral nil )nil booleans nil )"[bool, bool -> bool]" booleans nil )AND const-decl "[bool, bool -> bool]" booleans nil )"bool" reals nil )"bool" integral_def "analysis/" )"R" restrict nil )"[T, T -> boolean]" equalities nil )"bool" integral_def "analysis/" )"{S: real | integral?(a, b, ff, S)}" "analysis/" ))nil 3432190262"" (auto-rewrite "xis_lem" )"" (skosimp)"" "restrict_Integrable" "a" "a!1" "b" "b!1" "f" "extend[T2, T1, real, c!1](g!1)" ))"1" (replace -1)"1" (hide -1)"1" "restrict[T2, T1, real](extend[T2, T1, real, c!1](g!1))=g!1" )"1" (assert ) nil nil )"2" (hide 2)"2" (apply-extensionality :hide? t)"1" (expand "extend" )"1" (expand "restrict" ) (("1" (propax) nil nil ))nil ))nil )"2" (skosimp)"2" (lemma "sub_domain" ("x" "x!1" ))"2" (skosimp) (("2" (assert ) nil nil )) nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" (hide 2)"2" (skosimp)"2" (lemma "sub_domain" ("x" "x!1" ))"2" (skosimp) (("2" (assert ) nil nil )) nil )) nil ))nil ))nil ))nil ))nil ))nil )"[T, T -> boolean]" equalities nil )"R" restrict nil )nil restriction_integral nil )nil restriction_integral nil )nil numbers nil )nil booleans nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[number_field -> boolean]" reals nil )nil reals nil )"[real -> boolean]" restriction_integral nil )nil restriction_integral nil )"[real -> boolean]" restriction_integral nil )nil restriction_integral nil )"R" extend nil ))nil 3432189764"" (skosimp)"" (lemma "sub_domain" ("x" "b!1" ))"" (skosimp) (("" (assert ) nil nil )) nil )) nil ))nil )nil restriction_integral nil )"[real -> boolean]" restriction_integral nil )nil reals nil )"[number_field -> boolean]" reals nil )nil number_fields nil )"[number -> boolean]" number_fieldsnil )nil booleans nil )nil numbers nil )nil restriction_integral nil ))nil ))nil 3432189764"" (skosimp*)"" (lemma "sub_domain" ("x" "x!1" ))"" (skosimp) (("" (assert ) nil nil )) nil )) nil ))nil )nil restriction_integral nil )"[real -> boolean]" restriction_integral nil )nil reals nil )"[number_field -> boolean]" reals nil )nil number_fields nil )"[number -> boolean]" number_fieldsnil )nil booleans nil )nil numbers nil )nil restriction_integral nil ))nil ))nil 3432189764"" (skosimp)"" "extend_Integrable" "a" "a!1" "b" "b!1" "g" "g!1" "c" "c!1" ))"" (assert ) nil nil )) nil ))nil )nil restriction_integral nil )"[real -> boolean]" restriction_integral nil )nil reals nil )"[number_field -> boolean]" reals nil )nil number_fields nil )"[number -> boolean]" number_fieldsnil )nil booleans nil )nil numbers nil )nil restriction_integral nil ))nil ))nil 3432190639"" (skosimp)"" "extend_Integrable" "a" "a!1" "b" "b!1" "c" "c!1" "g" "g!1" ))"" (assert )"" "restrict_Integral" "a" "a!1" "b" "b!1" "f" "extend[T2, T1, real, c!1](g!1)" ))"1" (assert )"1" "restrict[T2, T1, real](extend[T2, T1, real, c!1](g!1))=g!1" )"1" (assert ) nil nil )"2" (hide-all-but 1)"2" (apply-extensionality :hide? t)"1" (grind) nil nil )"2" (skosimp)"2" (lemma "sub_domain" ("x" "x!1" ))"2" (skolem!) (("2" (assert ) nil nil )) nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" (skosimp)"2" (lemma "sub_domain" ("x" "x!1" ))"2" (skolem!) (("2" (assert ) nil nil )) nil )) nil ))nil ))nil ))nil ))nil ))nil )nil restriction_integral nil )"[real -> boolean]" restriction_integral nil )nil reals nil )"[number_field -> boolean]" reals nil )nil number_fields nil )"[number -> boolean]" number_fieldsnil )nil booleans nil )nil numbers nil )nil restriction_integral nil )"R" extend nil )nil restriction_integral nil )"[real -> boolean]" restriction_integral nil )nil restriction_integral nil )"[T, T -> boolean]" equalities nil )"R" restrict nil )nil restriction_integral nil ))
Messung V0.5 in Prozent C=100 H=100 G=100
¤ Dauer der Verarbeitung: 0.40 Sekunden
(vorverarbeitet am 2026-04-26)
¤ *© Formatika GbR, Deutschland
2026-05-26
