SSL interval_bolzano.prf
Interaktion und
(interval_bolzanonil 3321034255 ("" (grind-reals) nil nil )nil booleans nil )nil booleans nil )NOT const-decl "[bool -> bool]" booleans nil )nil reals nil )nil interval nil )"bool" interval nil )nil defined_types nil )"bool" interval_bolzano nil )nil numbers nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[number_field -> boolean]" reals nil )"bool" reals nil )nil real_types nil )"bool" reals nil )nil real_types nil )"posreal" nil )"(strict_total_order?[real])" real_props nil )"(strict_total_order?[real])" real_props nil )"(total_order?[real])" nil )nil real_props nil )"nnreal" interval nil ))nil ))nil 3321034255 ("" (grind-reals) nil nil )"posreal" nil )"(total_order?[real])" nil )"(strict_total_order?[real])" real_props nil )nil real_props nil )"nnreal" interval nil ))nil ))nil 3321034255 ("" (subtype-tcc) nil nil )nil booleans nil )nil booleans nil )NOT const-decl "[bool -> bool]" booleans nil )nil reals nil )nil interval nil )"bool" interval nil )nil defined_types nil )"bool" interval_bolzano nil )nil numbers nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[number_field -> boolean]" reals nil )"bool" reals nil )nil real_types nil )"bool" reals nil )nil real_types nil )"real" interval nil )"real" interval nil )"Interval" interval nil )"Interval" interval nil )"Interval" interval nil )"real" reals nil )"(strict_total_order?[real])" real_props nil )"(strict_total_order?[real])" real_props nil )"(total_order?[real])" nil )"(total_order?[real])" nil )"real" reals nil )"real" interval nil )"bool" interval nil ))nil ))nil 3321037604"" (skosimp* :preds? t)"" (lift-if)"" (lift-if)"" (assert )"" (split)"1" (flatten) (("1" (assert ) nil nil )) nil )"2" (flatten)"2" (lemma "log_nat_incr" )"2" "2" "size(Y1!1) / eps!1" "size(X!1) / eps!1" )"2" (assert )"2" (hide 3)"2" (lemma "Halves" )"2" (inst?) (("2" (assert ) nil nil )) nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"ProperInterval" intervalnil )"ProperInterval" intervalnil )"(strict_total_order?[real])" real_props nil )"(strict_total_order?[real])" real_props nil )"(total_order?[real])" nil )"[real -> boolean]" rationals nil )nil rationals nil )"[rational -> boolean]" integers nil )nil integers nil )nil integers nil )nil number_fields nil )"boolean" notequal nil )nil number_fields nil )"[numfield, nznum -> numfield]" number_fields nil )"real" interval nil )nil interval nil )"(total_order?[real])" nil )"nnreal" nil )nil log_nat "reals/" )"posint" nil )"nnreal" nil )nil interval nil )"posint" exponentiation nil )"nnreal" interval nil )nil booleans nil )nil booleans nil )NOT const-decl "[bool -> bool]" booleans nil )nil reals nil )nil interval nil )"bool" interval nil )nil defined_types nil )"bool" interval_bolzano nil )nil numbers nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[number_field -> boolean]" reals nil )"bool" reals nil )nil real_types nil )"bool" reals nil )nil real_types nil ))nil ))nil 3321037619"" (skosimp* :preds? t)"" (lemma "Halves_Incl" )"" (inst?)"" (assert )"" (flatten)"" (typepred "v!1(Prop?!1, Y1!1, eps!1)" )"1" (lemma "Incl_trans" )"1" (inst? -1 :where 2)"1" (inst?) (("1" (assert ) nil nil )) nil )) nil ))nil )"2" (lemma "bolzano_bisect_TCC4" )"2" (inst?)"2" (assert )"2" (inst?)"2" (assert )"2" (inst -1 "Y2!1" ) (("2" (assert ) nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )nil interval nil )"ProperInterval" intervalnil )"ProperInterval" intervalnil )"(strict_total_order?[real])" real_props nil )"(strict_total_order?[real])" real_props nil )"(total_order?[real])" nil )"bool" reals nil )"bool" interval nil )"[numfield, nznum -> numfield]" number_fields nil )nil number_fields nil )"[n: nat, {y | y < p AND x = p ^ n * y}]" log_nat"reals/" )"real" exponentiation nil )"boolean" notequal nil )OR const-decl "[bool, bool -> bool]" booleans nil )"[numfield, numfield -> numfield]" number_fields nil )"[T, T -> boolean]" equalities nil )AND const-decl "[bool, bool -> bool]" booleans nil )nil naturalnumbers nil )nil integers nil )nil integers nil )"[rational -> boolean]" integers nil )nil rationals nil )"[real -> boolean]" rationals nil )"[numfield, numfield -> numfield]" number_fields nil )"real" interval nil )IF const-decl "[boolean, T, T -> T]" if_def nil )nil number_fields nil )"bool" reals nil )"posint" nil )"nnreal" nil )"(total_order?[real])" nil )nil interval nil )nil interval_bolzano nil )nil interval nil )"posint" exponentiation nil )"nnreal" interval nil )nil booleans nil )nil booleans nil )NOT const-decl "[bool -> bool]" booleans nil )nil reals nil )nil interval nil )"bool" interval nil )nil defined_types nil )"bool" interval_bolzano nil )nil numbers nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[number_field -> boolean]" reals nil )"bool" reals nil )nil real_types nil )"bool" reals nil )nil real_types nil ))nil ))nil 3321057051 ("" (subtype-tcc) nil nil )nil booleans nil )nil booleans nil )NOT const-decl "[bool -> bool]" booleans nil )nil reals nil )nil interval nil )"bool" interval nil )nil defined_types nil )"bool" interval_bolzano nil )nil numbers nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[number_field -> boolean]" reals nil )"bool" reals nil )nil real_types nil )"bool" reals nil )nil real_types nil )"real" reals nil )"(total_order?[real])" nil )"(total_order?[real])" nil )"(strict_total_order?[real])" real_props nil )"(strict_total_order?[real])" real_props nil )"real" reals nil )nil interval nil )"real" interval nil )"real" interval nil )"real" interval nil )"Interval" interval nil )"Interval" interval nil )"Interval" interval nil )"real" reals nil ))nil ))nil 3403639539"" (skosimp* :preds? t)"" (lift-if)"" (lift-if)"" (assert )"" (split)"1" (flatten) (("1" (assert ) nil nil )) nil )"2" (flatten)"2" (lemma "log_nat_incr" )"2" "2" "size(Y2!1) / eps!1" "size(X!1) / eps!1" )"2" (assert )"2" (hide 3)"2" (lemma "Halves" )"2" (inst?) (("2" (assert ) nil nil )) nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"ProperInterval" intervalnil )"ProperInterval" intervalnil )"(strict_total_order?[real])" real_props nil )"(strict_total_order?[real])" real_props nil )"(total_order?[real])" nil )"[real -> boolean]" rationals nil )nil rationals nil )"[rational -> boolean]" integers nil )nil integers nil )nil integers nil )nil number_fields nil )"boolean" notequal nil )nil number_fields nil )"[numfield, nznum -> numfield]" number_fields nil )"real" interval nil )nil interval nil )"(total_order?[real])" nil )"nnreal" nil )nil log_nat "reals/" )"posint" nil )"nnreal" nil )nil interval nil )"posint" exponentiation nil )"nnreal" interval nil )nil booleans nil )nil booleans nil )NOT const-decl "[bool -> bool]" booleans nil )nil reals nil )nil interval nil )"bool" interval nil )nil defined_types nil )"bool" interval_bolzano nil )nil numbers nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[number_field -> boolean]" reals nil )"bool" reals nil )nil real_types nil )"bool" reals nil )nil real_types nil ))nil )nil 3321094616"" (skosimp* :preds? t)"" (lemma "Halves_Incl" )"" (inst?)"" (assert )"" (flatten)"" (name-replace "Y1" "HalfLeft(X!1)" :hide? nil )"" (name-replace "Y2" "HalfRight(X!1)" :hide? nil )"" (lift-if)"" (ground)"1" (typepred "v!1(Prop?!1, Y1, eps!1)" )"1" (lemma "Incl_trans" )"1" (inst? -1 :where 1)"1" (inst?) (("1" (assert ) nil nil )) nil ))nil ))nil ))nil )"2" (expand "Continuous?" -5)"2" (inst? -5)"2" (assert )"2" (typepred "v!1(Prop?!1, Y2, eps!1)" )"2" (lemma "Incl_trans" )"2" "2" "2" (assert ) nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"bool" interval nil )nil interval nil )"Interval" interval nil )nil interval nil )"real" interval nil )"[n: nat, {y | y < p AND x = p ^ n * y}]" log_nat"reals/" )"bool" interval nil )"Interval" interval nil )nil interval nil ))nil ))nil 3403640475"" (skosimp* :preds? t)"" (lemma "Halves_Incl" )"" (inst?)"" (assert )"" (flatten)"" (typepred "v!1(Prop?!1, Y2!1, eps!1)" )"1" (lemma "Incl_trans" )"1" (inst? -1 :where 3)"1" (inst?) (("1" (assert ) nil nil )) nil )"2" (expand "Continuous?" )"2" (inst?) (("2" (assert ) nil nil )) nil )) nil ))nil ))nil )"2" (lemma "bolzano_bisect_TCC7" )"2" (inst?)"2" (assert )"2" (inst -1 "Y1!1" )"2" (assert )"2" (inst -1 "Y2!1" ) (("2" (assert ) nil nil ))nil ))nil ))nil ))nil ))nil ))nil )"3" (expand "Continuous?" )"3" (inst?) (("3" (assert ) nil nil )) nil )) nil ))nil ))nil ))nil ))nil ))nil ))nil )nil interval nil )"ProperInterval" intervalnil )"ProperInterval" intervalnil )"(strict_total_order?[real])" real_props nil )"(strict_total_order?[real])" real_props nil )"(total_order?[real])" nil )"bool" reals nil )"bool" interval nil )"[numfield, nznum -> numfield]" number_fields nil )nil number_fields nil )"[n: nat, {y | y < p AND x = p ^ n * y}]" log_nat"reals/" )"real" exponentiation nil )"boolean" notequal nil )OR const-decl "[bool, bool -> bool]" booleans nil )"[numfield, numfield -> numfield]" number_fields nil )"[T, T -> boolean]" equalities nil )AND const-decl "[bool, bool -> bool]" booleans nil )nil naturalnumbers nil )nil integers nil )nil integers nil )"[rational -> boolean]" integers nil )nil rationals nil )"[real -> boolean]" rationals nil )"[numfield, numfield -> numfield]" number_fields nil )"real" interval nil )IF const-decl "[boolean, T, T -> T]" if_def nil )nil number_fields nil )"bool" reals nil )"posint" nil )"nnreal" nil )"(Continuous?)" interval_bolzano nil )"ProperInterval" interval_bolzano nil )"(total_order?[real])" nil )nil interval nil )nil interval_bolzano nil )nil interval nil )"posint" exponentiation nil )"nnreal" interval nil )nil booleans nil )nil booleans nil )NOT const-decl "[bool -> bool]" booleans nil )nil reals nil )nil interval nil )"bool" interval nil )nil defined_types nil )"bool" interval_bolzano nil )nil numbers nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[number_field -> boolean]" reals nil )"bool" reals nil )nil real_types nil )"bool" reals nil )nil real_types nil ))nil )nil 3403636065 ("" (subtype-tcc) nil nil ) nil nil ))nil 3321040119 ("" (grind) nil 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 )"bool" reals nil )nil real_types nil )"bool" interval nil )nil interval nil )"(total_order?[real])" nil )"real" reals nil )"(total_order?[real])" nil )"real" interval nil )"real" interval nil )"Interval" interval nil )"Interval" interval nil )"nonneg_real" sq "reals/" )"bool" interval_bolzano nil )"Interval" interval nil )"bool" interval_bolzano nil )"real" reals nil )"real" reals nil ))nil 3321038737"" (grind) (("" (cancel-by 1 "x!1" ) nil nil )) nil )nil real_props nil )nil real_props nil )nil real_props nil )"real" reals nil )"bool" booleans nil )"(bijective?[T, T])" identity nil )"bool" functions nil )"(strict_total_order?[real])" real_props nil )"boolean" notequal nil )"nnreal" interval_bolzano nil )AND const-decl "[bool, bool -> bool]" booleans nil )nil number_fields nil )nil number_fields nil )"[numfield, nznum -> numfield]" number_fields nil )"[numfield, numfield -> numfield]" number_fields nil )nil real_types nil )nil real_types nil )nil real_props nil )"nzreal" nil )"bool" reals nil )"[T, T -> boolean]" equalities nil )"nnreal" nil )"(total_order?[real])" nil )"(strict_total_order?[real])" real_props nil )"(total_order?[real])" 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 )"bool" reals nil )nil real_types nil )"bool" interval_bolzano nil )"nonneg_real" sq "reals/" )"bool" interval nil )"Interval" interval nil )max const-decl "{p: real | p >= m AND p >= n}" real_defs nil ))nil ))nil 3321039634"" (expand "NonNeg?" )"" (skeep)"" "bolzano_bisect(SqrtProp?(x), [| 0, max(1, x) |], eps)" )"" (expand * "Proper?" "<<" "Ge" )"" (flatten) (("" (assert ) nil nil )) nil )) nil ))nil ))nil ))nil )"bool" interval nil )nil interval nil )nil interval nil )"(total_order?[real])" nil )"nnreal" interval nil )"{z: nonneg_real | z >= x AND z >= y}" real_defs nil )"(total_order?[real])" nil )"(Continuous?)" interval_bolzanonil )nil booleans nil )nil booleans nil )NOT const-decl "[bool -> bool]" booleans nil )nil reals nil )nil interval nil )"bool" interval nil )nil defined_types nil )"bool" interval_bolzano nil )nil numbers nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[number_field -> boolean]" reals nil )"bool" reals nil )nil real_types nil )"bool" reals nil )nil real_types nil )AND const-decl "[bool, bool -> bool]" booleans nil )"bool" interval nil )"bool" reals nil )"real" interval nil )"{Y | Y << X AND Prop?(Y) AND size(Y) <= eps}" interval_bolzanonil )nil real_types nil )"bool" interval_bolzano nil )"Interval" interval nil )max const-decl "{p: real | p >= m AND p >= n}" real_defs nil )"bool" interval nil ))nil ))nil 3321038934"" (skeep)"" (typepred "sqrt_bisect(x, eps)" )"" (expand "sqrt_bisect" )"" "bolzano_bisect(SqrtProp?(x), [| 0, max(1, x) |], eps)" )"" "AA" "bolzano_bisect(SqrtProp?(x), [| 0, max(1, x) |], eps)" )"" (expand * "NonNeg?" "SqrtProp?" "Member?" "Ge" )"" (flatten)"" (both-sides-f -3 "sqrt" )"1" (rewrite "sqrt_sq" )"1" (both-sides-f -4 "sqrt" )"1" (rewrite "sqrt_sq" )"1" (expand "##" ) (("1" (assert ) nil nil ))nil ))nil )"2" (rewrite "sqrt_le" ) nil nil ))nil ))nil )"2" (rewrite "sqrt_le" ) nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"(NonNeg?)" interval_bolzano nil )nil real_types nil )"bool" reals nil )nil real_types nil )nil real_types nil )"bool" reals nil )"[number_field -> boolean]" reals nil )nil number_fields nil )"[number -> boolean]" number_fieldsnil )nil numbers nil )"bool" interval nil )nil interval nil )nil reals nil )NOT const-decl "[bool -> bool]" booleans nil )nil booleans nil )nil booleans nil )max const-decl "{p: real | p >= m AND p >= n}" real_defs nil )"Interval" interval nil )"bool" interval_bolzano nil )"{Y | Y << X AND Prop?(Y) AND size(Y) <= eps}" interval_bolzanonil )"real" interval nil )"bool" reals nil )"bool" interval nil )AND const-decl "[bool, bool -> bool]" booleans nil )"bool" interval_bolzano nil )nil defined_types nil )"bool" interval nil )"(Continuous?)" interval_bolzanonil )"bool" interval nil )"nonneg_real" sq "reals/" )"{nnz: nnreal | nnz * nnz = nnx}" sqrt "reals/" )"[numfield, numfield -> numfield]" number_fields nil )nil number_fields nil )"bool" functions nil )"(bijective?[T, T])" identity nil )"bool" booleans nil )"bool" interval nil )"(total_order?[real])" nil )"{z: nonneg_real | z >= x AND z >= y}" real_defs nil )"nnreal" interval nil )"(total_order?[real])" nil )nil sqrt "reals/" )nil sqrt "reals/" )"[T, T -> boolean]" equalities nil ))quality 100%
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2026-03-28
