(epsilon_lemmas0 1 nil 3253549178 "" (skosimp)"" (lemma "triangle" )"" (inst (epsilon_lemmas"" (auto-rewrite ("() "" (do-rewrite ("(inst-" x1-1 *x2"x2 !) y1!" java.lang.StringIndexOutOfBoundsException: Index 66 out of bounds for length 66"(-decl [, numfield->numfield" number_fields"(y1!1 < e2!1 *absy1!1)) "1" case "abs(x1!1 - y1!1) * abs(x2!1)) "1" (assert (t_times_lt_pos1 real_props"2" (delete -1 (abs_diff formula-decl nil abs_lemsreals") "2" (rewrite "lt_times_lt_pos1" 1 )2 "(lemma " abs_diff") " ( const-decl " {: nonneg_real | n> m AND n = -} real_defs2 " (ssert nil nil) nil)) nil ))nil ))nil ))nil )"2" (delete -1 2 )"2" (rewrite "le_times_le_pos" 1 ) nil nil )) nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )nil real_props nil )nil real_props nil "ool" realsnil )"[ (>= const-ecl " bool realsnil ) (< const- "bool" realsnil )"osreal" nil real_props)"total_order[real]" "(strict_total_order?[real])" real_props nil )nil real_props nil )nil abs_lems "reals/" )nil abs_lems "reals/" )eq -decl nil real_typesnil "real" reals nil )nil )nil )AND const- "bool,bool-> bool" booleansnil )eq -decl nil real_types)"nreal eq decl nil booleans nil )" nil )nil )"(total_order real_types nil) nil )"nnreal" nil )"nnreal" nil )"(strict_total_order?[real]) posreal_times_posreal_is_posreal application-judgement " posreal" "numfield numfield -> numfield]" number_fields nil )nil )"posreal" nil )"[numfield, numfield -> numfield]" number_fields nil )"[numfield, numfield -> numfield]" number_fields nil )eq -decl nil number_fields nil )nil reals nil )"[number_field -> boolean]" reals nil )nil number_fields nil )"[number -> boolean]" number_fieldsnil )nil booleans nil )nil numbers nil )"real" realsnil )eq -declnil number_fields nil )nil )"number_field->boolean]" reals)nil number_fields nil " skolem) "" case "EXISTS (u, v, w : posreal) : 1 /3 and abs(y1!1 ) * v < e!1 /3 and abs(y2!1 ) * w < e!1 /3 ") nil java.lang.StringIndexOutOfBoundsException: Index 68 out of bounds for length 68"1" (inst 1 "min(u!1, w!1)" "v!1" )"1" case "min(u!1, w!1) * v!1 <= u!1 *v!1and abs(y2!1)*minu!1 !)< (y21 !) "1" (flatten) (("1" (assert ) nil nil )) nil )"2" (delete -1 -2 -3 2 )2 "split "1" (rewrite "both_sides_times_pos_le1" )"" (assert ) nil nil ) nil )"2" (rewrite "le_times_le_pos" ) nil nil ))nil ))nil ))nil ))nil ))nil )"2" (deletejava.lang.StringIndexOutOfBoundsException: Index 22 out of bounds for length 22"2 case" min (u1 w!) !1 = u1 *v! abs(y2!1 ),1 <abs!)*w1 " "2" (replace 1 )"2" case "FORALL (1 rewrite both_sides_times_pos_le1) "1" (inst-cp (2 rewrite le_times_le_pos" nil) "1" (inst -1 "abs(y2!1)" "1" 1 "abs(y1 )java.lang.StringIndexOutOfBoundsException: Index 15 out of bounds for length 15 " /(abs(y2!) +1)) "1" (split)"1" (rewrite "div_cancel1" )"1" (assert ) nil nil )) nil )"2" (propax) nil nil ) ("3" (propax) nil ("2" nil ))nil )nil )"" (delete 1 2 )"(!) "f (abs(y2!)+1)" )"" ( div_mult_pos_lt1)nil )nil )nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"{n: nonneg_real | n >= m AND n >= -m}" real_defsnil )"[numfield -> numfield]" number_fields nil )"bool" reals nil )"[numfield, nznum -> numfield]" number_fields nil )nil number_fields )"boolean nil)) " )) eq (2 delete1 2 ) 2 )"ool reals nil) "" (rewrite "times_div1" java.lang.StringIndexOutOfBoundsException: Index 46 out of bounds for length 46eq -ecl nil real_typesnil java.lang.StringIndexOutOfBoundsException: Index 54 out of bounds for length 54"bool" reals nil )nil )AND n> m"real_defs eq -decl nil booleans -constdecl "[numfield > numfield]" number_fields nil nil reals nil )"[ - boolean] reals nil) eq -decl nil number_fields nil )"number ->boolean] number_fields nil )nil booleans nil )eq decl nil number_fields nil )"nreal" nil )"posreal" nil )"posreal" nil )" nonneg_realnonemptytype-eqdeclnilreal_types niljava.lang.StringIndexOutOfBoundsException: Index 58 out of bounds for length 58 min constdecl "{: real| p < m AND p <= n} real_defsnil) nil real_props nil )nil real_props nil )"(total_order?[real])" nil )nil reals nil )"(strict_total_order?[real])" real_propsnil )"posreal" (number_field_pred const-decl"[number -> boolean" number_fieldsnil nil numbers)nil nil "osreal nil )"[numfield, numfield- numfield" number_fields )nil )AND z< } real_defs)eq -decl nil reals nil )nil real_props min constdecl" =m p <n" real_defs nil )"nnreal" nil )nil real_props nil )nil )real_propsjava.lang.StringIndexOutOfBoundsException: Index 20 out of bounds for length 200 "" " skosimp "" (rewrite nnreal_plus_posreal_is_posrealapplication "" nil )nil booleans nil )"number- boolean] number_fields nil )" >boolean]" " reals nil) " skosimp "bool" reals nil )of bounds for length 58AND const-decl "[bool, bool -> bool]" booleans nil )eq -decl 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 )"bool" reals nil )eq -decl nil real_types nil )"(total_order?[real])" nil )"(strict_total_order?[real])" real_props nil )"real" reals nil ))nil ))0 1 nil 3253549178 "" (skosimp)"" (assert )"" (lemma "abs_eq_0" ("x" "x1!1" ))"" (replace 1 )"" (ground)"" (auto-rewrite "zero_times3" )"" case "abs(1 / x1!1 - 1 / y1!1) = abs(x1!1 - y1!1) / (abs(y1!1) * abs(x1!1))" )"1" (lemma "lt_div_lt_pos2" )"1" "abs(x1!1 - y1!1)" "abs(y1!1) * (abs(y1!1) - e1!1)" "abs(y1!1) * abs(x1!1)" "e1!1" )"1" (split)"1" (assert )"1" (replace -2 ) (("1" (propax) nil nil ))nil ))nil )"2" (propax) nil nil )"3" (delete -1 5 )"3" (rewrite "both_sides_times_pos_le2" )"3" "abs_diff" ("x" "y1!1" "y" "x1!1" ))"3" (rewrite "abs_diff_commute" -2 )"3" (assert ) nil nil )) nil ))nil ))nil ))nil ))nil )"2" (delete -1 5 )"2" (case "abs(y1!1) * (abs(y1!1) - e1!1) > 0" )"1" (assert ) nil nil )"2" (delete 2 )"2" (rewrite "pos_times_gt" ) nil nil ))nil ))nil ))nil ))nil ))nil )"2" (delete 5 -1 )"2" rewrite "minus_div1" "abs_div" "abs_mult" )"2" (assert )"2" (rewrite "abs_diff_commute" 1 )"2" (assert ) nil nil )) nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"nnreal" nil )"real" reals nil )"(total_order?[real])" nil )"(strict_total_order?[real])" real_props nil )nil real_props nil )nil real_props nil )nil real_props nil )nil real_props nil )nil real_props nil )nil real_props nil )"(total_order?[real])" nil )nil abs_lems "reals/" )"odd_int" integers nil )nil abs_lems "reals/" )1 skolem-const-decl "posreal" epsilon_lemmas nil )eq -decl nil real_types nil )"bool" reals nil )1 skolem-const-decl "real" epsilon_lemmas nil )nil booleansnil )"(strict_total_order?[real])" real_props nil )"real" reals nil )"[T, T -> boolean]" equalities nil )eq declnil booleansnil )nil )eq -declnil real_types nil "[bool bool - bool]" booleans)eq - 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 )"boolean" notequal nil )eq -decl nil number_fieldsnil "numfield, ->numfield" number_fields nil )"[numfield,numfield -> numfield" number_fieldsnil )nil abs_lems "reals/" )nil numbers nil )nil booleans nil )"[number (numfield nonempty-type-eqdecl nil number_fields nil) nil nil number_fields nil )"[ ->boolean] reals nil) nil reals nil )"nzreal" "numfield - ]" number_fieldsnil "eal reals nil)) nil ))0 1 nil 3253549178 real_ge_is_total_order-judgementtotal_order[eal"" x"" y11 " "" ( (real_minus_real_is_real application" reals )java.lang.StringIndexOutOfBoundsException: Index 69 out of bounds for length 69 "" (case (" (emma "1" ( (" (auto-ewrite" ero_times3") "" (inst absy11 *c!1 ") "1" (split)"1" "" "pz" "bsy1!1) " "" !"" "" 1 ")) "1" (assert )"1" case "e!1 / (1 + e!1) < (1 + e!1) / (1 + e!1)" )"1" (rewrite "div_simp" )"1" (assert ) nil nil )) nil )"2" (rewrite "both_sides_div_pos_lt1" ) nil nil ))nil ))nil )"2" (lemma "both_sides_times_pos_lt2" )"2" (inst -1 "abs(y1! nil) "2" (assert )"2" (delete 2 )"2" (rewrite "div_mult_pos_lt2" ) nil nil ))nil ))nil )nil ))nil )"2" (rewrite "pos_times_gt" ) nil nil ))nil ))nil )"2" (delete 2 3 4 )2 " (inst 1 " ! (2 e!1 ))2 (ewrite"oth_sides_div_pos_lt2" ) ") nil nil)) nil)java.lang.StringIndexOutOfBoundsException: Index 70 out of bounds for length 70 nil )nil ))nil ))nil ))nil )nil reals )"[number_field -> boolean] )) nil number_fields nil )"[number -> boolean]" number_fieldsnil "2" nil abs_lems "reals/" )"[numfield, numfield -> numfield]" number_fields)rewrite "minus_div1 abs_div" ") eq -decl nil number_fields nil )"" (assert ) nil nil )nil )eq -decl nil number_fieldsnil )nil )java.lang.StringIndexOutOfBoundsException: Index 19 out of bounds for length 19nil )"bool" reals nil )eq -decl nil booleans nil )" nil )"posreal" nil )"(strict_total_order?[real])" real_props nil )"[numfield, numfield -> numfield]" number_fields nil )AND const-decl "[bool, bool -> bool]" booleans nil )"[numfield -> numfield]" number_fields nil )"{n: nonneg_real | n >= m AND n >= -m}" real_defsnil )1 skolem-const-decl "real" epsilon_lemmas nil )1 skolem-const-decl "posreal" epsilon_lemmas nil )nil real_props nil )"[numfield, numfield -> numfield]" number_fields nil )"real" reals nil )nil real_props nil )"real" reals nil )nil real_props nil )eq -decl nil reals nil )nil real_props nil )"(strict_total_order?[real])" real_props nil )nil real_props nil )nil real_props nil )"posreal" nil )"nnreal" nil )"(total_order?[real])" nil ))nil ))0 1 nil 3253549178 "" (skosimp*)"" (rewrite "zero_times3" ) (("" (assert ) nil nil )) nil )) nil )"real" reals nil )nil real_props nil )nil nil booleans posrealnonempty-type-eq -declnil real_types )"number- boolean] number_fields nil )nil number_fieldsnil "number_field -> boolean" realsnil )nil reals nil )eq -declnil booleans nil )"ool realsniljava.lang.StringIndexOutOfBoundsException: Index 36 out of bounds for length 36 eq -decl nil real_types)AND -decl"bool bool -> bool]" booleansnil )eq -decl number_fieldsnil )"[numfield -> numfield]" number_fields nil )"{n: nonneg_real | n >= m AND n >= -m}" real_defsnil )"[numfield, numfield -> numfield]" number_fields nil )"bool" reals nil )eq -decl nil real_types nil )"(total_order?[real])" nil )"(strict_total_order?[real])" real_props nil ))nil ))0 1 nil 3253549178 "" (skosimp)"" (lemma "abs_eq_0" ("x" "y1!1" ))"" (assert )"" (lemma "inv_epsilon1" ("y1" "y1!1" "e" "e!1 * abs(y1!1)" ))"1" (assert )"1" (skosimp)"1" (inst 3 "e1!1" )"1" (assert )"1" (rewrite "div_mult_pos_lt1" )"1" "posreal_mult_closed" "numfield numfield - ]" number_fieldsnil "assert ) ) nil ))nil ))nil )nil --declnumbers)nil )nil ))nil ))nil )real_typesjava.lang.StringIndexOutOfBoundsException: Index 20 out of bounds for length 20nil )"((1 rewrite" ") " (2" (rewrite "oth_sides_div_pos_lt1" ) nil nil )nil ))nil numbers nil )nil abs_lems "reals" )"{n: nonneg_real | n >= m AND n >= -m}" real_defsnil )"[numfield -> numfield]" number_fields nil )AND const-decl "[bool, bool -> bool]" booleans nil )"[numfield, numfield -> numfield]" number_fields nil )eq -decl nil number_fields nil )eq -decl nil real_types nil )"bool" reals nil )eq -decl nil real_types nil )"bool" reals nil )eq -decl nil booleans nil )nil epsilon_lemmas nil )"(strict_total_order?[real])" real_props nil )"(strict_total_order?[real])" real_props nil )nil real_axioms nil )nil )"" reals nil )nil real_props nil )"[numfield, numfield -> numfield]" number_fields nil )"" th 20"real" reals nil )"(total_order?[real])" nil ))nil ))0 1 nil 3461939779 "" (skosimp)"" (split)"1" (grind) nil nil )"2" (flatten)"2" (lemma "archimedean" ("px" "x!1-y!1" ))"1" (skosimp)"1" (inst - "1/n!1" ) (("1" (assert ) nil nil )) nil )) nil )"2" (assert ) nil nil ))nil ))nil ))nil ))nil )"(total_order?[real])" nil )"[numfield, numfield -> numfield]" number_fields nil )eq -decl nil number_fields nil )eq -decl nil real_types nil )"bool" reals nil )eq -decl nil real_types nil )"bool" reals nil )eq -decl 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 )nil real_props nil )"real" reals nil )"(total_order?[real])" nil )"(strict_total_order?[real])" real_props nil )AND const-decl "[bool, bool -> bool]" booleans nil )"posrat" nil )"boolean" notequal nil )eq -decl nil number_fields nil )"[numfield, nznum -> numfield]" number_fields nil )"[real -> boolean]" rationals nil )nil rationals nil )"[rational -> boolean]" integers nil )eq -decl nil integers nil )eq -decl nil integers nil )eq -decl nil integers nil )"(strict_total_order?[real])" real_props nil )"real" reals nil ))nil )))
Messung V0.5 in Prozent C=100 H=100 G=100
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