Quelle lim_of_functions.prf
Sprache: Lisp
(lim_of_functionsnil 3299406886"" (expand "convergence" )"" (expand "convergence" )"" (expand "fullset" ) (("" (propax) nil nil )) nil )) nil ))nil )"real" reals nil )"bool" convergence_functions nil )"set" sets nil )"bool" lim_of_functions nil ))nil ))nil 3299406886"" (auto-rewrite "fullset" "member_adherent[T]" )"" (skolem!) (("" (assert ) nil nil )) nil )) nil )"set" sets nil )nil lim_of_functions nil )"[real -> boolean]" lim_of_functions nil )nil reals nil )"[number_field -> boolean]" reals nil )nil number_fields nil )"[number -> boolean]" number_fieldsnil )nil booleans nil )nil numbers nil )nil convergence_functions nil ))nil ))nil 3299406886"" (skosimp)"" (expand "convergence" )"" (use "convergence_unicity[T]" ) (("" (assert ) nil nil )) nil ))nil ))nil )"bool" lim_of_functions nil )nil booleans nil )nil defined_types nil )set type-eq-decl nil sets nil ) (fullset const-decl "set" sets nil )nil lim_of_functions nil )"[real -> boolean]" lim_of_functions nil )nil reals nil )"[number_field -> boolean]" reals nil )nil number_fields nil )"[number -> boolean]" number_fieldsnil )nil booleans nil )nil numbers nil )nil convergence_functions nil ))nil ))nil 3299406886"" (skosimp)"" (expand "convergence" )"" (use "convergence_in_domain[T]" )"" (expand "fullset" ) (("" (assert ) nil nil )) nil )) nil ))nil ))nil )"bool" lim_of_functions nil )nil booleans nil )nil defined_types nil )set type-eq-decl nil sets nil ) (fullset const-decl "set" sets nil )nil lim_of_functions nil )"[real -> boolean]" lim_of_functions nil )nil reals nil )"[number_field -> boolean]" reals nil )nil number_fields nil )"[number -> boolean]" number_fieldsnil )nil booleans nil )nil numbers nil )nil convergence_functions nil ))nil ))nil 3299406886"" (expand "convergence" )"" (grind :defs nil :rewrites "convergence_sum[T]" ) nil nil ))nil )"real" reals nil )nil convergence_functions nil )"[real -> boolean]" lim_of_functions nil )nil lim_of_functions nil )nil reals nil )"[number_field -> boolean]" reals nil )nil number_fields nil )"[number -> boolean]" number_fieldsnil )nil numbers nil )NOT const-decl "[bool -> bool]" booleans nil )nil booleans nil )nil booleans nil )"bool" lim_of_functions nil ))nil ))nil 3299406886"" (expand "convergence" )"" (grind :defs nil :rewrites "convergence_diff[T]" ) nil nil ))nil )"real" reals nil )nil convergence_functions nil )"[real -> boolean]" lim_of_functions nil )nil lim_of_functions nil )nil reals nil )"[number_field -> boolean]" reals nil )nil number_fields nil )"[number -> boolean]" number_fieldsnil )nil numbers nil )NOT const-decl "[bool -> bool]" booleans nil )nil booleans nil )nil booleans nil )"bool" lim_of_functions nil ))nil ))nil 3299406886"" (expand "convergence" )"" (grind :defs nil :rewrites "convergence_prod[T]" ) nil nil ))nil )"real" reals nil )nil convergence_functions nil )"[real -> boolean]" lim_of_functions nil )nil lim_of_functions nil )nil reals nil )"[number_field -> boolean]" reals nil )nil number_fields nil )"[number -> boolean]" number_fieldsnil )nil numbers nil )NOT const-decl "[bool -> bool]" booleans nil )nil booleans nil )nil booleans nil )"bool" lim_of_functions nil ))nil ))nil 3299406886"" (expand "convergence" )"" (grind :defs nil :rewrites "convergence_const[T]" ) nil nil ))nil )nil convergence_functions 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]" lim_of_functions nil )nil lim_of_functions nil )"bool" lim_of_functions nil ))nil ))nil 3299406886"" (expand "convergence" )"" (grind :defs nil :rewrites "convergence_scal[T]" ) nil nil ))nil )"real" reals nil )nil convergence_functions nil )"[real -> boolean]" lim_of_functions nil )nil lim_of_functions nil )nil reals nil )"[number_field -> boolean]" reals nil )nil number_fields nil )"[number -> boolean]" number_fieldsnil )nil numbers nil )NOT const-decl "[bool -> bool]" booleans nil )nil booleans nil )nil booleans nil )"bool" lim_of_functions nil ))nil ))nil 3299406886"" (expand "convergence" )"" (grind :defs nil :rewrites "convergence_neg[T]" ) nil nil ))nil )"real" reals nil )nil convergence_functions nil )"[real -> boolean]" lim_of_functions nil )nil lim_of_functions nil )nil reals nil )"[number_field -> boolean]" reals nil )nil number_fields nil )"[number -> boolean]" number_fieldsnil )nil numbers nil )NOT const-decl "[bool -> bool]" booleans nil )nil booleans nil )nil booleans nil )"bool" lim_of_functions nil ))nil ))nil 3299406886"" (expand "convergence" )"" (grind :defs nil :rewrites "convergence_div[T]" ) nil nil ))nil )"real" reals nil )nil convergence_functions nil )"[real -> boolean]" lim_of_functions nil )nil lim_of_functions nil )nil reals nil )"[number_field -> boolean]" reals nil )nil number_fields nil )"[number -> boolean]" number_fieldsnil )nil numbers nil )NOT const-decl "[bool -> bool]" booleans nil )nil booleans nil )nil booleans nil )"bool" lim_of_functions nil ))nil ))nil 3299406886"" (expand "convergence" )"" (grind :defs nil :rewrites "convergence_inv[T]" ) nil nil ))nil )"nzreal" nil )nil convergence_functions nil )"[real -> boolean]" lim_of_functions nil )nil lim_of_functions nil )nil reals nil )"[number_field -> boolean]" reals nil )nil number_fields nil )"[number -> boolean]" number_fieldsnil )nil numbers nil )NOT const-decl "[bool -> bool]" booleans nil )nil booleans nil )nil booleans nil )"bool" lim_of_functions nil ))nil ))nil 3299406886"" (expand "convergence" )"" (grind :defs nil :rewrites "convergence_identity[T]" ) nil nil ))nil )nil convergence_functions 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]" lim_of_functions nil )nil lim_of_functions nil )"bool" lim_of_functions nil ))nil ))nil 3299407298"" (expand "convergence" )"" (skosimp*)"" (expand "restrict" )"" (expand "convergence" )"" (skosimp*)"" (expand "fullset" )"" (inst + "epsilon!1" )"" (skosimp*) (("" (grind) nil nil )) nil )) nil ))nil ))nil ))nil ))nil ))nil ))nil )"real" reals nil )"bool" convergence_functions nil )"set" sets nil )"odd_int" integers nil )"real" reals nil )"{n: nonneg_real | n >= m AND n >= -m}" real_defsnil )"(strict_total_order?[real])" real_props 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 )"R" restrict nil )"bool" lim_of_functions nil ))nil )nil 3299406896"" (expand "convergence" )"" (skosimp*)"" (expand "restrict" )"" (expand "convergence" )"" (prop)"1" (lemma "adherence_fullset" )"1" (inst?)"1" (assert )"1" (typepred "a!1" ) (("1" (postpone) nil nil ))nil ))nil ))nil ))nil )"2" (skosimp*)"2" (expand "fullset" )"2" (inst + "epsilon!1" )"2" (skosimp*) (("2" (grind) nil nil )) nil )) nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )nil shostak))nil 3299423322"" (skosimp*)"" (prop)"1" (expand "convergence" )"1" (expand "fullset" )"1" (expand "convergence" )"1" (flatten)"1" (assert )"1" (skosimp*)"1" (inst -2 "epsilon!1" )"1" (skosimp*)"1" (inst + "delta!1" )"1" (skosimp*)"1" (inst?)"1" (assert ) (("1" (grind) nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" (expand "convergence" )"2" (expand "fullset" )"2" (expand "convergence" )"2" (flatten)"2" (assert )"2" (skosimp*)"2" (inst -2 "epsilon!1" )"2" (skosimp*)"2" (inst + "delta!1" )"2" (skosimp*)"2" (inst?)"2" (assert ) (("2" (grind) nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"set" sets nil )"(total_order?[real])" nil )"(strict_total_order?[real])" real_props nil )"[T -> nonneg_real]" real_fun_ops "reals/" )"setof[real]" convergence_functions nil )"{n: nonneg_real | n >= m AND n >= -m}" real_defsnil )"real" reals nil )"[real -> boolean]" lim_of_functions nil )nil lim_of_functions 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 )"bool" convergence_functions nil )"real" reals nil )"bool" lim_of_functions nil ))nil ))nil 3445335777"" "(LAMBDA (d: [f: [T -> real], {a | convergent?(f, a)}]): LAMBDA l : convergence(d`1, d`2, l)))") "" (skosimp*)"" (expand "nonempty?" )"" (expand "empty?" )"" (expand "member" )"" (expand "convergence" )"" (typepred "d!1`2" )"" (expand "convergent?" )"" (skosimp*)"" (inst - "l!1" )"" (expand "convergence" -1)"" (propax) nil nil )) nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"bool" sets nil )NOT const-decl "[bool -> bool]" booleans nil )"bool" sets nil )"(p)" sets nil )"bool" sets nil )set type-eq-decl nil sets nil )"bool" lim_of_functions nil )"bool" lim_of_functions nil )nil booleans nil )nil lim_of_functions nil )"[real -> boolean]" lim_of_functions nil )nil reals nil )"[number_field -> boolean]" reals nil )nil number_fields nil )"[number -> boolean]" number_fieldsnil )nil booleans nil )nil numbers nil ))nil ))nil 3299406886"" (skolem!)"" (name-replace "ll" "lim(f!1, x0!1)" :hide? nil )"" (expand "lim" -)"" "epsilon_ax" "p" "LAMBDA (l: real): convergence(f!1, x0!1, l)" ))"" (assert )"" (typepred "x0!1" )"" (expand "convergent?" ) (("" (propax) nil nil )) nil ))nil ))nil ))nil ))nil ))nil ))nil )nil numbers nil )nil booleans nil )"[T, T -> boolean]" equalities nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[number_field -> boolean]" reals nil )nil reals nil )"[real -> boolean]" lim_of_functions nil )nil lim_of_functions nil )nil booleans nil )"bool" lim_of_functions nil )"bool" lim_of_functions nil )"{l: real | convergence(f, x0, l)}" nil )nil epsilons nil )nil defined_types nil ))nil ))nil 3299406886"" (skolem!)"" (use "lim_fun_lemma" )"" (ground)"" (use "cv_unique" ("l2" "lim(f!1, x0!1)" ))"" (assert ) nil nil )) nil ))nil ))nil ))nil )nil lim_of_functions nil )"bool" lim_of_functions nil )nil booleans nil )nil lim_of_functions nil )"[real -> boolean]" lim_of_functions nil )nil reals nil )"[number_field -> boolean]" reals nil )nil number_fields nil )"[number -> boolean]" number_fieldsnil )nil booleans nil )nil numbers nil )nil lim_of_functions nil )"bool" lim_of_functions nil )"{l: real | convergence(f, x0, l)}" nil ))nil ))nil 3474799555"" (skosimp*)"" (rewrite "lim_fun_def" )"" (expand "convergence" )"" (expand "fullset" )"" (expand "convergence" )"" (typepred "l!1" )"" (split +)"1" (flatten) nil nil )"2" (flatten)"2" (split +)"1" (expand "adh" )"1" (skosimp*)"1" (assert )"1" (expand "convergent?" )"1" (skosimp*)"1" expand "convergence" )"1" expand "convergence" )"1" "1" expand "adh" )"1" "e!1" )"1" "1" "x!1" )nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" (propax) nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )nil lim_of_functions 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]" lim_of_functions nil )nil lim_of_functions nil )nil booleans nil )"bool" lim_of_functions nil )"set" sets nil )NOT const-decl "[bool -> bool]" booleans nil )"setof[real]" convergence_functions nil )"bool" reals nil )nil real_types nil )"bool" reals nil )nil real_types nil )"bool" convergence_functions nil )"bool" lim_of_functions nil )"real" reals nil ))nil 3299406886"" (skolem!)"" (prop)"1" (expand "convergent?" ) (("1" (inst?) nil nil )) nil )"2" (rewrite "lim_fun_def" )"2" (expand "convergent?" ) (("2" (inst?) nil nil )) nil )) nil )"3" (rewrite "lim_fun_def" ) nil nil ))nil ))nil )nil reals nil )"[number_field -> boolean]" reals nil )nil number_fields nil )"[number -> boolean]" number_fieldsnil )nil booleans nil )nil numbers nil )"bool" lim_of_functions nil )nil booleans nil )nil lim_of_functions nil )"[real -> boolean]" lim_of_functions nil )nil lim_of_functions nil ))nil ))nil 3445684497"" (grind :exclude "convergence" )"" (forward-chain "cv_in_domain" ) (("" (assert ) nil nil )) nil ))nil )nil lim_of_functions 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]" lim_of_functions nil )nil lim_of_functions nil )"bool" lim_of_functions nil ))nil ))nil 3299406886"" (skosimp)"" (rewrite "lim_fun_def" )"" (rewrite "convergent_in_domain" ) nil nil )) nil ))nil )nil lim_of_functions 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]" lim_of_functions nil )nil lim_of_functions nil )nil booleans nil )"bool" lim_of_functions nil )nil lim_of_functions nil ))nil ))nil 3445684383"" (expand "convergent?" )"" (skosimp*)"" (inst 1 "l!1 + l!2" ) (("" (rewrite "cv_sum" ) nil nil )) nil ))nil ))nil )nil lim_of_functions nil )"[real -> boolean]" lim_of_functions nil )nil lim_of_functions nil )"[numfield, numfield -> numfield]" number_fields nil )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" reals nil )"bool" lim_of_functions nil ))nil )nil 3299406886"" (expand "convergent" )"" (skosimp*)"" (inst 1 "l!1 + l!2" ) (("" (rewrite "cv_sum" ) nil nil )) nil ))nil ))nil )nil nil ))nil 3445684395"" (expand "convergent?" )"" (skosimp*)"" (forward-chain "cv_neg" ) (("" (inst?) nil nil )) nil )) nil ))nil )nil number_fields nil )"[numfield -> numfield]" number_fields nil )"real" reals nil )nil lim_of_functions nil )"[real -> boolean]" lim_of_functions nil )nil reals nil )"[number_field -> boolean]" reals nil )nil number_fields nil )"[number -> boolean]" number_fieldsnil )nil booleans nil )nil numbers nil )nil lim_of_functions nil )"bool" lim_of_functions nil ))nil )nil 3299406886"" (expand "convergent" )"" (skosimp*)"" (forward-chain "cv_neg" ) (("" (inst?) nil nil )) nil )) nil ))nil )nil nil ))nil 3299406886"" (expand "convergent?" )"" (skosimp*)"" (inst 1 "l!1 - l!2" ) (("" (rewrite "cv_diff" ) nil nil ))nil ))nil ))nil )nil lim_of_functions nil )"[real -> boolean]" lim_of_functions nil )nil lim_of_functions nil )"[numfield, numfield -> numfield]" number_fields nil )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" reals nil )"bool" lim_of_functions nil ))nil ))nil 3299406886"" (expand "convergent?" )"" (skosimp*)"" (inst 1 "l!1 * l!2" ) (("" (rewrite "cv_prod" ) nil nil ))nil ))nil ))nil )nil lim_of_functions nil )"[real -> boolean]" lim_of_functions nil )nil lim_of_functions nil )"[numfield, numfield -> numfield]" number_fields nil )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" reals nil )"bool" lim_of_functions nil ))nil ))nil 3299406886"" (expand "convergent?" )"" (skolem!)"" (inst?) (("" (rewrite "cv_const" ) nil nil )) nil )) nil ))nil )nil lim_of_functions nil )nil booleans nil )nil defined_types nil )"[real -> boolean]" lim_of_functions nil )nil lim_of_functions nil )"setof[real]" convergence_functions nil )set type-eq-decl nil sets nil ) (fullset const-decl "set" sets nil )nil reals nil )"[number_field -> boolean]" reals nil )nil number_fields nil )"[number -> boolean]" number_fieldsnil )nil booleans nil )nil numbers nil )"bool" lim_of_functions nil ))nil ))nil 3299406886"" (expand "convergent?" )"" (skosimp*)"" (inst 1 "b!1 * l!1" ) (("" (rewrite "cv_scal" ) nil nil ))nil ))nil ))nil )nil lim_of_functions nil )"[real -> boolean]" lim_of_functions nil )nil lim_of_functions nil )"[numfield, numfield -> numfield]" number_fields nil )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" reals nil )"bool" lim_of_functions nil ))nil ))nil 3299406886"" (skosimp)"" (rewrite "lim_fun_def" )"" (expand "convergent?" )"" (skosimp)"" (assert )"" (inst 2 "1/l!1" ) (("" (rewrite "cv_inv" ) nil nil ))nil ))nil ))nil ))nil ))nil ))nil )nil lim_of_functions 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]" lim_of_functions nil )nil lim_of_functions nil )"boolean" notequal nil )nil reals nil )nil booleans nil )"bool" lim_of_functions nil )"nzreal" nil )"[numfield, nznum -> numfield]" number_fields nil )nil number_fields nil )nil number_fields nil )nil lim_of_functions nil ))nil ))nil 3299406886"" (skosimp)"" (rewrite "lim_fun_def" )"" (expand "convergent?" )"" (skosimp*)"" (assert )"" (inst 2 "l!1 / l!2" ) (("" (rewrite "cv_div" ) nil nil ))nil ))nil ))nil ))nil ))nil ))nil )nil lim_of_functions 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]" lim_of_functions nil )nil lim_of_functions nil )"boolean" notequal nil )nil reals nil )nil booleans nil )"bool" lim_of_functions nil )"real" reals nil )"[numfield, nznum -> numfield]" number_fields nil )nil number_fields nil )nil number_fields nil )nil lim_of_functions nil ))nil ))nil 3299406886"" (skolem!)"" (expand "convergent?" )"" (use "cv_identity" ) (("" (inst?) nil nil )) nil )) nil ))nil )"bool" lim_of_functions nil )nil numbers nil )nil booleans nil )"[number -> boolean]" number_fieldsnil )nil number_fields nil )"[number_field -> boolean]" reals nil )nil reals nil )nil booleans nil )nil defined_types nil )"[real -> boolean]" lim_of_functions nil )nil lim_of_functions nil )"setof[real]" convergence_functions nil )set type-eq-decl nil sets nil ) (fullset const-decl "set" sets nil )nil lim_of_functions nil ))nil ))nil 3299406886"" (skosimp) (("" (rewrite "sum_fun_convergent" ) nil nil )) nil )nil lim_of_functions 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]" lim_of_functions nil )nil lim_of_functions nil ))nil ))nil 3299406886"" "lim_fun_lemma" "lim_fun_def" "sum_fun_convergent" "cv_sum" ))"" (skosimp) (("" (assert ) nil nil )) nil )) nil )nil lim_of_functions nil )nil lim_of_functions nil )nil lim_of_functions nil )"real" reals nil ))nil ))nil 3299406886"" (lemma "neg_fun_convergent" ) (("" (propax) nil nil )) nil )nil lim_of_functions nil )) nil ))nil 3299406886"" "lim_fun_lemma" "lim_fun_def" "neg_fun_convergent" "cv_neg" ))"" (skosimp) (("" (assert ) nil nil )) nil )) nil )nil lim_of_functions nil )nil lim_of_functions nil )nil lim_of_functions nil )"real" reals nil ))nil ))nil 3299406886"" (skosimp) (("" (rewrite "diff_fun_convergent" ) nil nil )) nil )nil lim_of_functions 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]" lim_of_functions nil )nil lim_of_functions nil ))nil ))nil 3299406886"" "lim_fun_lemma" "lim_fun_def" "diff_fun_convergent" "cv_diff" ))"" (skosimp) (("" (assert ) nil nil )) nil )) nil )nil lim_of_functions nil )nil lim_of_functions nil )nil lim_of_functions nil )"real" reals nil ))nil ))nil 3299406886"" (skosimp) (("" (rewrite "prod_fun_convergent" ) nil nil )) nil )nil lim_of_functions 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]" lim_of_functions nil )nil lim_of_functions nil ))nil ))nil 3299406886"" "lim_fun_lemma" "lim_fun_def" "prod_fun_convergent" "cv_prod" ))"" (skosimp) (("" (assert ) nil nil )) nil )) nil )nil lim_of_functions nil )nil lim_of_functions nil )nil lim_of_functions nil )"real" reals nil ))nil ))nil 3299406886"" (lemma "const_fun_convergent" ) (("" (propax) nil nil )) nil )nil lim_of_functions nil )) nil ))nil 3299406886"" "lim_fun_lemma" "lim_fun_def" "const_fun_convergent" "cv_const" ))"" (skosimp) (("" (assert ) nil nil )) nil )) nil )nil lim_of_functions nil )nil lim_of_functions nil ))nil ))nil 3299406886"" (lemma "scal_fun_convergent" ) (("" (propax) nil nil )) nil )nil lim_of_functions nil )) nil ))nil 3299406886"" "lim_fun_lemma" "lim_fun_def" "scal_fun_convergent" "cv_scal" )"" (skosimp) (("" (assert ) nil nil )) nil )) nil )nil lim_of_functions nil )nil lim_of_functions nil )nil lim_of_functions nil )"real" reals nil ))nil ))nil 3299406886"" (skosimp) (("" (rewrite "inv_fun_convergent" ) nil nil )) nil )nil lim_of_functions 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]" lim_of_functions nil )nil lim_of_functions nil )"boolean" notequal nil )nil reals nil ))nil ))nil 3299406886"" (skosimp)"" (assert )"" (delete 1)"" "lim_fun_def" "lim_fun_lemma" "inv_fun_convergent" ("cv_inv" ))"" (assert ) nil nil )) nil ))nil ))nil ))nil )"nzreal" nil )nil lim_of_functions nil )nil lim_of_functions nil ))nil ))nil 3299406886"" (skosimp) (("" (rewrite "div_fun_convergent" ) nil nil )) nil )nil lim_of_functions 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]" lim_of_functions nil )nil lim_of_functions nil )"boolean" notequal nil )nil reals nil ))nil ))nil 3299406886"" (skosimp)"" (assert )"" (delete 1)"" "lim_fun_def" "lim_fun_lemma" "div_fun_convergent" "cv_div" )"" (assert ) nil nil )) nil ))nil ))nil ))nil )"real" reals nil )nil lim_of_functions nil )nil lim_of_functions nil ))nil ))nil 3299406886"" (lemma "convergent_identity" ) (("" (propax) nil nil )) nil )nil lim_of_functions nil )) nil ))nil 3299406886"" "lim_fun_lemma" "lim_fun_def" "convergent_identity" "cv_identity" )"" (skolem!) (("" (assert ) nil nil )) nil )) nil )nil lim_of_functions nil )nil lim_of_functions nil ))nil ))nil 3299406886"" (skosimp)"" (assert )"" (name-replace "ll" "lim(f!1, a!1)" :hide? nil )"" (rewrite "lim_fun_def" )"" (expand "convergence" )"" (use "convergence_upper_bound[T]" )"" (ground)"" (delete -1 -2 2) (("" (grind) nil nil )) nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"(total_order?[real])" nil )nil lim_of_functions nil )nil convergence_functionsnil )nil defined_types nil )set type-eq-decl nil sets nil ) (fullset const-decl "set" sets nil )"{l: real | convergence(f, x0, l)}" nil )"bool" lim_of_functions nil )"bool" lim_of_functions nil )nil booleans nil )nil lim_of_functions nil )"[real -> boolean]" lim_of_functions nil )nil reals nil )"[number_field -> boolean]" reals nil )nil number_fields nil )"[number -> boolean]" number_fieldsnil )"[T, T -> boolean]" equalities nil )nil booleans nil )nil numbers nil ))nil ))nil 3299406886"" (skosimp)"" (assert )"" (name-replace "ll" "lim(f!1, a!1)" :hide? nil )"" (rewrite "lim_fun_def" )"" (expand "convergence" )"" (use "convergence_lower_bound[T]" ("b" "b!1" ))"" (ground)"" (delete -1 -2 2)"" (grind :if-match nil )"" (inst?) (("" (assert ) nil nil )) nil )) nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"(total_order?[real])" nil )nil lim_of_functions nil )nil convergence_functionsnil )nil defined_types nil )set type-eq-decl nil sets nil ) (fullset const-decl "set" sets nil )"(total_order?[real])" nil )"{l: real | convergence(f, x0, l)}" nil )"bool" lim_of_functions nil )"bool" lim_of_functions nil )nil booleans nil )nil lim_of_functions nil )"[real -> boolean]" lim_of_functions nil )nil reals nil )"[number_field -> boolean]" reals nil )nil number_fields nil )"[number -> boolean]" number_fieldsnil )"[T, T -> boolean]" equalities nil )nil booleans nil )nil numbers nil ))nil ))nil 3299406886"" (skosimp)"" (assert )"" (name-replace "ll1" "lim(f1!1, a!1)" :hide? nil )"" (name-replace "ll2" "lim(f2!1, a!1)" :hide? nil )"" (rewrite "lim_fun_def" )"" (rewrite "lim_fun_def" )"" (expand "convergence" )"" "convergence_order[T]" ("l1" "ll1" "l2" "ll2" ))"" (ground)"" (expand "fullset" +) (("" (propax) nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"(total_order?[real])" nil )nil convergence_functions nil )nil defined_types nil )set type-eq-decl nil sets nil ) (fullset const-decl "set" sets nil )nil lim_of_functions nil )"{l: real | convergence(f, x0, l)}" nil )"bool" lim_of_functions nil )"bool" lim_of_functions nil )nil booleans nil )nil lim_of_functions nil )"[real -> boolean]" lim_of_functions nil )nil reals nil )"[number_field -> boolean]" reals nil )nil number_fields nil )"[number -> boolean]" number_fieldsnil )"[T, T -> boolean]" equalities nil )nil booleans nil )nil numbers nil ))nil ))nil 3299406886"" (skosimp)"" (assert )"" (name-replace "ll" "lim(f!1, a!1)" :hide? nil )"" (rewrite "lim_fun_def" )"" (expand "convergence" )"" (use "subset_convergence2[T]" ("E1" "E!1" ))"" (ground)"1" (delete -2 -3)"1" (use "convergence_upper_bound[T]" )"1" (assert ) nil nil )) nil ))nil )"2" (rewrite "subset_fullset" ) nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"(total_order?[real])" nil )nil lim_of_functions nil )nil defined_types nil )nil convergence_functions nil )set type-eq-decl nil sets nil ) (fullset const-decl "set" sets nil )"setof[real]" convergence_functions nil )nil sets_lemmas nil )nil convergence_functionsnil )"(partial_order?[set[T]])" nil )"{l: real | convergence(f, x0, l)}" nil )"bool" lim_of_functions nil )"bool" lim_of_functions nil )nil booleans nil )nil lim_of_functions nil )"[real -> boolean]" lim_of_functions nil )nil reals nil )"[number_field -> boolean]" reals nil )nil number_fields nil )"[number -> boolean]" number_fieldsnil )"[T, T -> boolean]" equalities nil )nil booleans nil )nil numbers nil ))nil ))nil 3299406886"" (skosimp)"" (assert )"" (name-replace "ll" "lim(f!1, a!1)" :hide? nil )"" (rewrite "lim_fun_def" )"" (expand "convergence" )"" (use "subset_convergence2[T]" ("E1" "E!1" ))"" (ground)"1" (delete -2 -3)"1" (use "convergence_lower_bound[T]" ("b" "b!1" ))"1" (ground)"1" (delete -1 -2 2)"1" (skosimp)"1" (inst?) (("1" (assert ) nil nil )) nil ))nil ))nil ))nil ))nil ))nil )"2" (rewrite "subset_fullset" ) nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"(total_order?[real])" nil )nil lim_of_functions nil )nil defined_types nil )nil convergence_functions nil )set type-eq-decl nil sets nil ) (fullset const-decl "set" sets nil )"setof[real]" convergence_functions nil )nil sets_lemmas nil )"(total_order?[real])" nil )nil convergence_functionsnil )"(partial_order?[set[T]])" nil )"{l: real | convergence(f, x0, l)}" nil )"bool" lim_of_functions nil )"bool" lim_of_functions nil )nil booleans nil )nil lim_of_functions nil )"[real -> boolean]" lim_of_functions nil )nil reals nil )"[number_field -> boolean]" reals nil )nil number_fields nil )"[number -> boolean]" number_fieldsnil )"[T, T -> boolean]" equalities nil )nil booleans nil )nil numbers nil ))nil ))nil 3299406886"" (skosimp)"" (assert )"" (name-replace "ll1" "lim(f1!1, a!1)" :hide? nil )"" (name-replace "ll2" "lim(f2!1, a!1)" :hide? nil )"" (rewrite "lim_fun_def" )"" (rewrite "lim_fun_def" )"" (expand "convergence" )"" (use "subset_convergence2[T]" ("E1" "E!1" ))"" "subset_convergence2[T]" "E1" "E!1" "f" "f1!1" ))"" (rewrite "subset_fullset" )"" (ground)"" (delete -3 -4 -5 -6)"" (forward-chain "convergence_order[T]" )nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"(total_order?[real])" nil )nil defined_types nil )nil convergence_functions nil )set type-eq-decl nil sets nil ) (fullset const-decl "set" sets nil )"setof[real]" convergence_functions nil )nil sets_lemmas nil )nil convergence_functions nil )nil lim_of_functions nil )"{l: real | convergence(f, x0, l)}" nil )"bool" lim_of_functions nil )"bool" lim_of_functions nil )nil booleans nil )nil lim_of_functions nil )"[real -> boolean]" lim_of_functions nil )nil reals nil )"[number_field -> boolean]" reals nil )nil number_fields nil )"[number -> boolean]" number_fieldsnil )"[T, T -> boolean]" equalities nil )nil booleans nil )nil numbers nil ))nil )))quality 95%
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