(real_fun_on_compact_sets
(IMP_continuity_ms_def_TCC1 0
(IMP_continuity_ms_def_TCC1-1 nil 3460717941
("" (lemma "fullset_metric_space" ) (("" (propax) nil nil )) nil )
((fullset_metric_space formula-decl nil real_fun_on_compact_sets
nil ))
nil ))
(IMP_continuity_ms_def_TCC2 0
(IMP_continuity_ms_def_TCC2-1 nil 3460717941
("" (lemma "real_metric_space" )
(("" (inst - "fullset[real]" ) nil nil )) nil )
((number nonempty-type-decl nil numbers nil )
(boolean nonempty-type-decl nil booleans nil )
(number_field_pred const-decl "[number -> boolean]" number_fields
nil )
(number_field nonempty-type-from-decl nil number_fields nil )
(real_pred const-decl "[number_field -> boolean]" reals nil )
(real nonempty-type-from-decl nil reals nil )
(bool nonempty-type-eq-decl nil booleans nil )
(set type-eq-decl nil sets nil ) (fullset const-decl "set" sets nil )
(real_metric_space formula-decl nil real_metric_space nil ))
nil ))
(cont_on_compact_max 0
(cont_on_compact_max-1 nil 3460718129
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("2"
(hide-all-but (1 2 3))
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(expand "nonempty?" )
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(expand "empty?" )
(("2"
(inst + "n!1" )
(("2"
(expand "upper_bound?" )
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(inst
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("2"
(name
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(("1"
(inst "csl" "seq" )
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(expand "continuous?" )
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(expand "continuous_at?" )
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(("1"
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(lemma
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nil )
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(lemma
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(("2"
(expand
"metric_space?" )
(("2"
(prop)
(("2"
(expand
"space_symmetric?" )
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(inst
-
"p!1"
"seq(n!1)" )
(("1"
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-2)
(("1"
(propax)
nil
nil ))
nil )
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(expand
"fullset" )
(("2"
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nil
nil ))
nil )
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(expand
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(("3"
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("2"
(expand "nonempty?" )
(("2"
(expand "empty?" )
(("2"
(skosimp*)
(("2"
(expand "member" )
(("2"
(inst + "-n!1 - 1" )
(("2"
(expand "lower_bound?" )
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(typepred "s!1" )
(("2"
(expand "image" )
(("2"
(skosimp*)
(("2"
(typepred
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(replace -2)
(("2"
(inst
-
"x!2" )
(("2"
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("3" (expand "nonempty?" )
(("3" (expand "empty?" )
(("3" (expand "member" )
(("3"
(skosimp*)
(("3"
(inst - "f!1(x!1)" )
(("3"
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(("3" (inst + "x!1" ) nil nil ))
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((d formal-const-decl "[T, T -> nnreal]" real_fun_on_compact_sets
nil )
(nnreal type-eq-decl nil real_types nil )
(>= const-decl "bool" reals nil )
(bool nonempty-type-eq-decl nil booleans nil )
(real nonempty-type-from-decl nil reals nil )
(real_pred const-decl "[number_field -> boolean]" reals nil )
(number_field nonempty-type-from-decl nil number_fields nil )
(number_field_pred const-decl "[number -> boolean]" number_fields
nil )
(boolean nonempty-type-decl nil booleans nil )
(number nonempty-type-decl nil numbers nil )
(T formal-nonempty-type-decl nil real_fun_on_compact_sets nil )
(compact_sequence_limit formula-decl nil compactness nil )
(set type-eq-decl nil sets nil )
(x!1 skolem-const-decl "T" real_fun_on_compact_sets nil )
(bounded_below? const-decl "bool" bounded_real_defs nil )
(- const-decl "[numfield -> numfield]" number_fields nil )
(minus_int_is_int application-judgement "int" integers nil )
(p!1 skolem-const-decl "(S!1)" real_fun_on_compact_sets nil )
(seq skolem-const-decl
"[n: nat -> ({s: T | S!1(s) AND f!1(s) < -n})]"
real_fun_on_compact_sets nil )
(i!1 skolem-const-decl "int" real_fun_on_compact_sets nil )
(n!1 skolem-const-decl "above(5 + max(i!1, 0))"
real_fun_on_compact_sets nil )
(lower_bound? const-decl "bool" bounded_real_defs nil )
(p!1 skolem-const-decl "(S!1)" real_fun_on_compact_sets nil )
(seq skolem-const-decl
"[n: nat -> ({s: T | S!1(s) AND f!1(s) > n})]"
real_fun_on_compact_sets nil )
(i!1 skolem-const-decl "int" real_fun_on_compact_sets nil )
(n!1 skolem-const-decl "above(3 + max(i!1, 0))"
real_fun_on_compact_sets nil )
(bounded_above? const-decl "bool" bounded_real_defs nil )
(least_upper_bound? const-decl "bool" bounded_real_defs nil )
(t!2 skolem-const-decl "(S!1)" real_fun_on_compact_sets nil )
(minus_odd_is_odd application-judgement "odd_int" integers nil )
(continuous? const-decl "bool" continuity_ms_def nil )
(continuous_at? const-decl "bool" continuity_ms_def nil )
(ball const-decl "set[T]" metric_spaces nil )
(both_sides_div_pos_lt2 formula-decl nil real_props nil )
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil )
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil )
(rat_minus_rat_is_rat application-judgement "rat" rationals nil )
(NOT const-decl "[bool -> bool]" booleans nil )
(div_mult_pos_lt1 formula-decl nil real_props nil )
(div_mult_pos_le1 formula-decl nil real_props nil )
(both_sides_plus_lt2 formula-decl nil real_props nil )
(div_mult_pos_le2 formula-decl nil real_props nil )
(both_sides_plus_le2 formula-decl nil real_props nil )
(times_div2 formula-decl nil real_props nil )
(pos_times_le formula-decl nil real_props nil )
(pos_times_lt formula-decl nil real_props nil )
(minus_div1 formula-decl nil real_props nil )
(div_mult_pos_lt2 formula-decl nil real_props nil )
(neg_times_le formula-decl nil real_props nil )
(neg_times_lt formula-decl nil real_props nil )
(both_sides_times_pos_lt1 formula-decl nil real_props nil )
(both_sides_times_pos_le1 formula-decl nil real_props nil )
(add_div formula-decl nil real_props nil )
(posint_times_posint_is_posint application-judgement "posint"
integers nil )
(mult_divides1 application-judgement "(divides(n))" divides nil )
(mult_divides2 application-judgement "(divides(m))" divides nil )
(even_times_int_is_even application-judgement "even_int" integers
nil )
(real_times_real_is_real application-judgement "real" reals nil )
(int_times_even_is_even application-judgement "even_int" integers
nil )
(odd_plus_even_is_odd application-judgement "odd_int" integers nil )
(posrat_times_posrat_is_posrat application-judgement "posrat"
rationals nil )
(rat_div_nzrat_is_rat application-judgement "rat" rationals nil )
(int_minus_int_is_int application-judgement "int" integers nil )
(posreal_div_posreal_is_posreal application-judgement "posreal"
real_types nil )
(posint nonempty-type-eq-decl nil integers nil )
(above nonempty-type-eq-decl nil integers nil )
(both_sides_div_pos_ge2 formula-decl nil real_props nil )
(y!1 skolem-const-decl "real" real_fun_on_compact_sets nil )
(real_dist const-decl "nnreal" real_metric_space nil )
(Union const-decl "set" sets nil )
(subset? const-decl "bool" sets nil )
(open? const-decl "bool" metric_spaces nil )
(open_cover? const-decl "bool" compactness nil )
(injective? const-decl "bool" functions nil )
(is_finite const-decl "bool" finite_sets nil )
(finite_cover? const-decl "bool" compactness nil )
(compact? const-decl "bool" compactness nil )
(empty? const-decl "bool" sets nil )
(metric_space? const-decl "bool" metric_spaces_def nil )
(n!2 skolem-const-decl "above(n!1)" real_fun_on_compact_sets nil )
(n!1 skolem-const-decl "posnat" real_fun_on_compact_sets nil )
(seq skolem-const-decl
"[n: nat -> ({s: T | S!1(s) AND y!1 - f!1(s) < 1 / (n + 1)})]"
real_fun_on_compact_sets nil )
(p!1 skolem-const-decl "(S!1)" real_fun_on_compact_sets nil )
(fullset const-decl "set" sets nil )
(space_symmetric? const-decl "bool" metric_spaces_def nil )
(fullset_metric_space formula-decl nil real_fun_on_compact_sets
nil )
(both_sides_plus_gt1 formula-decl nil real_props nil )
(odd? const-decl "bool" integers nil )
(div_times formula-decl nil real_props nil )
(cross_mult formula-decl nil real_props nil )
(odd_times_odd_is_odd application-judgement "odd_int" integers nil )
(both_sides_plus_lt1 formula-decl nil real_props nil )
(* const-decl "[numfield, numfield -> numfield]" number_fields nil )
(TRUE const-decl "bool" booleans nil )
(id const-decl "(bijective?[T, T])" identity nil )
(bijective? const-decl "bool" functions nil )
(both_sides_times_pos_ge1_imp formula-decl nil extra_real_props
nil )
(even_plus_even_is_even application-judgement "even_int" integers
nil )
(times_div1 formula-decl nil real_props nil )
(nonzero_times3 formula-decl nil real_props nil )
(pos_times_gt formula-decl nil real_props nil )
(real_plus_real_is_real application-judgement "real" reals nil )
(posrat_plus_nnrat_is_posrat application-judgement "posrat"
rationals nil )
(nonneg_int nonempty-type-eq-decl nil integers nil )
(posnat nonempty-type-eq-decl nil integers nil )
(archimedean formula-decl nil real_props nil )
(nonneg_real nonempty-type-eq-decl nil real_types nil )
(posreal nonempty-type-eq-decl nil real_types nil )
(> const-decl "bool" reals nil )
(A skolem-const-decl "real" real_fun_on_compact_sets nil )
(real_div_nzreal_is_real application-judgement "real" reals nil )
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil )
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil )
(member const-decl "bool" sets nil )
(t!1 skolem-const-decl "(S!1)" real_fun_on_compact_sets nil )
(S!1 skolem-const-decl "set[T]" real_fun_on_compact_sets nil )
(f!1 skolem-const-decl "[T -> real]" real_fun_on_compact_sets nil )
(upper_bound? const-decl "bool" bounded_real_defs nil )
(posint_plus_nnint_is_posint application-judgement "posint"
integers nil )
(real_minus_real_is_real application-judgement "real" reals nil )
(nnint_plus_posint_is_posint application-judgement "posint"
integers nil )
(posrat_div_posrat_is_posrat application-judgement "posrat"
rationals nil )
(rational_pred const-decl "[real -> boolean]" rationals nil )
(rational nonempty-type-from-decl nil rationals nil )
(integer_pred const-decl "[rational -> boolean]" integers nil )
(int nonempty-type-eq-decl nil integers nil )
(nat nonempty-type-eq-decl nil naturalnumbers nil )
(AND const-decl "[bool, bool -> bool]" booleans nil )
(< const-decl "bool" reals nil )
(numfield nonempty-type-eq-decl nil number_fields nil )
(- const-decl "[numfield, numfield -> numfield]" number_fields nil )
(/= const-decl "boolean" notequal nil )
(nznum nonempty-type-eq-decl nil number_fields nil )
(/ const-decl "[numfield, nznum -> numfield]" number_fields nil )
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil )
(= const-decl "[T, T -> boolean]" equalities nil )
(choose const-decl "(p)" sets nil )
(axiom_of_archimedes formula-decl nil real_props nil )
(rat_max application-judgement "{s: rat | s >= q AND s >= r}"
real_defs nil )
(int_max application-judgement "{k: int | i <= k AND j <= k}"
real_defs nil )
(max const-decl "{p: real | p >= m AND p >= n}" real_defs nil )
(abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs
nil )
(minus_real_is_real application-judgement "real" reals nil )
(n!1 skolem-const-decl "above(2 + max(i!1, 0))"
real_fun_on_compact_sets nil )
(i!1 skolem-const-decl "int" real_fun_on_compact_sets nil )
(seq skolem-const-decl
"[n: nat -> ({s: T | S!1(s) AND f!1(s) > n})]"
real_fun_on_compact_sets nil )
(p!1 skolem-const-decl "(S!1)" real_fun_on_compact_sets nil )
(real_complete formula-decl nil bounded_real_defs nil )
(image const-decl "set[R]" function_image nil )
(bounded? const-decl "bool" bounded_real_defs nil )
(nonempty? const-decl "bool" sets nil ))
nil ))
(cont_on_compact_min 0
(cont_on_compact_min-1 nil 3460718233
("" (skosimp*)
(("" (lemma "cont_on_compact_max" )
(("" (inst - "S!1" "(Lambda (x: T): -f!1(x))" )
(("" (assert )
(("" (prop)
(("1" (skosimp*)
(("1" (inst + "s!1" )
(("1" (skosimp*)
(("1" (inst - "t!1" ) (("1" (assert ) nil nil )) nil ))
nil ))
nil ))
nil )
("2" (expand "continuous?" )
(("2" (skosimp*)
(("2" (inst - "x!1" )
(("2" (expand "continuous_at?" )
(("2" (skosimp*)
(("2" (inst - "epsilon!1" )
(("2" (skosimp*)
(("2" (inst + "delta!1" )
(("2" (skosimp*)
(("2"
(inst - "y!1" )
(("2"
(expand "member" )
(("2"
(expand "ball" )
(("2" (grind) nil nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
((cont_on_compact_max formula-decl nil real_fun_on_compact_sets nil )
(continuous? const-decl "bool" continuity_ms_def nil )
(member const-decl "bool" sets nil )
(NOT const-decl "[bool -> bool]" booleans nil )
(abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs
nil )
(real_dist const-decl "nnreal" real_metric_space nil )
(Union const-decl "set" sets nil )
(subset? const-decl "bool" sets nil )
(open? const-decl "bool" metric_spaces nil )
(d formal-const-decl "[T, T -> nnreal]" real_fun_on_compact_sets
nil )
(nnreal type-eq-decl nil real_types nil )
(open_cover? const-decl "bool" compactness nil )
(injective? const-decl "bool" functions nil )
(is_finite const-decl "bool" finite_sets nil )
(finite_cover? const-decl "bool" compactness nil )
(compact? const-decl "bool" compactness nil )
(empty? const-decl "bool" sets nil )
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil )
(real_minus_real_is_real application-judgement "real" reals nil )
(ball const-decl "set[T]" metric_spaces nil )
(>= const-decl "bool" reals nil )
(nonneg_real nonempty-type-eq-decl nil real_types nil )
(> const-decl "bool" reals nil )
(posreal nonempty-type-eq-decl nil real_types nil )
(continuous_at? const-decl "bool" continuity_ms_def nil )
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil )
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil )
(- const-decl "[numfield -> numfield]" number_fields nil )
(numfield nonempty-type-eq-decl nil number_fields nil )
(real nonempty-type-from-decl nil reals nil )
(real_pred const-decl "[number_field -> boolean]" reals nil )
(number_field nonempty-type-from-decl nil number_fields nil )
(number_field_pred const-decl "[number -> boolean]" number_fields
nil )
(number nonempty-type-decl nil numbers nil )
(set type-eq-decl nil sets nil )
(bool nonempty-type-eq-decl nil booleans nil )
(boolean nonempty-type-decl nil booleans nil )
(T formal-nonempty-type-decl nil real_fun_on_compact_sets nil )
(minus_real_is_real application-judgement "real" reals nil ))
nil )))
Messung V0.5 in Prozent C=100 H=100 G=100
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nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit,
noch Qualität der bereit gestellten Informationen zugesichert.0.62Bemerkung:
(vorverarbeitet am 2026-05-01)
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