(interval_reals
(open_ball?_lem 0
(open_ball?_lem-1 nil 3258223423 3292322828
("" (skosimp*)
(("" (prop)
(("1" (expand "open_ball?" )
(("1" (skosimp*)
(("1" (expand "open_ball" )
(("1" (expand "subset?" )
(("1" (expand "member" )
(("1" (inst + "delta!1" ) nil nil )) nil ))
nil ))
nil ))
nil ))
nil )
("2" (expand "open_ball?" )
(("2" (skosimp*)
(("2" (expand "subset?" )
(("2" (expand "member" )
(("2" (expand "open_ball" ) (("2" (inst + "r!1" ) nil nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
unchecked
((subset? const-decl "bool" sets 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 )
(>= 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 )
(member const-decl "bool" sets nil )
(open_ball const-decl "set[T]" open_sets nil )
(open_ball? const-decl "bool" open_sets nil ))
30503 110 nil nil ))
(open?_lem 0
(open?_lem-1 nil 3258223381 3292322828
("" (skosimp*) (("" (expand "open?" ) (("" (inst?) nil nil )) nil ))
nil )
unchecked
((open? const-decl "bool" open_sets 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 )
(T_pred const-decl "[real -> boolean]" open_sets nil )
(T formal-subtype-decl nil open_sets nil )
(bool nonempty-type-eq-decl nil booleans nil )
(set type-eq-decl nil sets nil ) nil nil )
20 20 t shostak))
(Open_empty 0
(Open_empty-1 nil 3320064681 3320064682 ("" (skosimp*) nil nil )
proved nil 1331 130 t shostak))
(open_intv_open 0
(open_intv_open-1 nil 3258299476 3292322828
("" (skosimp*)
(("" (expand "open?" )
(("" (skosimp*)
(("" (expand "open_ball?" )
(("" (inst + "min(x!1 -a!1,b!1-x!1)" )
(("1" (skosimp*) (("1" (grind) nil nil )) nil )
("2" (grind) nil nil ))
nil ))
nil ))
nil ))
nil ))
nil )
unchecked
((open? const-decl "bool" open_sets nil )
(open_ball? const-decl "bool" open_sets nil )
(abs const-decl "{n: nonneg_real | n >= m}" real_defs nil )
(posreal nonempty-type-eq-decl nil real_types nil )
(nonneg_real nonempty-type-eq-decl nil real_types nil )
(boolean nonempty-type-decl nil booleans nil )
(bool nonempty-type-eq-decl nil booleans nil )
(AND const-decl "[bool, bool -> bool]" booleans nil )
(number nonempty-type-decl nil numbers 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 )
(>= const-decl "bool" reals nil ) (<= const-decl "bool" reals nil )
(min const-decl "{p: real | p <= m AND p <= n}" real_defs nil )
(numfield nonempty-type-eq-decl nil number_fields nil )
(- const-decl "[numfield, numfield -> numfield]" number_fields nil )
(T_pred const-decl "[real -> boolean]" open_sets nil )
(T formal-subtype-decl nil open_sets nil )
(< const-decl "bool" reals nil ) nil nil nil
(> const-decl "bool" reals nil ))
224 220 t shostak))
(above_intv_open 0
(above_intv_open-1 nil 3258299818 3292322829
("" (skosimp*)
(("" (expand "open?" )
(("" (skosimp*)
(("" (expand "open_ball?" )
(("" (inst + "x!1-a!1" )
(("" (skosimp*) (("" (grind) nil nil )) nil )) nil ))
nil ))
nil ))
nil ))
nil )
unchecked
((open? const-decl "bool" open_sets nil )
(open_ball? const-decl "bool" open_sets nil )
(abs const-decl "{n: nonneg_real | n >= m}" real_defs nil )
(T formal-subtype-decl nil open_sets nil )
(T_pred const-decl "[real -> boolean]" open_sets nil )
(- const-decl "[numfield, numfield -> numfield]" number_fields nil )
(numfield nonempty-type-eq-decl nil number_fields nil )
(posreal nonempty-type-eq-decl nil real_types nil )
(> const-decl "bool" reals nil )
(nonneg_real nonempty-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 ))
99 100 t shostak))
(below_intv_open 0
(below_intv_open-1 nil 3258299894 3292322829
("" (skosimp*)
(("" (expand "open?" )
(("" (skosimp*)
(("" (expand "open_ball?" )
(("" (inst + "a!1-x!1" ) (("" (grind) nil nil )) nil )) nil ))
nil ))
nil ))
nil )
unchecked
((open? const-decl "bool" open_sets nil )
(open_ball? const-decl "bool" open_sets nil )
(abs const-decl "{n: nonneg_real | n >= m}" real_defs nil )
(NOT const-decl "[bool -> bool]" booleans nil )
(< const-decl "bool" reals nil )
(T formal-subtype-decl nil open_sets nil )
(T_pred const-decl "[real -> boolean]" open_sets nil )
(- const-decl "[numfield, numfield -> numfield]" number_fields nil )
(numfield nonempty-type-eq-decl nil number_fields nil )
(posreal nonempty-type-eq-decl nil real_types nil )
(> const-decl "bool" reals nil )
(nonneg_real nonempty-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 ))
103 110 nil nil ))
(union_open 0
(union_open-1 nil 3258299981 3292322829
("" (skosimp*)
(("" (expand "open?" )
(("" (skosimp*)
(("" (expand "open_ball?" )
(("" (typepred "x!1" )
(("" (expand "union" )
(("" (expand "member" )
(("" (split -2)
(("1" (hide -4)
(("1" (inst?)
(("1" (skosimp*)
(("1" (inst + "delta!1" )
(("1" (skosimp*)
(("1" (inst - "y!1" )
(("1" (assert ) nil nil )) nil ))
nil ))
nil ))
nil ))
nil ))
nil )
("2" (hide -3)
(("2" (inst?)
(("2" (skosimp*)
(("2" (inst + "delta!1" )
(("2" (skosimp*)
(("2" (inst - "y!1" )
(("2" (assert ) nil nil )) nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
unchecked
((open? const-decl "bool" open_sets nil )
(open_ball? const-decl "bool" open_sets nil ) nil nil nil
(posreal nonempty-type-eq-decl nil real_types nil )
(> const-decl "bool" reals nil )
(nonneg_real nonempty-type-eq-decl nil real_types nil )
(>= const-decl "bool" reals nil )
(member const-decl "bool" sets nil )
(boolean nonempty-type-decl nil booleans nil )
(bool nonempty-type-eq-decl nil booleans nil )
(NOT const-decl "[bool -> bool]" booleans nil )
(number nonempty-type-decl nil numbers 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 )
(T_pred const-decl "[real -> boolean]" open_sets nil )
(T formal-subtype-decl nil open_sets nil )
(set type-eq-decl nil sets nil ) (union const-decl "set" sets nil ))
165 170 t shostak))
(closed_intv_closed 0
(closed_intv_closed-1 nil 3258299631 3292322829
("" (skosimp*)
(("" (expand "closed?" )
((""
(case-replace "complement(LAMBDA (x): a!1 <= x AND x <= b!1) =
union(above_intv(b!1),below_intv(a!1))")
(("1" (hide -1)
(("1" (lemma "union_open" )
(("1" (inst?)
(("1" (assert )
(("1" (hide 2)
(("1" (lemma "above_intv_open " )
(("1" (inst?)
(("1" (assert )
(("1" (lemma "below_intv_open " )
(("1" (inst?) nil nil )) nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
("2" (hide 2)
(("2" (apply-extensionality 1 :hide? t)
(("2" (grind) nil nil )) nil ))
nil ))
nil ))
nil ))
nil )
unchecked
((closed? const-decl "bool" open_sets nil )
(member const-decl "bool" sets nil )
(below_intv_open formula-decl nil open_sets nil )
(above_intv_open formula-decl nil open_sets nil )
(union_open formula-decl nil open_sets nil )
(< const-decl "bool" reals nil ) (> const-decl "bool" reals nil )
(union const-decl "set" sets nil ) (<= const-decl "bool" reals nil )
(AND const-decl "[bool, bool -> bool]" booleans nil )
(complement const-decl "set" sets nil )
(= const-decl "[T, T -> boolean]" equalities nil )
(set type-eq-decl nil sets nil )
(bool nonempty-type-eq-decl nil booleans nil )
(T formal-subtype-decl nil open_sets nil )
(T_pred const-decl "[real -> boolean]" open_sets 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 ))
203 160 t shostak)))
quality 95%
¤ Dauer der Verarbeitung: 0.2 Sekunden
(vorverarbeitet)
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*© Formatika GbR, Deutschland