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(NOT const-decl "[bool -> bool]" booleans nil)
(real_div_nzreal_is_real application-judgement "real" reals nil)
(real_plus_real_is_real application-judgement "real" reals nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(nat_induction formula-decl nil naturalnumbers nil)
(pred type-eq-decl nil defined_types nil))
shostak))
(compact_seq_induction 0
(compact_seq_induction-1 nil 3460812837
("" (skolem 1 ("c" "d"))
(("" (prop)
(("" (expand "compact?")
(("" (skosimp*)
(("" (label "big_open_cov" -1)
(("" (label "exists_fs" 1)
(("" (label "smaller_sc" 2)
(("" (inst "smaller_sc" "XS!1")
(("" (assert)
(("" (induct "n" "smaller_sc")
(("1" (skosimp*)
(("1" (expand "seq_intv_scaf")
(("1" (inst "exists_fs" "XS!2")
(("1" (assert) nil nil)) nil))
nil))
nil)
("2" (skosimp*)
(("2" (name "W" "seq_intv_scaf(c,d,XS!1)(j!1)")
(("2" (replace -1)
(("2" (label "name_w" -1)
(("2"
(hide "name_w")
(("2"
(expand "seq_intv_scaf")
(("2"
(reveal "name_w")
(("2"
(replace "name_w")
(("2"
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"(EXISTS (XS: set[set[real]]):
subset?(XS, XS!1) AND
finite_cover?(XS,
LAMBDA
(x: real):
W`1 <= x
AND
x <= (W`1 + W`2) / 2))")
(("1"
(assert)
(("1"
(replace -1)
(("1"
(skosimp*)
(("1"
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(expand "member")
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"union")
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(expand
"member")
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(skolem
1
("x"))
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(inst
-
"x")
(("1"
(inst
-
"x")
(("1"
(prop)
nil
nil))
nil))
nil))
nil))
nil))
nil)
("2"
(expand
"finite_cover?")
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(prop)
(("1"
(lemma
"infinite_union[set[real]]")
(("1"
(inst
-
"XS!2"
"XS!3")
(("1"
(prop)
nil
nil))
nil))
nil)
("2"
(label
"XS3_ss"
-1)
(("2"
(label
"XS2_ss"
-6)
(("2"
(label
"XS3_oc"
-3)
(("2"
(label
"XS2_oc"
-5)
(("2"
(expand
"open_cover?")
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(prop)
(("1"
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"Union")
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(expand
"subset?")
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(expand
"member")
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(("1"
(skosimp*)
(("1"
(inst
"XS3_ss"
"a!1")
(("1"
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+
"a!1")
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(expand
"union")
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(expand
"member")
(("1"
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nil
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2"
(inst
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"x!1")
(("2"
(assert)
(("2"
(skosimp*)
(("2"
(inst
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"a!1")
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(expand
"union")
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nil
nil))
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nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2"
(skosimp*)
(("2"
(expand
"union")
(("2"
(expand
"member")
(("2"
(inst
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"C!1")
(("2"
(inst
-9
"C!1")
(("2"
(assert)
(("2"
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nil
nil))
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nil))
nil))
nil))
nil))
--> --------------------
--> maximum size reached
--> --------------------
¤ Dauer der Verarbeitung: 0.136 Sekunden
(vorverarbeitet)
¤
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