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("" (skolem 1 ("PP" _))
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(("2" (expand "length" +) (("2" (propax) nil nil)) nil)) nil))
nil))
nil)
((list type-decl nil list_adt nil)
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(T formal-type-decl nil more_list_props nil)
(list_induction formula-decl nil list_adt nil)
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shostak))
(nth_parm_TCC1 0
(nth_parm_TCC1-1 nil 3500358260
("" (skosimp* :preds? t)
(("" (use "length_parm") (("" (assert) nil nil)) nil)) nil)
((length_parm formula-decl nil more_list_props nil)
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nil))
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("" (skolem 1 ("PP" _ _))
(("" (induct "pl")
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nil))
nil))
nil)
("3" (grind)
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nil))
nil))
nil))
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(n!1 skolem-const-decl
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(cons1_var!1 skolem-const-decl "(PP)" more_list_props nil)
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shostak))
(every_parm 0
(every_parm-1 nil 3500357635
("" (skosimp* :preds? t)
(("" (iff)
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nil))
nil))
nil))
nil)
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nil))
nil))
nil))
nil))
nil))
nil)
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nil))
nil))
nil)
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nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
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(below type-eq-decl nil nat_types nil)
(nth_parm formula-decl nil more_list_props nil)
(i!1 skolem-const-decl "below(length[T](pl!1))" more_list_props
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(pl!1 skolem-const-decl "list[(P!1)]" more_list_props nil)
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(real_lt_is_strict_total_order name-judgement
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nil)
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(rational nonempty-type-from-decl nil rationals nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
(int nonempty-type-eq-decl nil integers nil)
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(PRED type-eq-decl nil defined_types nil)
(list type-decl nil list_adt nil)
(every adt-def-decl "boolean" list_adt nil))
shostak))
(append_parm 0
(append_parm-1 nil 3520967096
("" (skolem 1 ("P" "_" "_"))
(("" (induct "l1")
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(("2" (skosimp)
(("2" (expand "append" +)
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nil))
nil))
nil))
nil)
((list type-decl nil list_adt nil)
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(boolean nonempty-type-decl nil booleans nil)
(T formal-type-decl nil more_list_props nil)
(list_induction formula-decl nil list_adt nil))
shostak))
(append_append_cons 0
(append_append_cons-1 nil 3520141411
("" (induct "l1")
(("1" (grind) nil nil)
("2" (skeep :preds? t)
(("2" (skeep :preds? t)
(("2" (expand "append" 1 1)
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(("2" (decompose-equality 1) (("2" (inst?) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
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(list type-decl nil list_adt nil))
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("" (induct "l2")
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nil))
nil))
nil))
nil))
nil))
nil))
nil)
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(list type-decl nil list_adt nil))
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("" (induct "l1")
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(("2" (assert)
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nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((length_append formula-decl nil list_props nil)
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nil))
nil))
nil))
nil))
nil))
nil))
nil)
("3" (hide 2)
(("3" (skosimp :preds? t)
(("3" (rewrite "length_append") (("3" (assert) nil nil)) nil))
nil))
nil))
nil)
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real_props nil)
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(list type-decl nil list_adt nil)
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(integer_pred const-decl "[rational -> boolean]" integers nil)
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(< const-decl "bool" reals nil)
(length def-decl "nat" list_props nil)
(append def-decl "list[T]" list_props nil))
shostak))
(nth_append_above_TCC1 0
(nth_append_above_TCC1-1 nil 3520951758
("" (skosimp)
(("" (rewrite "length_append") (("" (assert) nil nil)) nil)) nil)
((length_append formula-decl nil list_props nil)
(list type-decl nil list_adt nil)
(T formal-type-decl nil more_list_props nil)
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(real_ge_is_total_order name-judgement "(total_order?[real])"
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("" (induct "l1")
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nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
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("" (induct "l1")
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((list_induction formula-decl nil list_adt nil)
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(list type-decl nil list_adt nil))
shostak))
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(ldiff_TCC1-1 nil 3520133815
("" (skeep :preds? t)
(("" (expand "tail?") (("" (assert) nil nil)) nil)) nil)
((tail? def-decl "bool" more_list_props nil)) nil))
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(ldiff_TCC2-1 nil 3520133815
("" (skeep :preds? t)
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("" (skeep :preds? t)
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nil))
nil)
((tail? def-decl "bool" more_list_props nil)
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("" (induct "l1")
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(("2" (expand "tail?" +)
(("2" (skeep :preds? t)
(("2" (hide 1) (("2" (inst?) nil nil)) nil)) nil))
nil))
nil))
nil))
nil)
((list_induction formula-decl nil list_adt nil)
(T formal-type-decl nil more_list_props nil)
(append def-decl "list[T]" list_props nil)
(tail? def-decl "bool" more_list_props nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil)
(list type-decl nil list_adt nil))
nil))
(ldiff_append 0
(ldiff_append-1 nil 3520132082
("" (induct "l1")
(("1" (grind) nil nil)
("2" (skeep :preds? t)
(("2" (skeep :preds? t)
(("2" (expand "append" +)
(("2" (expand "ldiff" +)
(("2" (lift-if)
(("2" (prop)
(("1" (lemma "append_equal_null")
(("1" (inst -1 "cons(cons1_var, cons2_var)" "l2")
(("1" (expand "append" -1 1)
(("1" (propax) nil nil)) nil))
nil))
nil)
("2" (hide 1)
(("2" (apply-extensionality :hide? t)
(("2" (inst?) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("3" (skeep :preds? t) (("3" (use "tail_append") nil nil)) nil))
nil)
((tail_append formula-decl nil more_list_props nil)
(list_cons_extensionality formula-decl nil list_adt nil)
(append_equal_null formula-decl nil more_list_props nil)
(cons? adt-recognizer-decl "[list -> boolean]" list_adt nil)
(cons adt-constructor-decl "[[T, list] -> (cons?)]" list_adt nil)
(list_induction formula-decl nil list_adt nil)
(T formal-type-decl nil more_list_props nil)
(ldiff def-decl "list[T]" more_list_props nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(list type-decl nil list_adt nil)
(boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(tail? def-decl "bool" more_list_props nil)
(append def-decl "list[T]" list_props nil))
shostak)))
¤ Dauer der Verarbeitung: 0.31 Sekunden
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