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(IUnion_extra
(upto?_TCC1 0
(upto?_TCC1-1 nil 3415314220 ("" (subtype-tcc) nil nil) nil nil))
(disjoint_subset 0
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(T formal-type-decl nil IUnion_extra nil)
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(member const-decl "bool" sets nil))
shostak))
(disjoint_commute 0
(disjoint_commute-1 nil 3415314299
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nil))
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(T formal-type-decl nil IUnion_extra nil)
(member const-decl "bool" sets nil))
shostak))
(IUnion_of_finite_is_finite 0
(IUnion_of_finite_is_finite-1 nil 3415314322
("" (induct "n")
(("1" (typepred "n!1") (("1" (propax) nil nil)) nil)
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(case-replace
"{x: T | EXISTS (i_1: upto?(1 + j!1)): f!1(i_1)(x)} = f!1(1)"
:hide? T)
(("1" (hide 2)
(("1" (decompose-equality 1)
(("1" (iff)
(("1" (prop)
(("1" (skosimp*)
(("1" (typepred "i!1")
(("1" (replaces -4)
(("1" (assert) nil nil)) nil))
nil))
nil)
("2" (inst 1 "1") nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (assert)
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(inst -1
"restrict[upto?(1 + j!1), upto?(j!1), set[T]](f!1)")
(("2" (prop)
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(("1"
(case-replace
"IUnion(LAMBDA (i: upto?(1 + j!1)): f!1(i)) = union(f!1(j!1 + 1),IUnion(LAMBDA (i: upto?(j!1)): f!1(i)))"
:hide? T)
(("1" (inst -3 "j!1 + 1")
(("1" (rewrite "finite_union" 2) nil nil)) nil)
("2" (hide (-1 -3 3))
(("2" (decompose-equality 1)
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(("1" (skosimp*)
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(expand "IUnion")
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(inst 3 "i!1")
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(("1" (assert) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (expand* "union" "member")
(("2" (prop)
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nil))
nil))
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nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (skosimp*)
(("2" (expand "restrict")
(("2" (inst -2 "i!1") nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((union const-decl "set" sets nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(finite_set type-eq-decl nil finite_sets nil)
(finite_union judgement-tcc nil finite_sets nil)
(i!1 skolem-const-decl "upto?(1 + j!1)" IUnion_extra nil)
(j!1 skolem-const-decl "nat" IUnion_extra nil)
(member const-decl "bool" sets nil)
(restrict const-decl "R" restrict nil)
(posint_plus_nnint_is_posint application-judgement "posint"
integers nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(odd_plus_even_is_odd application-judgement "odd_int" integers nil)
(nnint_plus_posint_is_posint application-judgement "posint"
integers nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(nat_induction formula-decl nil naturalnumbers nil)
(IUnion const-decl "set[T]" indexed_sets nil)
(is_finite const-decl "bool" finite_sets nil)
(set type-eq-decl nil sets nil)
(T formal-type-decl nil IUnion_extra nil)
(upto? nonempty-type-eq-decl nil IUnion_extra nil)
(<= const-decl "bool" reals nil)
(posnat nonempty-type-eq-decl nil integers nil)
(nonneg_int nonempty-type-eq-decl nil integers nil)
(> const-decl "bool" reals nil)
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
(pred type-eq-decl nil defined_types nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(>= const-decl "bool" reals nil)
(bool nonempty-type-eq-decl nil booleans nil)
(int nonempty-type-eq-decl nil integers nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
(rational nonempty-type-from-decl nil rationals nil)
(rational_pred const-decl "[real -> boolean]" rationals 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))
shostak))
(IUnion_of_finite_is_finite1 0
(IUnion_of_finite_is_finite1-1 nil 3415319375
("" (induct "n")
(("1" (typepred "n!1") (("1" (propax) nil nil)) nil)
("2" (assert) nil nil)
("3" (skosimp*)
(("3" (case "j!1 = 0")
(("1" (hide -2)
(("1" (expand "IUnion")
(("1" (inst -3 "0")
(("1"
(case-replace
"{x: T | EXISTS (i_1: below[1 + j!1]): f!1(i_1)(x)} = f!1(0)"
:hide? T)
(("1" (hide 2)
(("1" (decompose-equality 1)
(("1" (iff)
(("1" (prop)
(("1" (skosimp*)
(("1" (typepred "i!1")
(("1" (replaces -3)
(("1" (assert) nil nil)) nil))
nil))
nil)
("2" (inst 1 "0") nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (assert)
(("2"
(inst -1
"restrict[below[1 + j!1], below[j!1], set[T]](f!1)")
(("2" (prop)
(("1" (expand "restrict")
(("1"
(case-replace
"IUnion(LAMBDA (i: below[1 + j!1]): f!1(i)) = union(f!1(j!1),IUnion(LAMBDA (i: below[j!1]): f!1(i)))"
:hide? T)
(("1" (inst -3 "j!1")
(("1" (rewrite "finite_union" 2) nil nil)) nil)
("2" (hide (-1 -3 3))
(("2" (decompose-equality 1)
(("2" (iff)
(("2" (prop)
(("1" (expand "IUnion" -1)
(("1" (skosimp*)
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(expand* "union" "member")
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(flatten)
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(expand "IUnion")
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(inst 3 "i!1")
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(typepred "i!1")
(("1" (assert) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (expand* "union" "member")
(("2" (prop)
(("1"
(expand "IUnion")
(("1" (inst 1 "j!1") nil nil))
nil)
("2"
(expand "IUnion")
(("2"
(skosimp*)
(("2" (inst 1 "i!1") nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (skosimp*)
(("2" (expand "restrict")
(("2" (inst -2 "i!1") nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((union const-decl "set" sets nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(finite_set type-eq-decl nil finite_sets nil)
(finite_union judgement-tcc nil finite_sets nil)
(i!1 skolem-const-decl "below[1 + j!1]" IUnion_extra nil)
(j!1 skolem-const-decl "nat" IUnion_extra nil)
(member const-decl "bool" sets nil)
(restrict const-decl "R" restrict nil)
(posint_plus_nnint_is_posint application-judgement "posint"
integers nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(odd_plus_even_is_odd application-judgement "odd_int" integers nil)
(nnint_plus_posint_is_posint application-judgement "posint"
integers nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(posnat nonempty-type-eq-decl nil integers nil)
(nonneg_int nonempty-type-eq-decl nil integers nil)
(nat_induction formula-decl nil naturalnumbers nil)
(IUnion const-decl "set[T]" indexed_sets nil)
(is_finite const-decl "bool" finite_sets nil)
(set type-eq-decl nil sets nil)
(T formal-type-decl nil IUnion_extra nil)
(below type-eq-decl nil nat_types nil)
(< const-decl "bool" reals nil) (> const-decl "bool" reals nil)
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
(pred type-eq-decl nil defined_types nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(>= const-decl "bool" reals nil)
(bool nonempty-type-eq-decl nil booleans nil)
(int nonempty-type-eq-decl nil integers nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
(rational nonempty-type-from-decl nil rationals nil)
(rational_pred const-decl "[real -> boolean]" rationals 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))
shostak)))
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