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("" (skosimp*)
(("" (lemma "real_complete2")
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(("" (skosimp*)
(("" (prop) (("" (inst 1 "n!1") nil))))))))))))))
nil)
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nil))
(sup_TCC1 0
(sup_TCC1-1 nil 3506273121
(""
(inst 1 "(LAMBDA (s: sup_set): choose({x: real
| least_upper_bound(<=)(x, s)}))")
(("" (skosimp*)
(("" (lemma "sup_exists")
(("" (inst?)
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(T formal-subtype-decl nil bounded_reals nil)
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nil))
(sup_def 0
(sup_def-1 nil 3506273121
("" (skosimp*)
(("" (typepred "sup(Su!1)")
(("" (prop)
(("1" (assert) nil)
("2" (expand "least_upper_bound")
(("2" (flatten)
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(("2" (inst -2 "sup(Su!1)")
(("2" (assert) nil))))))))))))))
nil)
((sup const-decl "{x | least_upper_bound(<=)(x, Su)}" bounded_reals
nil)
(sup_set type-eq-decl nil bounded_reals nil)
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(setof type-eq-decl nil defined_types nil)
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(T formal-subtype-decl nil bounded_reals nil)
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(number_field_pred const-decl "[number -> boolean]" number_fields
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(real_le_is_total_order name-judgement "(total_order?[real])"
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nil))
(max_TCC1 0
(max_TCC1-1 nil 3506273121 ("" (subtype-tcc) nil nil)
((boolean nonempty-type-decl nil booleans nil)
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(number nonempty-type-decl nil numbers nil)
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(T formal-subtype-decl nil bounded_reals nil)
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(sup const-decl "{x | least_upper_bound(<=)(x, Su)}" bounded_reals
nil)
(max_set type-eq-decl nil bounded_reals nil)
(upper_bound const-decl "bool" bound_defs nil)
(empty? const-decl "bool" sets nil)
(member const-decl "bool" sets nil))
nil))
(max_def 0
(max_def-1 nil 3506273121
("" (skolem-typepred)
(("" (expand "max")
(("" (typepred "sup(W!1)")
(("" (prop)
(("1" (grind :exclude "upper_bound") nil)
("2" (grind :exclude "upper_bound")
(("2" (expand "upper_bound" -5)
(("2" (inst -5 "t!1")
(("2" (grind :exclude "upper_bound") nil))))))))))))))
nil)
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(max_set type-eq-decl nil bounded_reals nil)
(sup const-decl "{x | least_upper_bound(<=)(x, Su)}" bounded_reals
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(least_upper_bound const-decl "bool" bound_defs nil)
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(sup_set type-eq-decl nil bounded_reals nil)
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(set type-eq-decl nil sets nil)
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nil))
(inf_exists 0
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("" (skosimp*)
(("" (lemma "real_lower_complete2")
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(("" (typepred "Sl!1")
(("" (expand "below_bounded")
(("" (skosimp*)
(("" (prop) (("" (inst 1 "n!1") nil))))))))))))))
nil)
((T formal-subtype-decl nil bounded_reals nil)
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(number_field_pred const-decl "[number -> boolean]" number_fields
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(""
(inst 1 "(LAMBDA Sl: choose({x: real
| greatest_lower_bound(<=)(x, Sl)}))")
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(("" (lemma "inf_exists")
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(("" (grind :exclude "greatest_lower_bound") nil))))))))
nil)
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(("" (typepred "inf(Sl!1)")
(("" (prop)
(("1" (assert) nil)
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(("2" (flatten)
(("2" (inst -4 "x!1")
(("2" (inst -2 "inf(Sl!1)")
(("2" (assert) nil))))))))))))))
nil)
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(min_TCC1 0
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("" (skolem-typepred)
(("" (expand "min")
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(("" (prop)
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(("2" (inst -5 "t!1") (("2" (assert) nil))))))))))))))
nil)
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real_props nil)
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(boolean nonempty-type-decl nil booleans nil))
nil)))
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