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nil))
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(("" (lemma "bolzano_weierstrass4")
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(("1" (skosimp) (("1" (inst?) (("1" (assert) nil nil)) nil))
nil)
("2" (delete 2) (("2" (grind) nil nil)) nil))
nil))
nil))
nil))
nil)
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real_props nil)
(c!1 skolem-const-decl "real" continuity_interval nil)
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real_props nil)
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nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
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real_props nil)
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(rational_pred const-decl "[real -> boolean]" rationals nil)
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(real_pred const-decl "[number_field -> boolean]" reals nil)
(number_field nonempty-type-from-decl nil number_fields nil)
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nil))
nil))
nil))
nil)
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1
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nil)
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nil))
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nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
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(continuity_accumulation formula-decl nil continuity_props nil)
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(rational_pred const-decl "[real -> boolean]" rationals nil)
(rational nonempty-type-from-decl nil rationals nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
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nil))
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nil))
nil))
nil)
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(number_field_pred const-decl "[number -> boolean]" number_fields
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nil)
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nil))
nil))
nil)
nil nil))
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(lemma "epsilon_ax"
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((""
(lemma "supfun_is_sup[J]"
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nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
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nil)
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(integer_pred const-decl "[rational -> boolean]" integers nil)
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(/= const-decl "boolean" notequal nil)
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(/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
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(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(posint_plus_nnint_is_posint application-judgement "posint"
integers nil))
nil))
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(use "supfun_is_bound[J]")
((""
(name "eps" "sup(f!1) - f!1(c!1)")
((""
(assert)
((""
(use
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("x" "eps/2"))
((""
(skolem!)
((""
(inst -4 "eps/2" "a!1")
((""
(skosimp)
((""
(inst -6 "i!1")
((""
(case
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(("1"
(expand "abs")
(("1"
(lift-if)
(("1"
(ground)
nil
nil))
nil))
nil)
("2"
(rewrite
"both_sides_div_pos_lt2"
1)
(("2"
(assert)
nil
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
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nil)
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(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)
(continuous? const-decl "bool" continuous_functions nil)
(continuity_accumulation formula-decl nil continuity_props nil)
(O const-decl "T3" function_props nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
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"(strict_total_order?[real])" real_props nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
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(/= const-decl "boolean" notequal 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)
(archimedean2 formula-decl nil real_facts "reals/")
(real_div_nzreal_is_real application-judgement "real" reals nil)
(posnat nonempty-type-eq-decl nil integers nil)
(nonneg_int nonempty-type-eq-decl nil integers nil)
(both_sides_div_pos_lt2 formula-decl nil real_props nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs
nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(minus_real_is_real application-judgement "real" reals nil)
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(< const-decl "bool" reals nil)
(posrat_div_posrat_is_posrat application-judgement "posrat"
rationals nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(posint_plus_nnint_is_posint application-judgement "posint"
integers nil)
(bounded_above? const-decl "bool" real_fun_preds "reals/")
(supfun_is_bound formula-decl nil real_fun_supinf nil)
(accumulation const-decl "bool" convergence_sequences nil)
(real_minus_real_is_real application-judgement "real" reals nil))
nil))
(maximum_exists 0
(maximum_exists-1 nil 3442580979
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(("" (forward-chain "sup_is_reached")
(("" (skolem!)
(("" (inst?)
(("" (rewrite "max_upper_bound[J]")
(("" (assert) (("" (rewrite "bounded_from_above") nil nil))
nil))
nil))
nil))
nil))
nil))
nil)
((sup_is_reached formula-decl nil continuity_interval nil)
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(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)
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(<= const-decl "bool" reals nil)
(a formal-const-decl "real" continuity_interval nil)
(b formal-const-decl "{x: real | a <= x}" continuity_interval nil)
(J nonempty-type-eq-decl nil continuity_interval nil)
(bounded_from_above formula-decl nil continuity_interval nil)
(max_upper_bound formula-decl nil real_fun_supinf nil))
nil))
(max_pt_TCC1 0
(max_pt_TCC1-1 nil 3442580979
(""
(inst +
"(LAMBDA (f: {f | continuous?[J](f)}): choose({xj: J | is_maximum[J](xj, f)}))")
(("" (skosimp*)
(("" (lemma "maximum_exists")
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(("" (inst?)
(("" (expand "member") (("" (propax) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
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(member const-decl "bool" sets nil)
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(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))
nil))
(inf_is_reached_TCC1 0
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nil))
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(("" (use "sup_is_reached" ("f" "-f!1"))
(("" (split)
(("1" (skolem!)
(("1" (rewrite "supfun_neg[J]")
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("2" (rewrite "bounded_from_below") nil nil))
nil))
nil)
("2" (rewrite "neg_fun_continuous [J]") nil nil))
nil))
nil))
nil)
((sup_is_reached formula-decl nil continuity_interval nil)
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nil)
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nil)
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nil))
nil))
nil)
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