|
(unique
(unique_cauchy 0
(unique_cauchy-1 nil 3507981239
("" (skosimp*)
(("" (lemma "neg_lemma" ("x" "y!1" "cx" "cx!1"))
((""
(lemma "add_lemma"
("x" "x!1" "y" "-y!1" "cx" "cx!1" "cy" "cauchy_neg(cx!1)"))
(("" (replace -4)
(("" (replace -3)
(("" (simplify)
(("" (replace -2)
(("" (simplify)
(("" (hide (-2 -3 -4))
(("" (extensionality "[nat->int]")
((""
(inst -1 "cauchy_add(cx!1, cauchy_neg(cx!1))"
"cauchy_zero")
(("" (expand "cauchy_add" -1 1)
(("" (expand "cauchy_neg" -1 1)
(("" (expand "cauchy_zero" -1 1)
((""
(lemma "unique_cauchy_zero")
((""
(bash -2)
(("1"
(lemma "unique_cauchy_zero")
(("1"
(inst -1 "x!1-y!1")
(("1"
(hide (-2 -3))
(("1" (assert) nil nil))
nil))
nil))
nil)
("2" (grind) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((cauchy_real nonempty-type-eq-decl nil cauchy nil)
(cauchy_real? const-decl "bool" cauchy 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)
(neg_lemma formula-decl nil neg nil)
(real_plus_real_is_real application-judgement "real" reals nil)
(int_plus_int_is_int application-judgement "int" integers nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(real_minus_real_is_real application-judgement "real" reals nil)
(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
(round const-decl "int" prelude_aux nil)
(posrat_div_posrat_is_posrat application-judgement "posrat"
rationals nil)
(rat_plus_rat_is_rat application-judgement "rat" rationals nil)
(posint_plus_nnint_is_posint application-judgement "posint"
integers nil)
(rat_div_nzrat_is_rat application-judgement "rat" rationals nil)
(^ const-decl "real" exponentiation nil)
(cauchy_prop const-decl "bool" cauchy nil)
(posnat_expt application-judgement "posnat" exponentiation nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(unique_cauchy_zero formula-decl nil cauchy nil)
(minus_int_is_int application-judgement "int" integers nil)
(cauchy_add const-decl "cauchy_real" add nil)
(cauchy_nnreal? const-decl "bool" cauchy nil)
(cauchy_nnreal nonempty-type-eq-decl nil cauchy nil)
(cauchy_zero const-decl "cauchy_nnreal" cauchy nil)
(minus_real_is_real application-judgement "real" reals nil)
(add_lemma formula-decl nil add nil)
(cauchy_neg const-decl "cauchy_real" neg nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(- const-decl "[numfield -> numfield]" number_fields nil))
nil))
(cauchy_dich1 0
(cauchy_dich1-1 nil 3507981239
("" (skolem!)
(("" (split)
(("1" (flatten)
(("1" (expand "cauchy_posreal?")
(("1" (expand "cauchy_negreal?")
(("1" (skosimp*)
(("1" (typepred "x!1" "x!2")
(("1"
(lemma "unique_cauchy"
("x" "x!1" "y" "x!2" "cx" "nzcx!1"))
(("1" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil)
("2" (flatten)
(("2" (expand "cauchy_negreal?")
(("2" (expand "cauchy_posreal?")
(("2" (typepred "nzcx!1")
(("2" (expand "cauchy_nzreal?")
(("2" (skolem!)
(("2" (typepred "x!1")
(("2" (case "x!1<0")
(("1" (inst 1 "x!1") (("1" (assert) nil nil))
nil)
("2" (case "0)
(("1" (inst 3 "x!1") (("1" (assert) nil nil))
nil)
("2" (assert) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((cauchy_posreal? const-decl "bool" cauchy nil)
(cauchy_nzreal nonempty-type-eq-decl nil cauchy nil)
(cauchy_nzreal? const-decl "bool" cauchy nil)
(cauchy_real nonempty-type-eq-decl nil cauchy nil)
(cauchy_real? const-decl "bool" cauchy nil)
(nat nonempty-type-eq-decl nil naturalnumbers 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)
(unique_cauchy formula-decl nil unique nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(number nonempty-type-decl nil numbers 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)
(>= const-decl "bool" reals nil)
(nonneg_real nonempty-type-eq-decl nil real_types nil)
(> const-decl "bool" reals nil)
(posreal nonempty-type-eq-decl nil real_types nil)
(<= const-decl "bool" reals nil)
(nonpos_real nonempty-type-eq-decl nil real_types nil)
(< const-decl "bool" reals nil)
(negreal nonempty-type-eq-decl nil real_types nil)
(cauchy_negreal? const-decl "bool" cauchy nil)
(x!1 skolem-const-decl "nzreal" unique nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(nzreal nonempty-type-eq-decl nil reals nil)
(/= const-decl "boolean" notequal nil))
nil))
(cauchy_dich2 0
(cauchy_dich2-1 nil 3507981239
("" (skosimp*)
(("" (lemma "cauchy_dich1" ("nzcx" "nzcx!1"))
(("" (grind) nil nil)) nil))
nil)
((cauchy_nzreal nonempty-type-eq-decl nil cauchy nil)
(cauchy_nzreal? const-decl "bool" cauchy 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)
(cauchy_dich1 formula-decl nil unique nil))
nil))
(cauchy_dich3 0
(cauchy_dich3-1 nil 3507981239
("" (skosimp*)
(("" (expand "cauchy_nnreal?")
(("" (expand "cauchy_negreal?")
(("" (split)
(("1" (flatten)
(("1" (skosimp*)
(("1" (typepred "x!1" "x!2")
(("1"
(lemma "unique_cauchy"
("x" "x!1" "y" "x!2" "cx" "nncx!1"))
(("1" (assert) nil nil)) nil))
nil))
nil))
nil)
("2" (flatten)
(("2" (typepred "nncx!1")
(("2" (expand "cauchy_nnreal?") (("2" (propax) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((cauchy_nnreal? const-decl "bool" cauchy nil)
(cauchy_nnreal nonempty-type-eq-decl nil cauchy nil)
(cauchy_real nonempty-type-eq-decl nil cauchy nil)
(cauchy_real? const-decl "bool" cauchy nil)
(nat nonempty-type-eq-decl nil naturalnumbers 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)
(unique_cauchy formula-decl nil unique nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(number nonempty-type-decl nil numbers 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)
(>= const-decl "bool" reals nil)
(nnreal type-eq-decl nil real_types nil)
(<= const-decl "bool" reals nil)
(nonpos_real nonempty-type-eq-decl nil real_types nil)
(< const-decl "bool" reals nil)
(negreal nonempty-type-eq-decl nil real_types nil)
(cauchy_negreal? const-decl "bool" cauchy nil))
nil))
(cauchy_dich4 0
(cauchy_dich4-1 nil 3507981239
("" (skolem!)
(("" (expand "cauchy_npreal?")
(("" (expand "cauchy_posreal?")
(("" (split)
(("1" (skosimp*)
(("1"
(lemma "unique_cauchy"
("x" "x!1" "y" "x!2" "cx" "npcx!1"))
(("1" (typepred "x!1" "x!2") (("1" (assert) nil nil))
nil))
nil))
nil)
("2" (typepred "npcx!1")
(("2" (expand "cauchy_npreal?") (("2" (flatten) nil nil))
nil))
nil))
nil))
nil))
nil))
nil)
((cauchy_npreal? const-decl "bool" cauchy 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)
(npreal type-eq-decl nil real_types nil)
(<= const-decl "bool" reals nil)
(cauchy_npreal nonempty-type-eq-decl nil cauchy nil)
(cauchy_real nonempty-type-eq-decl nil cauchy nil)
(cauchy_real? const-decl "bool" cauchy 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)
(unique_cauchy formula-decl nil unique nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(cauchy_posreal? const-decl "bool" cauchy nil))
nil))
(cauchy_dich5 0
(cauchy_dich5-1 nil 3507981239
("" (skosimp*)
(("" (typepred "nzcx!1")
(("" (expand "cauchy_nzreal?")
(("" (expand "cauchy_negreal?")
(("" (expand "cauchy_posreal?")
(("" (skolem!)
(("" (typepred "x!1")
(("" (lemma "trich_lt" ("x" "x!1" "y" "0"))
(("" (split -1)
(("1" (inst 1 "x!1") (("1" (assert) nil nil)) nil)
("2" (assert) nil nil)
("3" (inst 2 "x!1") (("3" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((cauchy_nzreal nonempty-type-eq-decl nil cauchy nil)
(cauchy_nzreal? const-decl "bool" cauchy nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(>= const-decl "bool" reals 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)
(number nonempty-type-decl nil numbers nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil)
(cauchy_negreal? const-decl "bool" cauchy nil)
(trich_lt formula-decl nil real_props nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props 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)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(negreal nonempty-type-eq-decl nil real_types nil)
(< const-decl "bool" reals nil)
(nonpos_real nonempty-type-eq-decl nil real_types nil)
(<= const-decl "bool" reals nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(x!1 skolem-const-decl "nzreal" unique nil)
(nzreal nonempty-type-eq-decl nil reals nil)
(/= const-decl "boolean" notequal nil)
(cauchy_posreal? const-decl "bool" cauchy nil))
nil))
(cauchy_trich 0
(cauchy_trich-1 nil 3507981239
("" (skosimp*)
(("" (typepred "cx!1")
(("" (expand "cauchy_real?")
(("" (skolem!)
(("" (lemma "trich_lt" ("x" "x!1" "y" "0"))
(("" (split -1)
(("1" (expand "cauchy_negreal?")
(("1" (inst + "x!1") (("1" (assert) nil nil)) nil))
nil)
("2" (lemma "unique_cauchy_zero3" ("cx" "cx!1"))
(("2" (grind) nil nil)) nil)
("3" (expand "cauchy_posreal?")
(("3" (inst + "x!1") (("3" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((cauchy_real nonempty-type-eq-decl nil cauchy nil)
(cauchy_real? const-decl "bool" cauchy nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(>= const-decl "bool" reals 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)
(number nonempty-type-decl nil numbers nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(negreal nonempty-type-eq-decl nil real_types nil)
(< const-decl "bool" reals nil)
(nonpos_real nonempty-type-eq-decl nil real_types nil)
(<= const-decl "bool" reals nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(x!1 skolem-const-decl "real" unique nil)
(cauchy_negreal? const-decl "bool" cauchy nil)
(cauchy_posreal? const-decl "bool" cauchy nil)
(cauchy_prop const-decl "bool" cauchy nil)
(^ const-decl "real" exponentiation nil)
(posnat_expt application-judgement "posnat" exponentiation nil)
(unique_cauchy_zero3 formula-decl nil cauchy nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props 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)
(trich_lt formula-decl nil real_props nil))
nil))
(cauchy_pos_characteristic 0
(cauchy_pos_characteristic-1 nil 3507981239
("" (skosimp*)
(("" (typepred "pcx!1")
(("" (expand "cauchy_posreal?")
(("" (skolem!)
(("" (typepred "x!1")
(("" (expand "cauchy_prop")
(("" (inst - "p!1")
(("" (flatten)
(("" (lemma "expt_ge1" ("b" "2" "n" "p!1"))
((""
(lemma "lt_times_lt_pos1"
("px" "1" "y" "2^p!1" "nnz" "0" "w" "x!1"))
((""
(lemma "lt_plus_one_equiv_le"
("x" "0" "y" "pcx!1(p!1)"))
(("" (grind) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((cauchy_posreal nonempty-type-eq-decl nil cauchy nil)
(cauchy_posreal? const-decl "bool" cauchy nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(>= const-decl "bool" reals 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)
(number nonempty-type-decl nil numbers nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil)
(posint_exp application-judgement "posint" exponentiation nil)
(cauchy_prop const-decl "bool" cauchy nil)
(lt_times_lt_pos1 formula-decl nil real_props nil)
(OR const-decl "[bool, bool -> bool]" booleans nil)
(/= const-decl "boolean" notequal nil)
(^ const-decl "real" exponentiation nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(int_plus_int_is_int application-judgement "int" integers nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(nnint_times_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(int_times_even_is_even application-judgement "even_int" integers
nil)
(mult_divides1 application-judgement "(divides(n))" divides nil)
(mult_divides2 application-judgement "(divides(m))" divides nil)
(posreal_times_posreal_is_posreal application-judgement "posreal"
real_types nil)
(posnat_expt application-judgement "posnat" exponentiation nil)
(posrat_div_posrat_is_posrat application-judgement "posrat"
rationals nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(lt_plus_one_equiv_le formula-decl nil prelude_aux nil)
(above nonempty-type-eq-decl nil integers nil)
(expt_ge1 formula-decl nil exponentiation 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))
nil))
(cauchy_neg_characteristic 0
(cauchy_neg_characteristic-1 nil 3507981239
("" (skosimp*)
(("" (typepred "ncx!1")
(("" (expand "cauchy_negreal?")
(("" (skolem!)
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(("" (expand "cauchy_prop")
(("" (inst - "p!1")
(("" (flatten)
((""
(lemma "lt_equiv_le_plus_one"
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(("" (lemma "expt_ge1" ("b" "2" "n" "p!1"))
((""
(lemma "both_sides_times_pos_lt1"
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(("" (grind) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((cauchy_negreal nonempty-type-eq-decl nil cauchy nil)
(cauchy_negreal? const-decl "bool" cauchy nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(>= const-decl "bool" reals 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)
(number nonempty-type-decl nil numbers nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil)
(posint_exp application-judgement "posint" exponentiation nil)
(cauchy_prop const-decl "bool" cauchy nil)
(expt_ge1 formula-decl nil exponentiation nil)
(> const-decl "bool" reals nil)
(above nonempty-type-eq-decl nil integers nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(nzreal_times_nzreal_is_nzreal application-judgement "nzreal"
real_types nil)
(posnat_expt application-judgement "posnat" exponentiation nil)
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--> --------------------
--> maximum size reached
--> --------------------
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