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(continuous_functions_aux
(continuous_lr_def 0
(continuous_lr_def-2 nil 3462103233
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(("" (expand "right_continuous?")
(("" (expand "left_continuous?")
(("" (expand "right_continuous?")
(("" (expand "left_continuous?")
((""
(case-replace
"continuous?(f!1) IFF forall x0: FORALL epsilon : EXISTS delta : FORALL x :
abs(x - x0) < delta IMPLIES abs(f!1(x) - f!1(x0)) < epsilon")
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(skosimp)
(("1"
(inst - "x!1")
(("1"
(expand "abs" -3 1)
(("1" (assert) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
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(("2" (skosimp)
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(inst - "x!1")
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(expand "abs" -3 1)
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(expand "<=" -1)
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(split -1)
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(split -3)
(("1" (propax) nil nil)
("2" (assert) nil nil))
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(split -3)
(("1" (propax) nil nil)
("2" (assert) nil nil))
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nil))
nil))
nil))
nil))
nil))
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nil))
nil))
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nil)
("2" (skosimp*)
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(("2" (inst - "epsilon!1")
(("2" (inst - "x0!1")
(("2" (inst - "epsilon!1")
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(("2"
(inst + "min(delta!1,delta!2)")
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(expand "abs" -3)
(("2"
(case-replace "x!1-x0!1<0")
(("1"
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(("1"
(split -3)
(("1" (propax) nil nil)
("2" (assert) nil nil)
("3"
(expand "min")
(("3"
(case-replace
"delta!1 > delta!2")
(("1" (assert) nil nil)
("2" (assert) nil nil))
nil))
nil))
nil))
nil)
("2"
(assert)
(("2"
(hide -2)
(("2"
(inst - "x!1")
(("2" (assert) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (hide 2)
(("2" (expand "continuous?")
(("2" (split)
(("1" (skosimp*)
(("1" (inst - "x0!1")
(("1" (expand "continuous?")
(("1" (inst - "epsilon!1") nil nil)) nil))
nil))
nil)
("2" (skosimp*)
(("2" (expand "continuous?")
(("2" (inst - "x0!1") nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((right_continuous? const-decl "bool" continuous_functions_aux nil)
(real_minus_real_is_real application-judgement "real" reals nil)
(right_continuous? const-decl "bool" continuous_functions_aux nil)
(boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(IFF const-decl "[bool, 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)
(T_pred const-decl "[real -> boolean]" continuous_functions_aux
nil)
(T formal-subtype-decl nil continuous_functions_aux nil)
(continuous? const-decl "bool" continuous_functions "analysis/")
(>= 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)
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
(< const-decl "bool" reals nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(- const-decl "[numfield -> numfield]" number_fields nil)
(abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs
nil)
(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
(real_ge_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)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(<= const-decl "bool" reals nil)
(minus_real_is_real application-judgement "real" reals nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(min const-decl "{p: real | p <= m AND p <= n}" real_defs nil)
(posreal_min application-judgement
"{z: posreal | z <= x AND z <= y}" real_defs nil)
(continuous? const-decl "bool" continuous_functions "analysis/")
(left_continuous? const-decl "bool" continuous_functions_aux nil)
(left_continuous? const-decl "bool" continuous_functions_aux nil))
nil)
(continuous_lr_def-1 nil 3322045491
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(("" (expand "right_continuous")
(("" (expand "left_continuous")
(("" (expand "right_continuous")
(("" (expand "left_continuous")
((""
(case-replace
"continuous?(f!1) IFF forall x0: FORALL epsilon : EXISTS delta : FORALL x :
abs(x - x0) < delta IMPLIES abs(f!1(x) - f!1(x0)) < epsilon")
(("1" (hide -1)
(("1" (split)
(("1" (skosimp*)
(("1" (split 1)
(("1" (skosimp*)
(("1" (inst - "x0!1" "epsilon!1")
(("1" (skosimp)
(("1" (inst + "delta!1")
(("1"
(skosimp)
(("1"
(inst - "x!1")
(("1"
(expand "abs" -3 1)
(("1" (assert) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (skosimp*)
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(("2" (inst + "delta!1")
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(("2"
(inst - "x!1")
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(expand "abs" -3 1)
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(expand "<=" -1)
(("2"
(split -1)
(("1" (assert) nil nil)
("2" (assert) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (skosimp*)
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(("2" (inst - "epsilon!1")
(("2" (inst - "x0!1")
(("2" (inst - "epsilon!1")
(("2" (skosimp*)
(("2"
(inst + "min(delta!1,delta!2)")
(("2"
(skosimp*)
(("2"
(expand "abs" -3)
(("2"
(case-replace "x!1-x0!1<0")
(("1"
(inst -3 "x!1")
(("1"
(split -3)
(("1" (propax) nil nil)
("2" (assert) nil nil)
("3"
(expand "min")
(("3"
(case-replace
"delta!1 > delta!2")
(("1" (assert) nil nil)
("2" (assert) nil nil))
nil))
nil))
nil))
nil)
("2"
(assert)
(("2"
(hide -2)
(("2"
(inst - "x!1")
(("2" (assert) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (hide 2)
(("2" (expand "continuous?")
(("2" (split)
(("1" (skosimp*)
(("1" (inst - "x0!1")
(("1" (rewrite "continuity_def")
(("1" (inst - "epsilon!1") nil nil)) nil))
nil))
nil)
("2" (skosimp*)
(("2" (rewrite "continuity_def")
(("2" (inst - "x0!1") nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((continuity_def formula-decl nil continuous_functions "analysis/"))
shostak)))
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