|
(interm_value_thm
(interm_value1_TCC1 0
(interm_value1_TCC1-1 nil 3424520920 ("" (subtype-tcc) nil 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)
(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)
(continuous? const-decl "bool" continuous_functions nil)
(continuous? const-decl "bool" continuous_functions nil)
(real_minus_real_is_real application-judgement "real" reals nil))
nil))
(interm_value1_TCC2 0
(interm_value1_TCC2-1 nil 3424520920 ("" (subtype-tcc) nil 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)
(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)
(continuous? const-decl "bool" continuous_functions nil)
(continuous? const-decl "bool" continuous_functions nil)
(real_minus_real_is_real application-judgement "real" reals nil))
nil))
(interm_value1 0
(interm_value1-1 nil 3424520931
("" (skosimp*)
(("" (lemma "intermediate_value1[a!1,b!1]")
(("1" (inst?) (("1" (assert) nil nil)) nil)
("2" (assert) nil nil))
nil))
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)
(intermediate_value1 formula-decl nil continuity_interval nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(<= const-decl "bool" reals nil)
(bool nonempty-type-eq-decl nil booleans nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(closed_interval type-eq-decl nil intervals_real "reals/")
(J nonempty-type-eq-decl nil continuity_interval nil)
(AND const-decl "[bool, bool -> bool]" booleans nil))
shostak))
(interm_value2_TCC1 0
(interm_value2_TCC1-1 nil 3424520920 ("" (subtype-tcc) nil 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)
(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)
(continuous? const-decl "bool" continuous_functions nil)
(continuous? const-decl "bool" continuous_functions nil)
(real_minus_real_is_real application-judgement "real" reals nil))
nil))
(interm_value2 0
(interm_value2-1 nil 3424525492
("" (skosimp*)
(("" (lemma "intermediate_value2[a!1,b!1]")
(("1" (inst?) (("1" (assert) nil nil)) nil)
("2" (assert) nil nil))
nil))
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)
(intermediate_value2 formula-decl nil continuity_interval nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(<= const-decl "bool" reals nil)
(bool nonempty-type-eq-decl nil booleans nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(closed_interval type-eq-decl nil intervals_real "reals/")
(J nonempty-type-eq-decl nil continuity_interval nil)
(AND const-decl "[bool, bool -> bool]" booleans nil))
nil))
(interm_value3_TCC1 0
(interm_value3_TCC1-1 nil 3424520920 ("" (subtype-tcc) nil 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)
(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)
(continuous? const-decl "bool" continuous_functions nil)
(continuous? const-decl "bool" continuous_functions nil)
(real_minus_real_is_real application-judgement "real" reals nil))
nil))
(interm_value3 0
(interm_value3-1 nil 3424525507
("" (skosimp*)
(("" (lemma "intermediate_value3[a!1,b!1]")
(("1" (inst?) (("1" (assert) nil nil)) nil)
("2" (assert) nil nil))
nil))
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)
(intermediate_value3 formula-decl nil continuity_interval nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(<= const-decl "bool" reals nil)
(bool nonempty-type-eq-decl nil booleans nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(closed_interval type-eq-decl nil intervals_real "reals/")
(J nonempty-type-eq-decl nil continuity_interval nil)
(AND const-decl "[bool, bool -> bool]" booleans nil))
nil))
(interm_value4 0
(interm_value4-2 nil 3424525620
("" (skosimp*)
(("" (lemma "intermediate_value4[a!1,b!1]")
(("1" (inst?) (("1" (assert) nil nil)) nil)
("2" (assert) nil nil))
nil))
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)
(intermediate_value4 formula-decl nil continuity_interval nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(<= const-decl "bool" reals nil)
(bool nonempty-type-eq-decl nil booleans nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(closed_interval type-eq-decl nil intervals_real "reals/")
(J nonempty-type-eq-decl nil continuity_interval nil)
(AND const-decl "[bool, bool -> bool]" booleans nil))
nil)
(interm_value4-1 nil 3424525518
(";;; Proof interm_value1-1 for formula continuity_intv.interm_value1"
(skosimp*)
((";;; Proof interm_value1-1 for formula continuity_intv.interm_value1"
(lemma "intermediate_value1[a!1,b!1]")
(("1" (inst?) (("1" (assert) nil))) ("2" (assert) nil))))
";;; developed with shostak decision procedures")
nil nil))
(interm_value5 0
(interm_value5-1 nil 3501251206
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(("" (lemma "interm_value2")
(("" (case "p)
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("2" (hide 2)
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nil))
nil))
nil))
nil))
nil))
nil)
("3" (expand "fpq") (("3" (propax) nil nil)) nil)
("4" (expand "fpq") (("4" (propax) nil nil)) nil))
nil))
nil))
nil))
nil))
nil)
("2" (hide -1)
(("2" (lemma "interm_value4")
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(("2" (case "q/=p")
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nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("3" (expand "fqp")
(("3" (propax) nil nil)) nil)
("4" (expand "fqp")
(("4" (propax) nil nil)) nil))
nil))
nil))
nil))
nil))
nil)
("2" (flatten)
(("2" (inst + "p") (("2" (ground) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((closed_interval type-eq-decl nil intervals_real "reals/")
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(< const-decl "bool" reals nil)
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(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)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
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"(strict_total_order?[real])" real_props nil)
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real_props nil)
(>= const-decl "bool" reals nil)
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(> const-decl "bool" reals nil)
(posreal nonempty-type-eq-decl nil real_types nil)
(continuous? const-decl "bool" continuous_functions nil)
(real_minus_real_is_real application-judgement "real" reals nil)
(fpq skolem-const-decl "[closed_interval[real](p, q) -> real]"
interm_value_thm nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(interm_value4 formula-decl nil interm_value_thm nil)
(/= const-decl "boolean" notequal nil)
(fqp skolem-const-decl "[closed_interval[real](q, p) -> real]"
interm_value_thm nil)
(interm_value2 formula-decl nil interm_value_thm nil))
nil))
(cont_intv 0
(cont_intv-1 nil 3424526031
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(("" (expand "continuous?")
(("" (skosimp*)
(("" (inst - "x0!1")
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(("" (skosimp*)
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(("" (inst + "delta!1")
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(("" (inst?) (("" (assert) nil nil)) nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((continuous? const-decl "bool" continuous_functions nil)
(number nonempty-type-decl nil numbers nil)
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nil)
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real_props nil)
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"(strict_total_order?[real])" real_props nil)
(>= const-decl "bool" reals nil)
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(> const-decl "bool" reals nil)
(posreal nonempty-type-eq-decl nil real_types nil)
(continuous? const-decl "bool" continuous_functions nil)
(real_minus_real_is_real application-judgement "real" reals nil))
nil))
(cont_intv1 0
(cont_intv1-1 nil 3424525844
("" (skosimp*)
(("" (expand "restrict") (("" (propax) nil nil)) nil)) nil)
((restrict const-decl "R" restrict nil)) nil))
(interm_val1 0
(interm_val1-2 nil 3424525975
("" (skosimp*)
(("" (lemma "intermediate_value1[a!1,b!1]")
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(("1" (assert)
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(("1" (propax) nil nil)
("2" (hide 2)
(("2" (assert)
(("2" (expand "restrict") (("2" (propax) nil nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (assert) nil nil))
nil))
nil)
((real nonempty-type-from-decl nil reals nil)
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(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)
(intermediate_value1 formula-decl nil continuity_interval nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(<= const-decl "bool" reals nil)
(bool nonempty-type-eq-decl nil booleans nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(restrict const-decl "R" restrict nil)
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(J nonempty-type-eq-decl nil continuity_interval nil)
(AND const-decl "[bool, bool -> bool]" booleans nil))
nil)
(interm_val1-1 nil 3424521582
("" (skosimp*)
(("" (lemma "intermediate_value1[a!1,b!1]")
(("1" (inst?)
(("1" (assert)
(("1" (split -1)
(("1" (propax) nil nil)
("2" (hide 2)
(("2" (lemma "help")
(("2" (inst?) (("2" (assert) nil nil)) nil)) nil))
nil))
nil))
nil))
nil)
("2" (assert) nil nil))
nil))
nil)
((J nonempty-type-eq-decl nil continuity_interval nil)
(intermediate_value1 formula-decl nil continuity_interval nil))
shostak))
(interm_val2 0
(interm_val2-2 nil 3424526085
("" (skosimp*)
(("" (lemma "intermediate_value2[a!1,b!1]")
(("1" (inst?)
(("1" (assert)
(("1" (split -1)
(("1" (propax) nil nil)
("2" (hide 2)
(("2" (assert)
(("2" (expand "restrict") (("2" (propax) nil nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (assert) nil nil))
nil))
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)
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(number nonempty-type-decl nil numbers nil)
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(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(<= const-decl "bool" reals nil)
(bool nonempty-type-eq-decl nil booleans nil)
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"(strict_total_order?[real])" real_props nil)
(restrict const-decl "R" restrict nil)
(closed_interval type-eq-decl nil intervals_real "reals/")
(J nonempty-type-eq-decl nil continuity_interval nil)
(AND const-decl "[bool, bool -> bool]" booleans nil))
nil)
(interm_val2-1 nil 3424525950
(";;; Proof interm_val1-1 for formula continuity_intv.interm_val1"
(skosimp*)
((";;; Proof interm_val1-1 for formula continuity_intv.interm_val1"
(lemma "intermediate_value2[a!1,b!1]")
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(("1" (assert)
(("1" (split -1)
(("1" (propax) nil)
("2" (hide 2)
(("2" (lemma "help")
(("2" (inst?) (("2" (assert) nil)))))))))))))
("2" (assert) nil))))
";;; developed with shostak decision procedures")
nil nil))
(interm_val3 0
(interm_val3-1 nil 3424526101
("" (skosimp*)
(("" (lemma "intermediate_value3[a!1,b!1]")
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nil))
nil))
nil))
nil))
nil))
nil)
("2" (assert) nil nil))
nil))
nil)
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(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(boolean nonempty-type-decl nil booleans nil)
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(J nonempty-type-eq-decl nil continuity_interval nil)
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nil))
(interm_val4 0
(interm_val4-1 nil 3424526115
("" (skosimp*)
(("" (lemma "intermediate_value4[a!1,b!1]")
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nil))
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nil))
nil)
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nil)
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(real_le_is_total_order name-judgement "(total_order?[real])"
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nil))
(zeros_interm 0
(zeros_interm-1 nil 3424527168
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