(piecewise_continuous
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("" (lemma "connected_domain" ) (("" (propax) nil nil )) nil )
((connected_domain formula-decl nil piecewise_continuous nil )) nil ))
(IMP_fundamental_theorem_TCC2 0
(IMP_fundamental_theorem_TCC2-1 nil 3612542950
("" (lemma "not_one_element" ) (("" (propax) nil nil )) nil )
((not_one_element formula-decl nil piecewise_continuous nil )) nil ))
(piecewise_continuous?_TCC1 0
(piecewise_continuous?_TCC1-1 nil 3611578171
("" (skosimp*) (("" (assert ) nil nil )) nil )
((real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil ))
nil ))
(piecewise_continuous?_TCC2 0
(piecewise_continuous?_TCC2-1 nil 3611578171
("" (skosimp*) (("" (assert ) nil nil )) nil )
((nnint_plus_posint_is_posint application-judgement "posint"
integers nil )
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil ))
nil ))
(piecewise_continuous?_TCC3 0
(piecewise_continuous?_TCC3-1 nil 3611578171
("" (subtype-tcc) nil nil )
((strict_increasing? const-decl "bool" real_fun_preds "reals/" )
(continuous_on? const-decl "bool" continuous_functions nil )
(piecewise_continuous? const-decl "bool" piecewise_continuous nil )
(real_minus_real_is_real application-judgement "real" reals nil ))
nil ))
(piecewise_continuous?_TCC4 0
(piecewise_continuous?_TCC4-1 nil 3611578171
("" (skeep) (("" (assert ) nil nil )) nil )
((real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil ))
nil ))
(piecewise_continuous?_TCC5 0
(piecewise_continuous?_TCC5-1 nil 3611591182 ("" (grind) nil nil )
((strict_increasing? const-decl "bool" real_fun_preds "reals/" )
(abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs
nil )
(continuous_on? const-decl "bool" continuous_functions nil )
(piecewise_continuous? const-decl "bool" piecewise_continuous nil )
(real_minus_real_is_real application-judgement "real" reals nil ))
nil ))
(piecewise_continuous?_TCC6 0
(piecewise_continuous?_TCC6-1 nil 3611591182 ("" (grind) nil nil )
((strict_increasing? const-decl "bool" real_fun_preds "reals/" )
(abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs
nil )
(continuous_on? const-decl "bool" continuous_functions nil )
(piecewise_continuous? const-decl "bool" piecewise_continuous nil )
(real_minus_real_is_real application-judgement "real" reals nil ))
nil ))
(continuous_on_integrable 0
(continuous_on_integrable-1 nil 3611681282
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(("1"
(case " continuous_on?(LAMBDA (s: closed_interval[T](a!1, b!1)): f!1(s),
{xx: closed_interval[T](a!1, b!1) | TRUE})")
(("1" (assert )
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(("1" (skosimp*)
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(name
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(("1"
(case
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(("1"
(case
"step_function?(a!1, b!1, fmax(a!1, b!1, PP, f!1))" )
(("1"
(inst
+
"fmin(a!1,b!1,PP,f!1)"
"fmax(a!1,b!1,PP,f!1)" )
(("1"
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(case
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(("1"
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nil ))
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nil ))
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nil ))
nil ))
nil ))
nil ))
nil ))
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nil )
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(typepred
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nil )
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(typepred
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(("2"
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(inst
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nil )
("2"
(hide 2)
(("2"
(lemma
"width_eq_part" )
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(inst?)
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(assert )
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(replace -5)
(("2"
(case
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(("1"
(hide
-2
-6)
(("1"
(lemma
"integral_bound_abs" )
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(inst
-1
"eps!1/(2*(b!1-a!1))"
"a!1"
"b!1"
"fmax(a!1, b!1, PP, f!1) - fmin(a!1, b!1, PP, f!1)" )
(("1"
(name-replace
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"b!1-a!1" )
(("1"
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(split
-1)
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(name
"III"
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(("1"
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nil
nil ))
nil ))
nil )
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(assert )
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nil ))
nil ))
nil )
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2)
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(skosimp*)
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(expand
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1)
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(reveal
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(mult-by
1
"(2*BMA)" )
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(assert )
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nil ))
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nil ))
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nil ))
nil ))
nil ))
nil )
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(assert )
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(hide
-2
-4)
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(replace
-2)
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(replace
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(assert )
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(hide-all-but
1)
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(reveal
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1
"(2*BMA)" )
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(assert )
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nil ))
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nil ))
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nil ))
nil ))
nil ))
nil )
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(flatten)
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-2
-4)
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-1)
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(hide
-1)
(("2"
(replace
-1)
(("2"
(hide
-1)
(("2"
(name
"MIN_x"
"min_x(seq(PP)(ii!1), seq(PP)(1 + ii!1), f!1)" )
(("2"
(replace
-1)
(("2"
(name
"MAX_x"
"max_x(seq(PP)(ii!1), seq(PP)(1 + ii!1), f!1)" )
(("2"
(replace
-1)
(("2"
(case
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(inst
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"MIN_x" )
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(lemma
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(expand
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(inst?)
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(assert )
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nil ))
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nil ))
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(ground)
nil
nil )
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(ground)
nil
nil ))
nil )
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(assert )
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(hide-all-but
(-2
-3
-16
1))
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(typepred
"MAX_x" )
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(typepred
"MIN_x" )
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(hide
-1
-4
-5
-8
-9
-10)
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(expand
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(ground)
nil
nil ))
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nil ))
nil ))
nil ))
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nil )
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(assert )
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(hide-all-but
1)
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(skeep)
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(typepred
"x" )
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(typepred
"y" )
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(expand
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(lift-if)
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(ground)
nil
nil ))
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nil ))
nil ))
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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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(hide
2)
(("2"
(rewrite
"fmax_ge" )
nil
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
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(hide
-3
-4
-6
-8
2)
(("2"
(replace
-1)
(("2"
(hide
-1
-2
-3)
(("2"
(name-replace
"BMA"
"b!1-a!1" )
(("2"
(mult-by
1
"(1 + floor(BMA / delta!1))" )
(("1"
(div-by
1
"delta!1" )
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(assert )
nil
nil ))
nil )
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(hide
2)
(("2"
(reveal
-3)
(("2"
(assert )
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(case-replace
"BMA / delta!1 >= 0" )
(("1"
(assert )
nil
nil )
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(hide
2)
(("2"
(mult-by
1
"delta!1" )
(("2"
(assert )
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(reveal
-4)
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(assert )
nil
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
("2"
(hide 2)
(("2"
(lemma "integral_diff" )
(("2"
(inst
-1
"a!1"
"b!1"
"fmax(a!1, b!1, PP, f!1)"
"fmin(a!1, b!1, PP, f!1)" )
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(assert )
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(split -1)
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(flatten)
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(assert )
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(expand "-" )
(("1"
(propax)
nil
nil ))
nil ))
nil ))
nil )
("2"
(hide 2)
(("2"
(rewrite
"step_function_integrable?" )
nil
nil ))
nil )
("3"
(hide 2)
(("3"
(rewrite
"step_function_integrable?" )
nil
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
("2"
(hide 2)
(("2"
(rewrite "fmax_step" )
nil
nil ))
nil ))
nil )
("2"
(hide 2)
(("2"
(rewrite "fmin_step" )
nil
nil ))
nil )
("3"
(hide 2)
(("3"
(skosimp*)
(("3"
(hide -1 -2 -3)
(("3"
(expand "continuous_on?" )
(("3"
(expand "continuous?" )
(("3"
(inst - "x!1" )
(("3"
(skeep)
(("3"
(inst - "epsilon" )
(("3"
(skeep)
(("3"
(inst + "delta" )
(("3"
(skeep)
(("3"
(inst - "x" )
(("3"
(expand
"restrict" )
(("3"
(assert )
nil
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
("2"
(assert )
(("2"
(mult-by 1 "delta!1" )
(("2"
(assert )
(("2"
(case
"floor((b!1 - a!1) / delta!1)>=0" )
(("1"
(mult-by -1 "delta!1" )
(("1" (assert ) nil nil ))
nil )
("2"
(assert )
(("2"
(mult-by -2 "1/delta!1" )
(("2" (assert ) nil nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
("2" (hide 2)
(("2"
(split +)
(("1"
(mult-by 1 "b!1-a!1" )
(("1" (assert ) nil nil ))
nil )
("2"
(mult-by 1 "b!1-a!1" )
(("2" (assert ) nil nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
("2" (hide -1 2)
(("2" (expand "continuous_on?" )
(("2" (propax) nil nil )) nil ))
nil ))
nil ))
nil ))
nil ))
nil )
("2" (assert ) nil nil ) ("3" (assert ) nil nil ))
nil )
("2" (expand "not_one_element?" )
(("2" (skosimp*)
(("2" (typepred "x!1" )
(("2" (inst-cp 1 "a!1" )
(("2" (inst-cp 1 "b!1" ) (("2" (assert ) nil nil )) nil ))
nil ))
nil ))
nil ))
nil )
("3" (lemma "connected_domain" )
(("3" (expand "connected?" )
(("3" (assert )
(("3" (skosimp*)
(("3" (lemma "connected_domain" )
(("3" (expand "connected?" )
(("3" (inst -1 "a!1" "b!1" "z!1" )
(("3" (assert ) nil nil )) nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
((closed_interval type-eq-decl nil intervals_real "reals/" )
(<= const-decl "bool" reals nil )
(AND const-decl "[bool, bool -> bool]" booleans nil )
(bool nonempty-type-eq-decl nil booleans nil )
(T formal-nonempty-subtype-decl nil piecewise_continuous nil )
(T_pred const-decl "[real -> boolean]" piecewise_continuous 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 )
(connected? const-decl "bool" deriv_domain_def nil )
(not_one_element? const-decl "bool" deriv_domain_def nil )
(restrict const-decl "R" restrict nil )
(real_minus_real_is_real application-judgement "real" reals nil )
(real_plus_real_is_real application-judgement "real" reals nil )
(both_sides_times_pos_lt1 formula-decl nil real_props nil )
(posreal_times_posreal_is_posreal application-judgement "posreal"
real_types nil )
(both_sides_times_pos_le1_imp formula-decl nil extra_real_props
nil )
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil )
(OR const-decl "[bool, bool -> bool]" booleans nil )
(integrable? const-decl "bool" integral_def nil )
(integral? const-decl "bool" integral_def nil )
(integral const-decl "{S: real | integral?(a, b, ff, S)}"
integral_def nil )
(posint_plus_nnint_is_posint application-judgement "posint"
integers nil )
(NOT const-decl "[bool -> bool]" booleans nil )
(minus_odd_is_odd application-judgement "odd_int" integers nil )
(abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs
nil )
(both_sides_times_pos_le1 formula-decl nil real_props nil )
(div_cancel2 formula-decl nil real_props nil )
(nonzero_real nonempty-type-eq-decl nil reals nil )
(- const-decl "[numfield -> numfield]" number_fields nil )
(minus_real_is_real application-judgement "real" reals nil )
(finseq_appl const-decl "[below[length(fs)] -> T]" finite_sequences
nil )
(* const-decl "[numfield, numfield -> numfield]" number_fields nil )
(real_times_real_is_real application-judgement "real" reals nil )
(nnreal_times_nnreal_is_nnreal application-judgement "nnreal"
real_types nil )
(both_sides_times_pos_ge1 formula-decl nil real_props nil )
(both_sides_div_pos_lt1 formula-decl nil real_props nil )
(times_div_cancel1 formula-decl nil extra_real_props nil )
(both_sides_times_pos_ge1_imp formula-decl nil extra_real_props
nil )
(int_minus_int_is_int application-judgement "int" integers nil )
(floor const-decl "{i | i <= x & x < i + 1}" floor_ceil nil )
(integer nonempty-type-from-decl nil integers nil )
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil )
(below type-eq-decl nil naturalnumbers nil )
(above nonempty-type-eq-decl nil integers 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 )
(< const-decl "bool" reals nil )
(= const-decl "[T, T -> boolean]" equalities nil )
(below type-eq-decl nil nat_types nil )
(nat nonempty-type-eq-decl nil naturalnumbers nil )
(real_div_nzreal_is_real application-judgement "real" reals nil )
(int_plus_int_is_int application-judgement "int" integers nil )
(- const-decl "[numfield, numfield -> numfield]" number_fields 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 )
(/ const-decl "[numfield, nznum -> numfield]" number_fields nil )
(nznum nonempty-type-eq-decl nil number_fields nil )
(/= const-decl "boolean" notequal nil )
(numfield nonempty-type-eq-decl nil number_fields nil )
(>= const-decl "bool" reals nil )
(nzreal_div_nzreal_is_nzreal application-judgement "nzreal"
real_types nil )
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil )
(posreal_div_posreal_is_posreal application-judgement "posreal"
real_types nil )
(real_gt_is_strict_total_order name-judgement
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nil shostak)))
Messung V0.5 in Prozent C=100 H=100 G=100
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