Quellcode-Bibliothek integral_cont.prf
Sprache: unbekannt
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(integral_cont
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nil))
nil)
((partition type-eq-decl nil integral_def nil)
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(below type-eq-decl nil naturalnumbers nil)
(< const-decl "bool" reals nil) (>= const-decl "bool" reals nil)
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(integer_pred const-decl "[rational -> boolean]" integers nil)
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(= const-decl "[T, T -> boolean]" equalities nil)
(> const-decl "bool" reals nil)
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(closed_interval type-eq-decl nil intervals_real "reals/")
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(nat nonempty-type-eq-decl nil naturalnumbers nil)
(<= const-decl "bool" reals nil)
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(number_field_pred const-decl "[number -> boolean]" number_fields
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(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil)
(abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs
nil)
(real_lt_is_strict_total_order name-judgement
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(real_le_is_total_order name-judgement "(total_order?[real])"
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(minus_real_is_real application-judgement "real" reals nil)
(posint_plus_nnint_is_posint application-judgement "posint"
integers nil)
(real_minus_real_is_real application-judgement "real" reals nil))
nil))
(continuous_integrable 0
(continuous_integrable-3 nil 3477657179
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("2"
(hide 2)
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((closed_interval type-eq-decl nil intervals_real "reals/")
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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)
(unif_cont_interval formula-decl nil unif_cont_fun 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)
(continuity_def formula-decl nil continuous_functions nil)
(extend const-decl "R" extend nil)
(abs_0 formula-decl nil abs_lems "reals/")
(fullset const-decl "set" sets nil)
(adh const-decl "setof[real]" convergence_functions nil)
(convergence const-decl "bool" convergence_functions nil)
(convergence const-decl "bool" lim_of_functions nil)
(continuous_on_def formula-decl nil continuous_functions nil)
(step_to_integrable formula-decl nil integral_step nil)
(real_minus_real_is_real application-judgement "real" reals nil)
(uniformly_continuous? const-decl "bool" unif_cont_fun nil)
(both_sides_times_pos_le1_imp formula-decl nil extra_real_props
nil)
(step_function? const-decl "bool" step_fun_def nil)
(continuous? const-decl "bool" continuous_functions nil)
(fun_cont_on type-eq-decl nil integral_cont_scaf nil)
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
(fun_cont_on type-eq-decl nil interval_minmax nil)
(min_x const-decl "{mx: T |
a <= mx AND
mx <= b AND
(FORALL (x: T): a <= x AND x <= b IMPLIES f(mx) <= f(x))}"
interval_minmax nil)
(OR const-decl "[bool, bool -> bool]" booleans nil)
(fmin const-decl "{ff: [T -> real] |
LET xx = seq(P) IN
FORALL (ii: below(length(P) - 1)):
FORALL (x: T):
(xx(ii) < x AND x < xx(ii + 1) IMPLIES
ff(x) = f(min_x(xx(ii), xx(ii + 1), f)))
AND ((xx(ii) = x OR x = xx(ii + 1)) IMPLIES ff(x) = f(x))}"
integral_cont_scaf nil)
(fmax_step formula-decl nil integral_cont_scaf nil)
(integrable? const-decl "bool" integral_def nil)
(- const-decl "[T -> real]" real_fun_ops "reals/")
(integral? const-decl "bool" integral_def nil)
(integral const-decl "{S: real | integral?(a, b, ff, S)}"
integral_def nil)
(part_induction formula-decl nil integral_def nil)
(posint_plus_nnint_is_posint application-judgement "posint"
integers nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(width_eq_part formula-decl nil integral_def nil)
(width const-decl "posreal" integral_def nil)
(integral_bound_abs formula-decl nil integral_prep 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)
(BMA skolem-const-decl "real" integral_cont 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)
(finite_sequence type-eq-decl nil finite_sequences nil)
(partition type-eq-decl nil integral_def nil)
(in_interval formula-decl nil integral_cont nil)
(PP skolem-const-decl
"{fs: finite_sequence[{x | a!1 <= x AND x <= b!1}] |
length(fs) > 1 AND
seq(fs)(0) = a!1 AND
seq(fs)(length(fs) - 1) = b!1 AND
(FORALL (ii: below(length(fs) - 1)):
seq(fs)(ii) < seq(fs)(1 + ii))}" integral_cont nil)
(ii!1 skolem-const-decl "below(length(PP) - 1)" integral_cont nil)
(f!1 skolem-const-decl "[T -> real]" integral_cont nil)
(MAX_x skolem-const-decl "{mx: T |
seq(PP)(ii!1) <= mx AND
mx <= seq(PP)(1 + ii!1) AND
(FORALL (x: T):
seq(PP)(ii!1) <= x AND x <= seq(PP)(1 + ii!1) IMPLIES
f!1(mx) >= f!1(x))}" integral_cont nil)
(MIN_x skolem-const-decl "{mx: T |
seq(PP)(ii!1) <= mx AND
mx <= seq(PP)(1 + ii!1) AND
(FORALL (x: T):
seq(PP)(ii!1) <= x AND x <= seq(PP)(1 + ii!1) IMPLIES
f!1(mx) <= f!1(x))}" integral_cont nil)
(width_lem formula-decl nil integral_def nil)
(finseq_appl const-decl "[below[length(fs)] -> T]" finite_sequences
nil)
(fmax_ge formula-decl nil integral_cont_scaf 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)
(BMA skolem-const-decl "real" integral_cont nil)
(delta!1 skolem-const-decl "posreal" integral_cont nil)
(both_sides_times_pos_ge1_imp formula-decl nil extra_real_props
nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(integral_diff formula-decl nil integral_prep nil)
(step_function_integrable? formula-decl nil integral_step nil)
(fmax const-decl "{ff: [T -> real] |
LET xx = seq(P) IN
FORALL (ii: below(length(P) - 1)):
FORALL (x: T):
(xx(ii) < x AND x < xx(ii + 1) IMPLIES
ff(x) = f(max_x(xx(ii), xx(ii + 1), f)))
AND ((xx(ii) = x OR x = xx(ii + 1)) IMPLIES ff(x) = f(x))}"
integral_cont_scaf nil)
(max_x const-decl "{mx: T |
a <= mx AND
mx <= b AND
(FORALL (x: T): a <= x AND x <= b IMPLIES f(mx) >= f(x))}"
interval_minmax nil)
(fmin_step formula-decl nil integral_cont_scaf nil)
(cont_restrict formula-decl nil integral_cont_scaf nil)
(floor const-decl "{i | i <= x & x < i + 1}" floor_ceil nil)
(integer nonempty-type-from-decl nil integers nil)
(eq_partition const-decl "partition(a, b)" integral_def 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)
(eps!1 skolem-const-decl "posreal" integral_cont 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
"(strict_total_order?[real])" real_props nil)
(TRUE const-decl "bool" booleans nil)
(continuous_on? const-decl "bool" continuous_functions nil)
(setof type-eq-decl nil defined_types nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(b!1 skolem-const-decl "T" integral_cont nil)
(a!1 skolem-const-decl "T" integral_cont nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(connected_domain formula-decl nil integral_cont nil))
nil)
(continuous_integrable-2 nil 3292320666
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a <= mx AND
mx <= b AND
(FORALL (x: T): a <= x AND x <= b IMPLIES f(mx) <= f(x))}"
interval_minmax nil)
(fmin const-decl "{ff: [T -> real] |
LET xx = seq(P) IN
FORALL (ii: below(length(P) - 1)):
FORALL (x: T):
(xx(ii) < x AND x < xx(ii + 1) IMPLIES
ff(x) = f(min_x(xx(ii), xx(ii + 1), f)))
AND ((xx(ii) = x OR x = xx(ii + 1)) IMPLIES ff(x) = f(x))}"
integral_cont_scaf nil)
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integral_def nil)
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(fmax const-decl "{ff: [T -> real] |
LET xx = seq(P) IN
FORALL (ii: below(length(P) - 1)):
FORALL (x: T):
(xx(ii) < x AND x < xx(ii + 1) IMPLIES
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("2" (typepred "y!1")
(("2" (expand "extend")
(("2" (ground) nil nil)) nil))
nil))
nil))
nil))
nil))
nil)
("3" (hide -1 -3 2)
(("3" (expand "subset?")
(("3" (skosimp*)
(("3" (expand "member")
(("3" (expand "extend") (("3" (ground) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (assert) nil nil) ("3" (assert) nil nil))
nil)
("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)
("3" (skosimp*)
(("3" (lemma "connected_domain")
(("3" (inst -1 "a!1" "b!1" "z!1") (("3" (assert) nil nil))
nil))
nil))
nil))
nil))
nil)
((step_function? const-decl "bool" step_fun_def nil)
(fmin const-decl "{ff: [T -> real] |
LET xx = seq(P) IN
FORALL (ii: below(length(P) - 1)):
FORALL (x: T):
(xx(ii) < x AND x < xx(ii + 1) IMPLIES
ff(x) = f(min_x(xx(ii), xx(ii + 1), f)))
AND ((xx(ii) = x OR x = xx(ii + 1)) IMPLIES ff(x) = f(x))}"
integral_cont_scaf 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)
(part_induction formula-decl nil integral_def nil)
(cont_restrict formula-decl nil integral_cont_scaf nil)
(cont_interv formula-decl nil integral_cont_scaf nil)
(width_eq_part formula-decl nil integral_def nil)
(width const-decl "posreal" integral_def nil)
(integral_bound_abs formula-decl nil integral_prep nil)
(width_lem formula-decl nil integral_def nil)
(integral_diff formula-decl nil integral_prep nil)
(step_function_integrable? formula-decl nil integral_step nil)
(fmax const-decl "{ff: [T -> real] |
LET xx = seq(P) IN
FORALL (ii: below(length(P) - 1)):
FORALL (x: T):
(xx(ii) < x AND x < xx(ii + 1) IMPLIES
ff(x) = f(max_x(xx(ii), xx(ii + 1), f)))
AND ((xx(ii) = x OR x = xx(ii + 1)) IMPLIES ff(x) = f(x))}"
integral_cont_scaf nil)
(partition type-eq-decl nil integral_def nil)
(eq_partition const-decl "partition(a, b)" integral_def nil)
(step_to_integrable formula-decl nil integral_step nil)
(adh const-decl "setof[real]" convergence_functions nil)
(convergence const-decl "bool" convergence_functions nil))
nil))
(cont_fun_integrable 0
(cont_fun_integrable-1 nil 3313938280
("" (skosimp*)
(("" (lemma "continuous_integrable")
(("" (inst?)
(("" (assert)
(("" (skosimp*)
(("" (expand "continuous?" -2) (("" (inst?) nil nil)) nil))
nil))
nil))
nil))
nil))
nil)
((continuous_integrable formula-decl nil integral_cont nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(continuous? const-decl "bool" continuous_functions nil)
(bool nonempty-type-eq-decl nil booleans nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(<= const-decl "bool" reals nil)
(closed_interval type-eq-decl nil intervals_real "reals/")
(T formal-subtype-decl nil integral_cont nil)
(T_pred const-decl "[real -> boolean]" integral_cont 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))
shostak)))
| Messung V0.5 in Prozent |
|---|
| | | |
[Verzeichnis aufwärts0.359unsichere VerbindungÜbersetzung europäischer Sprachen durch Browser2026-04-25]
|
2026-05-26
|