|
(absconv_series
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(("" (split -1)
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("2" (hide 2) (("2" (skosimp) nil nil)) nil))
nil))
nil)
((single_nz_series_conv formula-decl nil series_lems nil)
(number nonempty-type-decl nil numbers nil)
(boolean nonempty-type-decl nil booleans 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)
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(rational_pred const-decl "[real -> boolean]" rationals nil)
(rational nonempty-type-from-decl nil rationals nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
(int nonempty-type-eq-decl nil integers nil)
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(nat nonempty-type-eq-decl nil naturalnumbers nil)
(sequence type-eq-decl nil sequences nil))
shostak)
(Convergent_Series_TCC1-1 nil 3351489385 ("" (subtype-tcc) nil nil)
nil nil))
(absconvergent_series_TCC1 0
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nil))
nil))
nil))
nil)
((abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs
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(abs const-decl "sequence[real]" series nil)
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(sequence type-eq-decl nil sequences 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))
shostak))
(absconvergent_series_is_convergent 0
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nil))
nil))
nil)
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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)
(number nonempty-type-decl nil numbers nil)
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(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil)
(convergent_abs formula-decl nil series nil))
shostak))
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(lemma "bij_inv_is_bij_alt"
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(("1"
(lemma "abs_series_bij"
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(("1" (split -1)
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(lemma "extensionality"
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(("2"
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(case-replace
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(expand "o" 1)
(("1" (propax) nil nil))
nil)
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(hide 2)
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(apply-extensionality 1 :hide? t)
(("2"
(expand "o")
(("2"
(lemma
"comp_inverse_right_alt"
("f"
"phi!1"
"g"
"x!2"
"r"
"x!3"))
(("2" (propax) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (typepred "aa!1")
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(("2" (hide-all-but (-1 -6 1))
(("2"
(lemma
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(("2"
(split -1)
(("1"
(hide -2 -3)
(("1"
(expand "o ")
(("1"
(expand "abs")
(("1" (propax) nil nil))
nil))
nil))
nil)
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(case-replace
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(("2"
(hide-all-but 1)
(("2"
(apply-extensionality :hide? t)
(("2" (grind) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("3" (propax) nil nil))
nil)
("2" (propax) nil nil))
nil)
("2" (propax) nil nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (flatten)
(("2"
(lemma "abs_series_bij"
("a" "aa!1" "phi" "phi!1" "x" "x!1"))
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(("2" (expand "absconvergent?")
(("2" (propax) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((bijective? const-decl "bool" functions nil)
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(>= const-decl "bool" reals nil)
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(integer_pred const-decl "[rational -> boolean]" integers nil)
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(rational_pred const-decl "[real -> boolean]" rationals nil)
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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)
(number nonempty-type-decl nil numbers nil)
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(boolean nonempty-type-decl nil booleans nil)
(exists1 const-decl "bool" exists1 nil)
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(absconvergent? const-decl "bool" absconv_series nil)
(O const-decl "T3" function_props nil)
(sequence type-eq-decl nil sequences nil)
(abs_series_bij formula-decl nil series_lems nil)
(minus_real_is_real application-judgement "real" reals nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs
nil)
(abs const-decl "sequence[real]" series nil)
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(extensionality formula-decl nil functions nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(comp_inverse_right_alt formula-decl nil function_inverse_def nil)
(assoc formula-decl nil function_props2 nil)
(inverse? const-decl "bool" function_inverse_def nil)
(bij_inv_is_bij_alt formula-decl nil function_inverse_def nil)
(bijective_inverse_exists formula-decl nil function_inverse_def
nil))
shostak))
(abs_series_bij_conv_abs 0
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("" (skosimp)
(("" (lemma "abs_series_bij_abs" ("aa" "aa!1" "phi" "phi!1"))
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(("1" (inst - "l!1")
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nil)
("2" (skosimp*)
(("2" (inst - "l!1")
(("2" (inst + "l!1") (("2" (assert) nil nil)) nil)) nil))
nil))
nil))
nil))
nil))
nil)
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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)
(abs_series_bij_abs formula-decl nil absconv_series nil)
(convergent? const-decl "bool" convergence_sequences "analysis/"))
shostak))
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(abs_series_bij_limit_abs_TCC1-1 nil 3351601341
("" (skosimp)
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nil))
nil))
nil)
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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)
(number nonempty-type-decl nil numbers nil)
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(boolean nonempty-type-decl nil booleans nil)
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nil))
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(lemma "limit_equiv"
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(lemma "absconvergent_series_is_convergent"
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(("" (assert)
(("" (rewrite "limit_equiv" -4) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((bijective? const-decl "bool" functions nil)
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(absconvergent? const-decl "bool" absconv_series nil)
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(integer_pred const-decl "[rational -> boolean]" integers nil)
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(rational_pred const-decl "[real -> boolean]" rationals nil)
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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)
(abs_series_bij_abs formula-decl nil absconv_series nil)
(limit_equiv formula-decl nil convergence_ops "analysis/")
(absconvergent_series_is_convergent judgement-tcc nil
absconv_series nil)
(O const-decl "T3" function_props nil)
(series const-decl "sequence[real]" series nil)
(limit const-decl "real" convergence_sequences "analysis/")
(convergent? const-decl "bool" convergence_sequences "analysis/")
(NOT const-decl "[bool -> bool]" booleans nil))
shostak))
(extract_convergent 0
(extract_convergent-1 nil 3323310225
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(("" (skosimp*)
(("" (inst + "l!1")
((""
(lemma "convergence_subsequence"
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(("" (assert)
(("" (hide-all-but 1)
(("" (expand "subseq")
(("" (inst + "f!1")
(("" (expand "o") (("" (propax) nil nil)) nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((extraction type-eq-decl nil sequence_props "analysis/")
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(sequence type-eq-decl nil sequences 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)
(convergence_subsequence formula-decl nil convergence_sequences
"analysis/")
(subseq const-decl "bool" sequence_props "analysis/")
(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)
(convergent? const-decl "bool" convergence_sequences "analysis/"))
shostak))
(extract_comp 0
(extract_comp-1 nil 3323305712
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(("" (typepred "f!1")
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(("1" (induct "x_1")
(("1" (inst - "0")
(("1" (replace -1)
(("1" (hide -1)
(("1" (expand "sigma")
(("1" (expand "sigma") (("1" (propax) nil nil))
nil))
nil))
nil))
nil))
nil)
("2" (skosimp*)
(("2" (inst - "j!1+1")
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(("2"
(expand "sigma" 1 1)
(("2"
(name-replace
"F"
"LAMBDA (n_1: nat):
IF EXISTS (m_1: nat): n_1 = f!1(m_1) THEN a!1(n_1)
ELSE 0
ENDIF")
(("2"
(replace -1 1)
(("2"
(hide -1)
(("2"
(replace -1 1 rl)
(("2"
(lemma
"sigma_split"
("low"
"0"
"high"
"f!1(1 + j!1)"
"F"
"F"
"z"
"f!1(j!1)"))
(("2"
(assert)
(("2" (assert) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("3" (typepred "f!1")
(("3" (skosimp) (("3" (assert) nil nil)) nil)) nil))
nil)
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(split -1)
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(case-replace
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(("1"
(assert)
(("1"
(hide -1)
(("1"
(lemma
"sigma_restrict_eq[nat]"
("low"
"0"
"high"
"f!1(0)-1"
"F"
"LAMBDA n: IF EXISTS m: n = f!1(m) THEN a!1(n) ELSE 0 ENDIF"
"G"
"LAMBDA n: 0"))
(("1"
(split -1)
(("1"
(rewrite "sigma_zero")
nil
nil)
("2"
(hide 2)
(("2"
(expand "restrict")
(("2"
(apply-extensionality
1
:hide?
t)
(("2"
(typepred "x!1")
(("2"
(case
"x!1)
(("1"
(assert)
(("1"
(case-replace
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(("1"
(hide 1)
(("1"
(skosimp)
(("1"
(typepred
"m!1")
(("1"
(expand
">=")
(("1"
(expand
"<="
-1)
(("1"
(split
-1)
(("1"
(inst
-
"0"
"m!1")
(("1"
(assert)
nil
nil))
nil)
("2"
(replace
-1
*
rl)
(("2"
(assert)
nil
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2"
(replace
1
2)
(("2"
(propax)
nil
nil))
nil))
nil))
nil)
("2"
(assert)
nil
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (inst + "0") nil nil))
nil))
nil))
nil)
("2"
(replace -1 * rl)
(("2"
(expand "sigma" 1)
(("2"
(case-replace
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(("1"
(expand "sigma")
(("1" (propax) nil nil))
nil)
("2" (inst + "0") nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
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(expand "sigma" 2)
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(assert)
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(case-replace
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(("1"
(case-replace
"1 + f!1(n!1 - 1) = f!1(n!1)")
(("1"
(expand "sigma")
(("1" (propax) nil nil))
nil)
("2"
(assert)
(("2"
(hide -1)
(("2"
(lemma
"sigma_restrict_eq[nat]"
("low"
"1 + f!1(n!1 - 1)"
"high"
"f!1(n!1) - 1"
"F"
"LAMBDA n: IF EXISTS m: n = f!1(m) THEN a!1(n) ELSE 0 ENDIF"
"G"
"lambda n:0"))
(("2"
(split -1)
(("1"
(rewrite
"sigma_zero[nat]")
nil
nil)
("2"
(hide 4)
(("2"
(expand "restrict")
(("2"
(apply-extensionality
1
:hide?
t)
(("2"
(typepred "x!1")
(("2"
(lift-if 1)
(("2"
(case-replace
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(("2"
(replace
1
2)
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(flatten)
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(case-replace
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(("1"
(skosimp)
(("1"
(replace
-1)
(("1"
(hide
-1
3)
(("1"
(lemma
"trich_lt"
("x"
"m!1"
"y"
"n!1"))
(("1"
(split
-1)
(("1"
(case
"m!1=n!1-1")
(("1"
(assert)
nil
nil)
("2"
(inst
-
"m!1"
"n!1-1")
(("2"
(assert)
nil
nil))
nil))
nil)
("2"
(assert)
nil
nil)
("3"
(inst
-
"n!1"
"m!1")
(("3"
(assert)
nil
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2"
(replace
1
4)
(("2"
(propax)
nil
nil))
nil))
nil))
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nil))
nil))
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nil))
nil))
nil))
nil))
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("2" (inst + "n!1") nil nil))
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nil))
nil))
nil))
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nil))
nil))
nil)
("3" (hide-all-but 1) (("3" (grind) nil nil)) nil)
("4" (skosimp*) (("4" (assert) nil nil)) nil)
("5" (skosimp*) (("5" (assert) nil nil)) nil))
nil)
("2" (skosimp*) (("2" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil)
((extraction type-eq-decl nil sequence_props "analysis/")
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(int nonempty-type-eq-decl nil integers nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
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(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
--> --------------------
--> maximum size reached
--> --------------------
¤ Dauer der Verarbeitung: 0.47 Sekunden
(vorverarbeitet)
¤
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