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nil))
nil))
nil))
nil))
nil))
nil))
nil)
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nil))
nil)
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real_props nil)
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nil))
(IMP_power_series_deriv_TCC1 0
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nil)
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(real_pred const-decl "[number_field -> boolean]" reals 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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shostak))
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(("" (lemma not_one_element)
(("" (lemma connected_deriv_domain[T]) (("" (assert) nil nil))
nil))
nil))
nil)
((not_one_element formula-decl nil taylor_series nil)
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nil)
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(real_pred const-decl "[number_field -> boolean]" reals nil)
(real nonempty-type-from-decl nil reals nil)
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("2" (inst - "XX" "-XX" "0")
(("2" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
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(bool nonempty-type-eq-decl nil booleans nil)
(T formal-nonempty-subtype-decl nil taylor_series nil)
(T_pred const-decl "[real -> boolean]" taylor_series nil)
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(real_pred const-decl "[number_field -> boolean]" reals nil)
(number_field nonempty-type-from-decl nil number_fields nil)
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real_props nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
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(ball formula-decl nil taylor_series nil))
shostak))
(Inf_sum_0 0
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(("" (assert)
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(("" (expand "powerseq")
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(case-replace "(LAMBDA (k: nat): a!1(k) * 0 ^ k) =
(LAMBDA (k: nat):
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(case-replace "(LAMBDA (n: nat):
sigma(0, n,
(LAMBDA (k: nat): IF k = 0 THEN a!1(0) ELSE 0 ENDIF))) =
(LAMBDA (n: nat): a!1(0) )")
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nil))
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nil)
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(inst?)
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(expand "sigma")
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(assert)
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(expand "restrict")
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(lemma "sigma_const")
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(inst?)
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(assert)
nil
nil))
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nil))
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nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
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(("2" (ground) (("2" (grind) nil nil)) nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
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(even_minus_odd_is_odd application-judgement "odd_int" integers
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(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
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(sigma_nat application-judgement "nat" sigma_nat "reals/")
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(int_times_even_is_even application-judgement "even_int" integers
nil)
(int_plus_int_is_int application-judgement "int" integers nil)
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(sigma_restrict_to formula-decl nil sigma "reals/")
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nil)
(real_lt_is_strict_total_order name-judgement
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(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
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"(strict_total_order?[real])" real_props nil)
(zero_hat formula-decl nil exponent_props "reals/")
(nat_expt application-judgement "nat" exponentiation nil)
(nzrat_div_nzrat_is_nzrat application-judgement "nzrat" rationals
nil)
(expt def-decl "real" exponentiation nil)
(powerseq const-decl "sequence[real]" power_series nil))
shostak))
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(("" (assert)
(("" (expand "derivseq")
(("" (name-replace "FNX" "factorial(n!1 + x!1)")
(("" (field 1) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil)
((nderivseq const-decl "sequence[real]" taylor_series nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
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(odd_minus_odd_is_even application-judgement "even_int" integers
nil)
(even_minus_odd_is_odd application-judgement "odd_int" integers
nil)
(odd_plus_odd_is_even application-judgement "even_int" integers
nil)
(int_plus_int_is_int application-judgement "int" integers nil)
(mult_divides2 application-judgement "(divides(m))" divides nil)
(mult_divides1 application-judgement "(divides(n))" divides nil)
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(derivseq const-decl "sequence[real]" power_series_derivseq nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
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(bool nonempty-type-eq-decl nil booleans 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)
(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
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(boolean nonempty-type-decl nil booleans nil)
(number nonempty-type-decl nil numbers nil))
shostak))
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(("1" (expand "nderivseq")
(("1"
(case-replace
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(("1" (apply-extensionality 1 :hide? t) nil nil)) nil))
nil))
nil)
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(("2" (rewrite "nderivseq_lem")
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(("2" (assert)
(("2" (hide 2) (("2" (rewrite "conv_derivseq") nil nil))
nil))
nil))
nil))
nil))
nil))
nil)
((derivseq const-decl "sequence[real]" power_series_derivseq nil)
(conv_derivseq formula-decl nil power_series_derivseq nil)
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(/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
(nonneg_int nonempty-type-eq-decl nil integers nil)
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(posnat nonempty-type-eq-decl nil integers nil)
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(posrat_div_posrat_is_posrat application-judgement "posrat"
rationals nil)
(real_times_real_is_real application-judgement "real" reals nil)
(nat_induction formula-decl nil naturalnumbers nil)
(nderivseq const-decl "sequence[real]" taylor_series nil)
(conv_powerseries? const-decl "bool" power_series_conv nil)
(T formal-nonempty-subtype-decl nil taylor_series nil)
(T_pred const-decl "[real -> boolean]" taylor_series nil)
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
(sequence type-eq-decl nil sequences nil)
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(nat nonempty-type-eq-decl nil naturalnumbers nil)
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(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)
(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))
(Inf_sum_derivable_n_times_TCC1 0
(Inf_sum_derivable_n_times_TCC1-1 nil 3471697763
("" (skosimp*)
(("" (lemma "deriv_domain") (("" (inst?) nil nil)) nil)) nil)
((deriv_domain formula-decl nil taylor_series nil)) nil))
(Inf_sum_derivable_n_times 0
(Inf_sum_derivable_n_times-1 nil 3298373838
("" (induct "n")
(("1" (skosimp*)
(("1" (expand "derivable_n_times?") (("1" (propax) nil nil))
nil))
nil)
("2" (skosimp*)
(("2" (expand "derivable_n_times?" 1)
(("2" (rewrite "Inf_sum_derivable")
(("2" (inst - "derivseq(a!1)")
(("2" (rewrite "conv_derivseq")
(("2" (rewrite "deriv_Inf_sum") nil nil)) nil))
nil))
nil))
nil))
nil)
("3" (hide 2)
(("3" (lemma "not_one_element") (("3" (skosimp*) nil nil)) nil))
nil)
("4" (hide 2)
(("4" (lemma "connected_domain") (("4" (skosimp*) nil nil)) nil))
nil))
nil)
((Inf_sum_derivable formula-decl nil power_series_deriv nil)
(conv_derivseq formula-decl nil power_series_derivseq nil)
(deriv_Inf_sum formula-decl nil power_series_deriv nil)
(derivseq const-decl "sequence[real]" power_series_derivseq nil)
(nat_induction formula-decl nil naturalnumbers nil)
(Inf_sum const-decl "real" power_series_conv nil)
(derivable_n_times? def-decl "bool" nth_derivatives "analysis/")
(conv_powerseries? const-decl "bool" power_series_conv nil)
(T formal-nonempty-subtype-decl nil taylor_series nil)
(T_pred const-decl "[real -> boolean]" taylor_series nil)
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
(sequence type-eq-decl nil sequences nil)
(pred type-eq-decl nil defined_types 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)
(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))
(nderiv_Inf_sum_TCC1 0
(nderiv_Inf_sum_TCC1-1 nil 3298366314
("" (skosimp*) (("" (rewrite "Inf_sum_derivable_n_times") nil nil))
nil)
((Inf_sum_derivable_n_times formula-decl nil taylor_series 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)
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(integer_pred const-decl "[rational -> boolean]" integers nil)
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(bool nonempty-type-eq-decl nil booleans nil)
(>= const-decl "bool" reals nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(sequence type-eq-decl nil sequences nil))
shostak))
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(nderiv_Inf_sum_TCC2-1 nil 3298366314
("" (skosimp*)
(("" (lemma " conv_nderivseq")
(("" (inst?) (("" (assert) nil nil)) nil)) nil))
nil)
((conv_nderivseq formula-decl nil taylor_series nil)
(sequence type-eq-decl nil sequences nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
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(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)
(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))
(nderiv_Inf_sum 0
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(("1" (skosimp*)
(("1" (expand "nderiv")
(("1" (expand "nderivseq")
(("1"
(case-replace
"(LAMBDA (k: nat): factorial(k) / factorial(k) * a!1(k)) = a!1")
(("1" (hide 2)
(("1" (apply-extensionality 1 :hide? t) nil nil)) nil))
nil))
nil))
nil))
nil)
("2" (skosimp*)
(("2" (expand "nderiv" 1)
(("2" (lemma "deriv_Inf_sum")
(("2" (inst?)
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(("2" (inst?)
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(("2" (replace -1)
(("2" (hide -1)
(("2"
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--> --------------------
--> maximum size reached
--> --------------------
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