|
(series
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real_props nil))
shostak))
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nil))
nil))
nil))
nil))
nil)
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shostak))
(geometric_series_TCC1 0
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((/= const-decl "boolean" notequal nil)) shostak))
(geometric_series_aux1_TCC1 0
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(/= const-decl "boolean" notequal nil))
shostak))
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nil)
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(("1" (rewrite "expt_x1")
(("1"
(lemma "minus_div2"
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(("1" (assert) nil nil)) nil))
nil)
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nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
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nil)
((NOT const-decl "[bool -> bool]" booleans nil)
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integers nil)
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(odd_minus_even_is_odd application-judgement "odd_int" integers
nil)
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nil)
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real_props nil)
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integers nil)
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nil)
(mult_divides1 application-judgement "(divides(n))" divides nil)
(mult_divides2 application-judgement "(divides(m))" divides nil)
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(* const-decl "[numfield, numfield -> numfield]" number_fields nil)
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(expt def-decl "real" exponentiation nil)
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(nnint_plus_posint_is_posint application-judgement "posint"
integers nil)
(real_minus_real_is_real application-judgement "real" reals nil))
shostak))
(geometric_series_aux_odd_TCC1 0
(geometric_series_aux_odd_TCC1-1 nil 3251280973 ("" (grind) nil nil)
((boolean nonempty-type-decl nil booleans nil)
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nil)
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(int nonempty-type-eq-decl nil integers nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
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real_props nil)
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"(strict_total_order?[real])" real_props nil)
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(odd_minus_odd_is_even application-judgement "even_int" integers
nil)
(odd? const-decl "bool" integers nil)
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nil)
(mult_divides1 application-judgement "(divides(n))" divides nil)
(mult_divides2 application-judgement "(divides(m))" divides nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(rat_div_nzrat_is_rat application-judgement "rat" rationals nil))
shostak))
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"w"
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(lemma
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"x!1"
"i"
"2"
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(assert)
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nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
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nil))
nil))
nil)
("2" (assert) nil nil))
nil)
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nil)
("3"
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(lemma "lt_times_lt_neg1"
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"-1"
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"x!1"
"z"
"-1"
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"x!1"
"i"
"2"
"j"
"j!1+1"))
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(lemma
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("n0x"
"x!1"
"i"
"1"
"j"
"1"))
(("1"
(rewrite "expt_x1")
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nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (assert) nil nil))
nil)
("2" (assert) nil nil))
nil))
nil))
nil))
nil)
("2" (assert) nil nil) ("3" (assert) nil nil)
("4" (assert) nil nil))
nil)
("2" (assert) nil nil))
nil)
("2" (assert) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((even_times_int_is_even application-judgement "even_int" integers
nil)
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(mult_divides2 application-judgement "(divides(m))" divides nil)
(odd? const-decl "bool" integers nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(real_plus_real_is_real application-judgement "real" reals nil)
(rat_div_nzrat_is_rat application-judgement "rat" rationals nil)
(odd_plus_even_is_odd application-judgement "odd_int" integers nil)
(odd_minus_odd_is_even application-judgement "even_int" integers
nil)
(real_times_real_is_real application-judgement "real" reals nil)
(div_div2 formula-decl nil real_props nil)
(expt_plus formula-decl nil exponentiation nil)
(lt_times_lt_pos1 formula-decl nil real_props nil)
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(posreal nonempty-type-eq-decl nil real_types nil)
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(AND const-decl "[bool, bool -> bool]" booleans nil)
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(even_plus_even_is_even application-judgement "even_int" integers
nil)
(posint_plus_nnint_is_posint application-judgement "posint"
integers nil)
(odd_plus_odd_is_even application-judgement "even_int" integers
nil)
(rat_times_rat_is_rat application-judgement "rat" rationals nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
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(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(expt_x1 formula-decl nil exponentiation nil)
(nzreal nonempty-type-eq-decl nil reals nil)
(expt_times formula-decl nil exponentiation nil)
(odd_minus_even_is_odd application-judgement "odd_int" integers
nil)
(int_times_even_is_even application-judgement "even_int" integers
nil)
(even_minus_even_is_even application-judgement "even_int" integers
nil)
(even_plus_odd_is_odd application-judgement "odd_int" integers nil)
(nnint_times_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(nat_exp application-judgement "nat" exponentiation nil)
(nat_expt application-judgement "nat" exponentiation nil)
(nzrat_div_nzrat_is_nzrat application-judgement "nzrat" rationals
nil)
(even_minus_odd_is_odd application-judgement "odd_int" integers
nil)
(expt def-decl "real" exponentiation nil)
(lt_times_lt_neg1 formula-decl nil real_props nil)
(- const-decl "[numfield -> numfield]" number_fields nil)
(odd_times_odd_is_odd application-judgement "odd_int" integers nil)
(negreal nonempty-type-eq-decl nil real_types nil)
(< const-decl "bool" reals nil)
(nonpos_real nonempty-type-eq-decl nil real_types nil)
(<= const-decl "bool" reals nil)
(negreal_times_negreal_is_posreal judgement-tcc nil real_types nil)
(trichotomy formula-decl nil real_axioms nil)
(^ const-decl "real" exponentiation nil)
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(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
(/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
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real_props nil)
(* const-decl "[numfield, numfield -> numfield]" number_fields nil)
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(boolean nonempty-type-decl nil booleans nil)
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(/= const-decl "boolean" notequal nil)
(nonzero_real nonempty-type-eq-decl nil reals nil)
(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))
shostak))
(geometric_series_aux_even_TCC1 0
(geometric_series_aux_even_TCC1-1 nil 3251280976
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(("" (skosimp*)
(("" (lemma "div_cancel2" ("x" "j!1" "n0z" "2"))
(("" (replace -5)
(("" (replace -1) (("" (assert) nil nil)) nil)) nil))
nil))
nil))
nil)
((rat_div_nzrat_is_rat application-judgement "rat" rationals nil)
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(even_times_int_is_even application-judgement "even_int" integers
nil)
(div_cancel2 formula-decl nil real_props 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)
(real nonempty-type-from-decl nil reals nil)
(/= const-decl "boolean" notequal nil)
(nonzero_real nonempty-type-eq-decl nil reals nil)
(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)
(even? const-decl "bool" integers nil)
(rat_minus_rat_is_rat application-judgement "rat" rationals nil)
(nnrat_div_posrat_is_nnrat application-judgement "nonneg_rat"
rationals nil))
shostak))
(geometric_series_aux_even_TCC2 0
(geometric_series_aux_even_TCC2-1 nil 3251280976 ("" (grind) nil nil)
((even? const-decl "bool" integers nil)
(/= const-decl "boolean" notequal nil))
shostak))
(geometric_series_aux_even 0
(geometric_series_aux_even-1 nil 3251279760
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(("" (skosimp*)
(("" (expand "sum")
(("" (assert)
((""
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((""
(lemma "even_plus_odd_is_odd" ("e1" "n!1" "o2" "-1"))
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(("" (lemma "trich_lt" ("x" "n!1" "y" "2"))
(("" (split -1)
(("1" (grind) nil nil) ("2" (grind) nil nil)
("3" (grind) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((rat_minus_rat_is_rat application-judgement "rat" rationals nil)
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nil)
(int_plus_int_is_int application-judgement "int" integers nil)
(rat_div_nzrat_is_rat application-judgement "rat" rationals nil)
(^ const-decl "real" exponentiation nil)
(expt def-decl "real" exponentiation nil)
(geometric_series const-decl "[nat -> real]" series nil)
(trich_lt formula-decl nil real_props nil)
(- const-decl "[numfield -> numfield]" number_fields nil)
(odd_int nonempty-type-eq-decl nil integers nil)
(odd? const-decl "bool" integers nil)
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(even_plus_odd_is_odd judgement-tcc nil integers nil)
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real_props nil)
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(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)
(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)
(bool nonempty-type-eq-decl nil booleans nil)
(>= const-decl "bool" reals nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
(sum def-decl "real" series nil)
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(("1" (replace -4 1)
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(even_times_int_is_even application-judgement "even_int" integers
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nil))
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(inst + "n!1-1")
nil
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nil))
nil))
nil)
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real_types nil)
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(geometric_series_pos_limit 0
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(lemma "geometric_series_approx_set_pos_least_upper_bound"
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(/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
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nil))
shostak)))
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