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((""
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"y"
"2 ^ -(1 + p!1) + sx!1 ^ pn!1"
"pz"
"2^p!1"))
((""
(lemma
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"(-(rx!1 * e1!1)) ^ pn!1"
"x"
"sx!1 ^ pn!1 - 2 ^ -(1 + p!1)"
"pz"
"2^p!1"))
((""
(assert)
nil
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
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nil))
nil))
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nil))
nil))
nil))
nil))
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nil))
nil))
nil))
nil))
nil))
nil)
((posnat nonempty-type-eq-decl nil integers nil)
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(>= const-decl "bool" reals nil)
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(int nonempty-type-eq-decl nil 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
nil)
(boolean nonempty-type-decl nil booleans nil)
(number nonempty-type-decl nil numbers nil)
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(rat nonempty-type-eq-decl nil rationals nil)
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(* const-decl "[numfield, numfield -> numfield]" number_fields nil)
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(div_mult_pos_lt2 formula-decl nil real_props nil)
(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
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(minus_odd_is_odd application-judgement "odd_int" integers nil)
(posint_plus_nnint_is_posint application-judgement "posint"
integers nil)
(real_div_nzreal_is_real application-judgement "real" reals nil)
(posint_exp application-judgement "posint" exponentiation nil)
(int_plus_int_is_int application-judgement "int" integers nil)
(minus_int_is_int application-judgement "int" integers nil)
(posrat_exp application-judgement "posrat" exponentiation nil)
(nnrat_exp application-judgement "nnrat" exponentiation nil)
(real_plus_real_is_real application-judgement "real" reals nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(real_minus_real_is_real application-judgement "real" reals nil)
(both_sides_times_pos_lt1 formula-decl nil real_props nil)
(posrat_times_posrat_is_posrat application-judgement "posrat"
rationals nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(both_sides_expt_pos_lt formula-decl nil exponentiation nil)
(minus_real_is_real application-judgement "real" reals nil)
(<= const-decl "bool" reals nil)
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(negreal nonempty-type-eq-decl nil real_types nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(expt def-decl "real" exponentiation nil)
(nzreal nonempty-type-eq-decl nil reals nil)
(expt_plus formula-decl nil exponentiation nil)
(div_mult_pos_lt1 formula-decl nil real_props nil)
(rat_plus_rat_is_rat application-judgement "rat" rationals nil)
(smallreal nonempty-type-eq-decl nil prelude_aux nil)
(< const-decl "bool" reals nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(- const-decl "[numfield -> numfield]" number_fields nil)
(lemma_A4 formula-decl nil appendix nil)
(nnint_plus_posint_is_posint application-judgement "posint"
integers nil)
(minus_nzint_is_nzint application-judgement "nzint" integers nil))
nil))
(cauchy_power_lt1_snz_odd_TCC1 0
(cauchy_power_lt1_snz_odd_TCC1-1 nil 3250077324
("" (subtype-tcc) nil nil)
((odd? const-decl "bool" integers nil)
(ln const-decl "real" ln_exp "lnexp_fnd/")
(Integral const-decl "real" integral_def "analysis/")
(log2 const-decl "real" prelude_aux nil)
(/= const-decl "boolean" notequal nil)
(int_plus_int_is_int application-judgement "int" integers nil)
(posint_plus_nnint_is_posint application-judgement "posint"
integers nil)
(mult_divides2 application-judgement "(divides(m))" divides nil)
(mult_divides1 application-judgement "(divides(n))" divides nil)
(even_times_int_is_even application-judgement "even_int" integers
nil))
nil))
(cauchy_power_lt1_snz_odd_TCC2 0
(cauchy_power_lt1_snz_odd_TCC2-1 nil 3250077324
("" (subtype-tcc) nil nil)
((^ const-decl "real" exponentiation nil)
(round const-decl "int" prelude_aux nil)
(ln const-decl "real" ln_exp "lnexp_fnd/")
(Integral const-decl "real" integral_def "analysis/")
(log2 const-decl "real" prelude_aux nil)
(odd? const-decl "bool" integers nil)
(/= const-decl "boolean" notequal nil)
(mult_divides2 application-judgement "(divides(m))" divides nil)
(mult_divides1 application-judgement "(divides(n))" divides nil)
(even_times_int_is_even application-judgement "even_int" integers
nil)
(int_plus_int_is_int application-judgement "int" integers nil)
(posint_plus_nnint_is_posint application-judgement "posint"
integers nil)
(real_times_real_is_real application-judgement "real" reals nil)
(posnat_expt application-judgement "posnat" exponentiation nil))
nil))
(cauchy_power_lt1_snz_odd 0
(cauchy_power_lt1_snz_odd-1 nil 3250077324
("" (skosimp*)
(("" (lemma "expt_neg_odd" ("n" "pn!1"))
(("" (replace -2 -1)
((""
(lemma "lemma_A2_generalized"
("r" "Y!1" "x" "(rx!1 * e1!1) ^ pn!1 * 2 ^ p!1"))
((""
(lemma "lemma_A4"
("pn" "pn!1" "e1" "e1!1" "n" "p!1+1" "x" "sx!1" "e2"
"2^-(p!1+1)"))
((""
(lemma "lemma_A4"
("pn" "pn!1" "e1" "e1!1" "n" "p!1+1" "x" "sx!1" "e2"
"2^-(p!1+1)"))
((""
(lemma "div_mult_pos_lt1"
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(("" (assert)
(("" (flatten)
(("" (replace -15)
(("" (rewrite "expt_0pn")
(("" (lemma "trich_lt" ("x" "rx!1" "y" "0"))
(("" (split -1)
(("1" (inst-cp - "rx!1*e1!1")
(("1"
(replace -14)
(("1"
(lemma
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(("1"
(lemma
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("x"
"sx!1 ^ pn!1 - 2 ^ -(1 + p!1)"
"y"
"0"
"pz"
"2^p!1"))
(("1"
(assert)
(("1"
(lemma
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"2"
"i"
"-(1 + p!1)"
"j"
"p!1"))
(("1"
(expand "^" -1 1)
(("1"
(expand "expt")
(("1"
(expand "expt")
(("1"
(replace -1 -2 rl)
(("1"
(lemma
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"y"
"0"
"pz"
"2^p!1"))
(("1"
(lemma
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"0"
"y"
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(("1"
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"pn!1"
"px"
"-sx!1"
"py"
"-(sx!1 - e1!1)"))
(("1"
(name-replace
"AA"
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"px"
"-e1!1 * rx!1"
"py"
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("x"
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"y"
"-B"
"pz"
"2^p!1"))
(("1"
(assert)
nil
nil))
nil))
nil))
nil))
nil))
nil)
("2"
(lemma
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("nx"
"-e1!1"
"ny"
"rx!1"))
(("2"
(assert)
nil
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2"
(lemma
"both_sides_times_neg_gt2"
("nz"
"-1"
"x"
"rx!1*e1!1"
"y"
--> --------------------
--> maximum size reached
--> --------------------
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