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real_props nil )
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real_props nil )
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real_types nil )
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real_props nil )
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real_types nil )
(* const-decl "[numfield, numfield -> numfield]" number_fields nil )
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real_types nil )
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nil )
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real_types nil )
(* const-decl "[T -> real]" real_fun_ops "reals/" )
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lim_of_composition "analysis/" )
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indefinite_integral "analysis/" )
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integral_split_scaf "analysis/" )
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"analysis/" )
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nil )
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nil )
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real_types nil )
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nil )
(- const-decl "[numfield, numfield -> numfield]" number_fields nil )
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shostak))
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nil )
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(- const-decl "[numfield -> numfield]" number_fields nil )
(nzreal_gt_m1 nonempty-type-eq-decl nil ln_exp_ineq nil ))
shostak))
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real_props nil )
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rationals nil )
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real_props nil ))
shostak))
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(lemma "ln_ineq1" ("xgtm1" "-px!1" ))
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(hide -1 -2 -4 -5 2)
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"x"
"1/(1-px!1)"
"y"
"3/2" ))
(("2"
(replace -1 1)
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((abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs
nil )
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(ln_1 formula-decl nil ln_exp nil )
(minus_odd_is_odd application-judgement "odd_int" integers nil )
(posreal_times_posreal_is_posreal application-judgement "posreal"
real_types nil )
(both_sides_plus_lt1 formula-decl nil real_props nil )
(- const-decl "[numfield -> numfield]" number_fields nil )
(ln const-decl "real" ln_exp nil )
(/= const-decl "boolean" notequal nil )
(nznum nonempty-type-eq-decl nil number_fields nil )
(/ const-decl "[numfield, nznum -> numfield]" number_fields nil )
(* const-decl "[numfield, numfield -> numfield]" number_fields nil )
(<= const-decl "bool" reals nil )
(div_mult_pos_le1 formula-decl nil real_props nil )
(real_times_real_is_real application-judgement "real" reals 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 )
(both_sides_times_neg_le1 formula-decl nil real_props nil )
(nzrat_div_nzrat_is_nzrat application-judgement "nzrat" rationals
nil )
(both_sides_times_pos_le1 formula-decl nil real_props nil )
(nzreal_div_nzreal_is_nzreal application-judgement "nzreal"
real_types nil )
(nzreal_gt_m1 nonempty-type-eq-decl nil ln_exp_ineq nil )
(nzreal nonempty-type-eq-decl nil reals nil )
(ln_ineq1 formula-decl nil ln_exp_ineq nil )
(minus_nzreal_is_nzreal application-judgement "nzreal" real_types
nil )
(deriv_id_fun formula-decl nil derivatives "analysis/" )
(deriv_const_fun formula-decl nil derivatives "analysis/" )
(diff_derivable_fun formula-decl nil derivatives "analysis/" )
(- const-decl "[T -> real]" real_fun_ops "reals/" )
(ln_derivable formula-decl nil ln_exp nil )
(composition_derivable_fun formula-decl nil chain_rule "analysis/" )
(O const-decl "T3" function_props nil )
(sum_derivable_fun formula-decl nil derivatives "analysis/" )
(+ const-decl "[T -> real]" real_fun_ops "reals/" )
(negative_derivative formula-decl nil derivative_props "analysis/" )
(connected? const-decl "bool" deriv_domain_def "analysis/" )
(NOT const-decl "[bool -> bool]" booleans nil )
(extensionality_postulate formula-decl nil functions nil )
(derivable? const-decl "bool" derivatives_def "analysis/" )
(deriv const-decl "real" derivatives_def "analysis/" )
(div_mult_pos_lt2 formula-decl nil real_props nil )
(deriv_domain_open formula-decl nil deriv_domain "analysis/" )
(open_interval type-eq-decl nil intervals_real "reals/" )
(deriv const-decl "[T -> real]" derivatives "analysis/" )
(deriv_sum_fun formula-decl nil derivatives "analysis/" )
(nzreal_times_nzreal_is_nzreal application-judgement "nzreal"
real_types nil )
(* const-decl "[T -> real]" real_fun_ops "reals/" )
(deriv_comp_fun formula-decl nil chain_rule "analysis/" )
(* const-decl "[T -> real]" real_fun_ops "reals/" )
(deriv_scal_fun formula-decl nil derivatives "analysis/" )
(scal_derivable_fun formula-decl nil derivatives "analysis/" )
(deriv_fun type-eq-decl nil derivatives "analysis/" )
(derivable? const-decl "bool" derivatives "analysis/" )
(deriv_diff_fun formula-decl nil derivatives "analysis/" )
(I const-decl "(bijective?[T, T])" identity nil )
(const_derivable_fun formula-decl nil derivatives "analysis/" )
(not_one_element? const-decl "bool" deriv_domain_def "analysis/" )
(deriv_domain? const-decl "bool" deriv_domain_def "analysis/" )
(identity_derivable_fun formula-decl nil derivatives "analysis/" )
(G skolem-const-decl "[{x: posreal | 1/3 < x & x < 1} -> real]"
ln_exp_ineq nil )
(strict_decreasing? const-decl "bool" real_fun_preds "reals/" )
(minus_even_is_even application-judgement "even_int" integers nil )
(minus_nzint_is_nzint application-judgement "nzint" integers nil )
(real_gtm1_le1 nonempty-type-eq-decl nil ln_exp_series_alt nil )
(nat nonempty-type-eq-decl nil naturalnumbers 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 )
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"y"
"3/2" ))
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--> maximum size reached
--> --------------------
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