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hyperbolicx.prf
Interaktion und
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(hyperbolicx (sinh_lemma 0 (sinh_lemma-1 nil 3394197876 ("" (skosimp) (("" (expand "sinh") (("" (expand "cauchy_sinh") (("" (lemma "exp_lemma" ("x" "x!1" "cx" "cx!1")) (("" (lemma "neg_lemma" ("x" "x!1" "cx" "cx!1")) (("" (assert) (("" (lemma "exp_lemma" ("x" "-x!1" "cx" "cauchy_neg(cx!1)")) (("" (assert) (("" (lemma "sub_lemma" ("x" "exp(x!1)" "cx" "cauchy_exp(cx!1)" "y" "exp(-x!1)" "cy" "cauchy_exp(cauchy_neg(cx!1))")) (("" (assert) (("" (lemma "lemma_div2n" ("x" "exp(x!1) - exp(-x!1)" "cx" "cauchy_sub(cauchy_exp(cx!1),cauchy_exp(cauchy_neg(cx!1)))" "n" "1")) (("" (assert) (("" (expand "div2n") (("" (rewrite "expt_x1") nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((sinh const-decl "real" hyperbolic "lnexp_fnd/") (cauchy_real nonempty-type-eq-decl nil cauchy nil) (cauchy_real? const-decl "bool" cauchy 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) (exp_lemma formula-decl nil exp nil) (cauchy_exp_is_posreal application-judgement "cauchy_posreal" exp nil) (minus_real_is_real application-judgement "real" reals nil) (real_minus_real_is_real application-judgement "real" reals nil) (real_div_nzreal_is_real application-judgement "real" reals nil) (posint_exp application-judgement "posint" exponentiation nil) (expt_x1 formula-decl nil exponentiation nil) (div2n const-decl "real" shift nil) (- const-decl "[numfield, numfield -> numfield]" number_fields nil) (cauchy_sub const-decl "cauchy_real" sub nil) (lemma_div2n formula-decl nil shift nil) (sub_lemma formula-decl nil sub nil) (cauchy_exp const-decl "[nat -> int]" exp nil) (nonneg_real nonempty-type-eq-decl nil real_types nil) (> const-decl "bool" reals nil) (posreal nonempty-type-eq-decl nil real_types nil) (= const-decl "[T, T -> boolean]" equalities nil) (ln const-decl "real" ln_exp "lnexp_fnd/") (exp const-decl "{py | x = ln(py)}" ln_exp "lnexp_fnd/") (- const-decl "[numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (cauchy_neg const-decl "cauchy_real" neg nil) (neg_lemma formula-decl nil neg nil) (cauchy_sinh const-decl "[nat -> int]" hyperbolicx nil)) shostak)) (cosh_lemma 0 (cosh_lemma-1 nil 3394198044 ("" (skosimp) (("" (expand "cauchy_cosh") (("" (expand "cosh") (("" (lemma "neg_lemma" ("x" "x!1" "cx" "cx!1")) (("" (assert) (("" (lemma "exp_lemma" ("x" "x!1" "cx" "cx!1")) (("" (lemma "exp_lemma" ("x" "-x!1" "cx" "cauchy_neg(cx!1)")) (("" (assert) (("" (lemma "add_lemma" ("x" "exp(x!1)" "cx" "cauchy_exp(cx!1)" "y" "exp(-x!1)" "cy" "cauchy_exp(cauchy_neg(cx!1))")) (("" (assert) (("" (lemma "lemma_div2n" ("x" "exp(-x!1) + exp(x!1)" "cx" "cauchy_add(cauchy_exp(cx!1),cauchy_exp(cauchy_neg(cx!1)))" "n" "1")) (("" (assert) (("" (expand "div2n") (("" (rewrite "expt_x1") nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((cauchy_cosh const-decl "[nat -> int]" hyperbolicx nil) (cauchy_real nonempty-type-eq-decl nil cauchy nil) (cauchy_real? const-decl "bool" cauchy 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) (neg_lemma formula-decl nil neg nil) (exp_lemma formula-decl nil exp nil) (posint_exp application-judgement "posint" exponentiation nil) (expt_x1 formula-decl nil exponentiation nil) (div2n const-decl "real" shift nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (cauchy_add const-decl "cauchy_real" add nil) (lemma_div2n formula-decl nil shift nil) (add_lemma formula-decl nil add nil) (cauchy_exp const-decl "[nat -> int]" exp nil) (nonneg_real nonempty-type-eq-decl nil real_types nil) (> const-decl "bool" reals nil) (posreal nonempty-type-eq-decl nil real_types nil) (= const-decl "[T, T -> boolean]" equalities nil) (ln const-decl "real" ln_exp "lnexp_fnd/") (exp const-decl "{py | x = ln(py)}" ln_exp "lnexp_fnd/") (- const-decl "[numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (cauchy_neg const-decl "cauchy_real" neg nil) (posreal_div_posreal_is_posreal application-judgement "posreal" real_types nil) (posreal_plus_nnreal_is_posreal application-judgement "posreal" real_types nil) (minus_real_is_real application-judgement "real" reals nil) (cauchy_exp_is_posreal application-judgement "cauchy_posreal" exp nil) (cosh const-decl "posreal_ge1" hyperbolic "lnexp_fnd/")) shostak)) (cauchy_sinh_type 0 (cauchy_sinh_type-1 nil 3394196253 ("" (skosimp) (("" (typepred "cx!1") (("" (expand "cauchy_real?") (("" (skosimp) (("" (lemma "sinh_lemma" ("x" "x!1" "cx" "cx!1")) (("" (inst + "sinh(x!1)") (("" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil) ((cauchy_real nonempty-type-eq-decl nil cauchy nil) (cauchy_real? const-decl "bool" cauchy nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (>= const-decl "bool" reals 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) (number nonempty-type-decl nil numbers nil) (NOT const-decl "[bool -> bool]" booleans nil) (bool nonempty-type-eq-decl nil booleans nil) (boolean nonempty-type-decl nil booleans nil) (sinh const-decl "real" hyperbolic "lnexp_fnd/") (sinh_lemma formula-decl nil hyperbolicx nil)) nil)) (cauchy_cosh_type 0 (cauchy_cosh_type-1 nil 3394196253 ("" (skosimp) (("" (typepred "cx!1") (("" (expand "cauchy_real?") (("" (skosimp) (("" (lemma "cosh_lemma" ("x" "x!1" "cx" "cx!1")) (("" (expand "cauchy_posreal?") (("" (inst + "cosh(x!1)") (("1" (assert) nil nil) ("2" (typepred "cosh(x!1)") (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((cauchy_real nonempty-type-eq-decl nil cauchy nil) (cauchy_real? const-decl "bool" cauchy nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (>= const-decl "bool" reals 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) (number nonempty-type-decl nil numbers nil) (NOT const-decl "[bool -> bool]" booleans nil) (bool nonempty-type-eq-decl nil booleans nil) (boolean nonempty-type-decl nil booleans nil) (cauchy_posreal? const-decl "bool" cauchy nil) (nonneg_real nonempty-type-eq-decl nil real_types nil) (posreal nonempty-type-eq-decl nil real_types nil) (> const-decl "bool" reals nil) (x!1 skolem-const-decl "real" hyperbolicx nil) (cosh const-decl "posreal_ge1" hyperbolic "lnexp_fnd/") (posreal_ge1 nonempty-type-eq-decl nil hyperbolic "lnexp_fnd/") (AND const-decl "[bool, bool -> bool]" booleans nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (cosh_lemma formula-decl nil hyperbolicx nil)) nil)) (cauchy_coth_TCC1 0 (cauchy_coth_TCC1-1 nil 3394195229 ("" (skosimp) (("" (typepred "cnzx!1") (("" (expand "cauchy_nzreal?") (("" (skosimp) (("" (lemma "sinh_lemma" ("x" "x!1" "cx" "cnzx!1")) (("" (assert) (("" (inst + "sinh(x!1)") (("" (hide -1 -2) (("" (typepred "x!1") (("" (lemma "sinh_strict_increasing") (("" (expand "strict_increasing?") (("" (lemma "trichotomy" ("x" "x!1")) (("" (split -1) (("1" (inst - "0" "x!1") (("1" (rewrite "sinh_0") (("1" (assert) nil nil)) nil)) nil) ("2" (assert) nil nil) ("3" (inst - "x!1" "0") (("3" (rewrite "sinh_0") (("3" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((cauchy_nzreal nonempty-type-eq-decl nil cauchy nil) (cauchy_nzreal? const-decl "bool" cauchy nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (>= const-decl "bool" reals 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) (number nonempty-type-decl nil numbers nil) (NOT const-decl "[bool -> bool]" booleans nil) (bool nonempty-type-eq-decl nil booleans nil) (boolean nonempty-type-decl nil booleans nil) (sinh_strict_increasing formula-decl nil hyperbolic "lnexp_fnd/") (trichotomy formula-decl nil real_axioms nil) (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (sinh_0 formula-decl nil hyperbolic "lnexp_fnd/") (strict_increasing? const-decl "bool" real_fun_preds "reals/") (x!1 skolem-const-decl "nzreal" hyperbolicx nil) (sinh const-decl "real" hyperbolic "lnexp_fnd/") (sinh_lemma formula-decl nil hyperbolicx nil) (cauchy_real? const-decl "bool" cauchy nil) (cauchy_real nonempty-type-eq-decl nil cauchy nil) (/= const-decl "boolean" notequal nil) (nzreal nonempty-type-eq-decl nil reals nil)) nil)) (tanh_lemma 0 (tanh_lemma-1 nil 3394198250 ("" (skosimp) (("" (expand "tanh") (("" (expand "cauchy_tanh") (("" (lemma "sinh_lemma" ("x" "x!1" "cx" "cx!1")) (("" (lemma "cosh_lemma" ("x" "x!1" "cx" "cx!1")) (("" (assert) (("" (lemma "div_lemma" ("x" "sinh(x!1)" "cx" "cauchy_sinh(cx!1)" "nzy" "cosh(x!1)" "nzcy" "cauchy_cosh(cx!1)")) (("" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((tanh const-decl "real_abs_lt1" hyperbolic "lnexp_fnd/") (cauchy_real nonempty-type-eq-decl nil cauchy nil) (cauchy_real? const-decl "bool" cauchy 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) (sinh_lemma formula-decl nil hyperbolicx nil) (cauchy_cosh_type application-judgement "cauchy_posreal" hyperbolicx nil) (cauchy_sinh_type application-judgement "cauchy_real" hyperbolicx nil) (real_div_nzreal_is_real application-judgement "real" reals nil) (div_lemma formula-decl nil div nil) (cauchy_sinh const-decl "[nat -> int]" hyperbolicx nil) (cauchy_nzreal? const-decl "bool" cauchy nil) (cauchy_nzreal nonempty-type-eq-decl nil cauchy nil) (cauchy_cosh const-decl "[nat -> int]" hyperbolicx nil) (/= const-decl "boolean" notequal nil) (nonzero_real nonempty-type-eq-decl nil reals nil) (posreal_ge1 nonempty-type-eq-decl nil hyperbolic "lnexp_fnd/") (cosh const-decl "posreal_ge1" hyperbolic "lnexp_fnd/") (sinh const-decl "real" hyperbolic "lnexp_fnd/") (cosh_lemma formula-decl nil hyperbolicx nil) (cauchy_tanh const-decl "[nat -> int]" hyperbolicx nil)) shostak)) (sech_lemma 0 (sech_lemma-1 nil 3394198358 ("" (skosimp) (("" (expand "sech") (("" (expand "cauchy_sech") (("" (lemma "cosh_lemma" ("x" "x!1" "cx" "cx!1")) (("" (assert) (("" (lemma "inv_lemma" ("nzx" "cosh(x!1)" "nzcx" "cauchy_cosh(cx!1)")) (("" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil) ((sech const-decl "posreal_le1" hyperbolic "lnexp_fnd/") (cauchy_real nonempty-type-eq-decl nil cauchy nil) (cauchy_real? const-decl "bool" cauchy 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]" java.lang.StringIndexOutOfBoundsExcep (rational(" (rational_predconstdecl"[- " nil) realnonempty-from-nil reals nil) (real_pred lemmasjava.lang.StringIndexOutOfBoundsException: Index 38 out of bound (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" java.lang.StringIndexOutOfBoundsEx nil) boolean nonempty-typedecl booleans (nonempty-decl numbers java.lang.StringIndexOutOfBoundsException: Index 47 out of (cosh_lemma formula-decl nil(" expand "java.lang.StringIndexOutOfBoundsException: In (cosh const-decl "posreal_ge1" hyperbolic "lnexp_fnd/") (posreal_ge1) (nzreal nonempty-type-eq-decl nil reals nil) (/= const-decl "boolean" notequal nil) (cauchy_coshnil)java.lang.StringIndexOutOfBoundsException: Index 27 out of bound nil) (cauchy_nzreal)java.lang.StringIndexOutOfBoundsException: Index 11 out of bounds inv_lemmaformula-ecl inv) (-java.lang.StringIndexOutOfBoundsException: Range [55, 54) out of bounds for le java.lang.StringIndexOutOfBoundsException: Range [16, 15) out of bounds for leng (int ---declnil) nil) java.lang.StringIndexOutOfBoundsException: Range [17, 16) out of bounds for leng (rationa const- "[eal > java.lang.StringIndexOutOfBoundsException: Range [48, 47) out coth_lemmajava.lang.StringIndexOutOfBoundsException: Index 14 out of bounds for (coth_lemma-1 nil 3394198526 ("" (skosimp) ("( ") (("" (expand " ) (("" (real_minus_real_is_realjava.lang.StringIndexOutOfBoundsException: Range [41 ( l ""(x""zx1 cx" "nzx!") (("" (assert) ((iv2ndeclr"shift ) (("" (rewrite "div_div1") sub_lemma formula- nilsub nil) (("1" (lemma "div_lemma" ("""osh!) c""cnzx1" "nzy" "sinh(nzx!1)" "nzcy" "cauchy_sinh(cnzx!(n -decl"eal ""java.lang.StringIndexOutOfBoundsException: Index (("1" (assert) nil nil)) nil)) (cauchy_neg const-decl "cauchy_real" neg nil) "" hide-all- 1) (2"(emma "sinh_0) (("2" (lemma "sinh_strict_increasing") (("2" (expand "strict_increasing?") (("2" (lemma "trichotomy" ((""(expand "cosh") (("2" (split -1) (("1" ( ("x" "-x!1" "cx" "ca1)) 1 a nil) ) 2assert)nil nil) " e(!1 +expx) "" "!1" "0) (("3" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((cauchy_coth const-decl "[nat -> int]" hyperbolicx nil) (nzreal nonempty-type-eq-decl nil reals nil) (/= const-decl "boolean" notequal nil) (cauchy_nzreal nonempty-type-eq-decl nil cauchy nil) (cauchy_nzreal? const-decl "bool" cauchy nil) (cauchy_real nonempty-type-eq-decl nil cauchy nil) (cauchy_real? const-decl "bool" cauchy nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (>= const-decl "bool" reals nil) (bool -type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty--from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) r -type-decl reals nil) (real_pred const-decl "[number_field (n decl real "nexp_fnd/) (umber_field java.lang.StringIndexOutOfBoundsException: Range [27, 26) out of bou (java.lang.StringIndexOutOfBoundsException: Range [23, 22) out of bounds for len nil) java.lang.StringIndexOutOfBoundsException: Range [9, 8) out of bounds for length (-typedeclnil nil ( "cauchy_real?") (" skosimpjava.lang.StringIndexOutOfBoundsException: Index 22 out of bounds for l nil)(" inst+ sx)" ( a) nilnil ) (cauchy_cosh_type) icx niljava.lang.StringIndexOutOfBoundsException: Index 21 out of bounds for leng (nzreal_div_nzreal_is_nzreal (cauchy_real? const-decl "bool" cauchy real_types nil) (cosh consti nonempty--q nil nil) (nonemptyeq- nilhyperbolic"nexp_fnd/) (sinh const-decl "real" hyperbolic "lnexp_fnd/") (nonempty-ype-eclnil nil) (div_div1 formula-decl nil real_props nil) (real_div_nzreal_is_real application-number_field nonempty-type-from-decl niljava.l (real_times_real_is_real application-judgement "real" reals nil) (div_lemma(umber -type numbers) NOT const-"[bool -> bool]" booleans nil) (cauchy_sinh const-decl "[nat -> int]" hyperbolicx nil) (sinh_0s const r"hyperbolic l" (strict_increasing? const-decl "bool" java.lang.StringIndexOutOfBoundsException: In ("(skosimp "(strict_total_order?[real])" real_props(" (xpandcjava.lang.StringIndexOutOfBounds (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (trichotomy formula-decl nil real_axioms nil) easingformula-ecl lnexp_fnd/) (tanh const-decl "real_abs_lt1" hyperbolic "lnexp_fnd/") (cosh_lemma formula-decl nil hyperbolicx nil) (coth const-decl ("1" (ssert) nil ) (csch_lemma 0 (csch_lemma-1 nil 3394198422 ("" (skosimp) (("" nil)) (("" (assert) (("" (expand " nil) (("" (expand "csch") ((at--declniljava.lang.StringIndexOutOfBoundsException: Index 54 out of bounds f (lemma "inv_lemma" ("nzx" "(eal nonempty-ype-nil reals ) (("" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil) ((nzreal nonempty-type-eq-decl nil reals nil) " nil (cauchy_nzrealtype-q-ecl nil) (cauchy_nzreal? const-decl "bool" cauchy nil) (cauchy_real nonempty-typex1skolem--decl "eal"hyperbolicx nil) (?const-ecl ""cauchynil) ( nil naturalnumbers java.lang.StringIndexOutOfBoundsException: Range [54, 53) out (>(eal_ge_is_total_orderjudgement(otal_order?[real])" real_props java.lang.StringIndexOutOfBoundsException: Index 20 out of bounds for il) (nteger_pred const- [ >boolean] integers java.lang.StringIndexOutOfBoundsException: In (rational nonempty-type-from-decl nilcauchy_coth_TCC1-1 nil 3394195229 ((" (java.lang.StringIndexOutOfBoundsException: Range [19, 18) out of bounds for (real nonempty-type-from-(("" (lemma "sinh_lemma(x x1 cx""1)java.lang.StringIndexOutO (java.lang.StringIndexOutOfBoundsException: Range [14, 7) out of bounds for leng n nonemptytype-decl number_fields) (number_field_pred const-decl "[number -> java.lang.StringIndexOutOfBoundsException: nil) (" expand"" ) (sinh_lemma formula-decl nil hyperbolicx nil) (cauchy_csch const-decl "( (cauchy_sinh_type application-judgement "cauchy_real" hyperbolicx nil) (inv_lemma formula-decl nil inv nil) (cauchy_sinh const-decl "[nat -> int nil)java.lang.StringIndexOutOfBoundsException: In (sinh const-decl "real" hyperbolic "lnexp_fnd/") (nzreal_div_nzreal_is_nzreal application-judgement "nzreal" real_types nil) (csch const "3" shostak) (cauchy_tanh_type 0 (cauchy_tanh_type-1 nil 3394196253 ("" (skosimp) (("" (typepred "cx!1") (("" (expandnil)) (("" (skosimp) (("" (lemma "tanh_lemma" ("x" "x!1" "cx" "cx!1")) ( nil)) (("" (typepred "tanh(x!1)") (("" (nil) (("" (inst + " nil)) nil)) (cauchy_nzreal? constdecl "ool cauchy nil) nil)) nil)) nil))java.lang.StringIndexOutOfBoundsException: Index 11 out of bounds for lengt nil) ((cauchy_real nonempty-type(ationalnonempty--from nil (decl bool" nil natnonempty-ypeeqnil naturalnumbers java.lang.StringIndexOutOfBoundsException: Ind (>= const-decl "bool" reals nil) int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (type-from-decl nil rationalsnil) (rational_pred nil (eal nonempty-type-from-ecl reals niljava.lang.StringIndexOutOfBoundsException: Ind (real_pred const-decl "[number_field -> boolean]" reals bool nonempty-type-eq-decl nil boo (number_field (sinh_strict_increasing formula-ecl hyperbolicl/) (number_field_pred const-decl "(trichotomy formula-ecl real_axioms java.lang.StringIn nil) ( --eclnil numbers NOT-ecl"[bool >bool] nil) booleansnil -typedecl nil niljava.lang.StringIndexOutOfBoundsException: Index 49 out of bounds c?const-ecl ""cauchy nil) (smallreal nonempty-type-eq-decl nil prelude_aux java.lang.StringIndexOutOfBoundsExc (tanh const-decl "real_abs_lt1" hyperbolic "lnexp_fnd/") ( nonemptytype--eclnil "nexp_fnd/) (( 0 (- const-decl "[numfield -> numfield]" number_fields java.lang.StringIndexOutOfBoundsEx (numfield nonempty-type-eq-decl nil number_fields nil) (< const-decl "bool" reals nil) (formula-ecl nilhyperbolicx ) nil)) (cauchy_coth_type 0 (cauchy_coth_type-1 nil 3394196253 ("" (skosimp) (("" (typepred "("x" "sinhx!1) "cx cauchy_sinhcx!) "" ("(xpand cauchy_nzreal?java.lang.StringIndexOutOfBoundsException: Index 36 out of (("" (skosimp) (("" (lemma "coth_lemma" ("nzx ) (("" (assert) ((""(tanh-decl real_abs_lt1 "/) (auchy_realnonemptytype-- cauchynil) (("" (split -1) (("1" (assert) nil nil) ("2" (assert) nil java.lang.StringIndexOutOfBoundsException: In nil) nil) )java.lang.StringIndexOutOfBoundsException: Index 19 out of bounds for length 19 nil)) nil)) ) nil)) nil) ((cauchy_nzrealjava.lang.StringIndexOutOfBoundsException: Range [33, 32) out of (cauchy_nzreal(auchy_cosh_type application-judgement "cauchy_posreal" (nat nonempty-type-eq-decl nil naturalnumbers nil) (>= const-decl "bool" reals nil) ( nonempty-type--ecl integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) ( nil) (real nonempty-type-from-decl nil reals nil (auchy_nzreal? const-ecl"bool"cauchy nil) nstdecl "number_field >boolean] nil) (number_field nonempty-type-from-decl nil number_fields nil) (number_field_pred const-decl "[ nonzero_real -type-q- nilreals nil) niljava.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 9 (umber nonempty-type-decl nil numbers nil) (NOT const-decl "[bool - bool]" booleansnil) (bool (cauchy_tanhconst-decl "nat -> (boolean nonempty-type-decl nil booleans nil) (x!1 skolem- (java.lang.StringIndexOutOfBoundsException: Range [15, 13) out of bou (minus_odd_is_odd application-judgement "java.lang.StringIndexOutOfBoundsException (real_lt_is_strict_total_order name-judgement "strict_total_order?[eal)"real_props nil) (coth const-decl "real_abs_gt1" hyperbolic "lnexp_fnd/") (real_abs_gt1 nonempty-type-eq-decl nil hyperbolic "lnexp_fnd/") (- const-decl "[numfield -> numfield]" number_fields nil) (-type-eq-decl nil number_fields nil) (< const-decl "bool" reals nil) (OR const-decl "[bool, bool -> bool]" booleans nil) (coth_lemma formula-decl nil hyperbolicx nil) (/= const-decl "boolean" notequal nil) (nzreal nonempty-type-eq-decl nil reals nil)) nil)) (cauchy_csch_type 0 (cauchy_csch_type-1 nil 3394196253 ("" (skosimp) (("" (typepred "cnzx!1") (" (expand "cauchy_nzreal?) 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(("" (lemma(real_pred const- "number_fieldboolean] reals ) (("" (split -1) (("1" (inst - "0" "x!1") (("1" (rewrite "sinh_0") (("1" (coshconst-decl"osreal_ge1"hyperbolicl/) nil)) nil) ("2" (assert) nil nil) x1 "") (("3" "sinh_0") (("3" (assert) nil nil)) nil)) nil)) shostak) nil)) nil) nil)) nil)) nil)) nil) nil)) nil)) nil)) nil)) nil)) nil)) nil) (cnonemptytypeeqdeclnil cauchynil) (cauchy_nzreal? const-decl "bool" cauchy nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (>= const-decl "bool" reals nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (""(hide-- ) (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 -> (nst 0 nzx nil) (number nonempty-type-decl nil numbers nil) (NOT const-decl "[ " assert) nil) (bool nonempty-type-eq-decl nil booleans nil) (boolean nonempty-type-decl nil booleans nil) (sinh_strict_increasing formula-decl nil hyperbolic "lnexp_fnd/") (trichotomy formula-decl nil real_axioms nil) (nzreal_div_nzreal_is_nzrealnil) real_types nil) (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (sinh_0 formula-decl nil hyperbolic "lnexp_fnd/") ( ) (x!1 skolem-const-decl "nzreal" hyperbolicx nil ) (csch const-decl "real" hyperbolic "lnexp_fnd/") (csch_lemma formula-decl nil hyperbolicx nil) (/= const-decl " - "hyperbolicxjava.lang.StringIndexOutOfBoundsException: Index 59 o (nzreal nonempty-type-eq-decl nil reals nil)) / decl boolean java.lang.StringIndexOutOfB c? const-""cauchyniljava.lang.StringIndexOutOfBoundsException: Index 49 out of bo (cauchy_sech_type 0 (cauchy_sech_type-1 nil 3394196253 ("" (skosimp) (( java.lang.StringIndexOutOfBoundsException: Range [10, 9) out of bounds for len "java.lang.StringIndexOutOfBoundsException: Range [32, 31) out of bounds for len (("" (skosimp) (("" (lemma "sech_lemma" ("x" "x!1" "cx" "cx(eal nonempty-from- nil) ("java.lang.StringIndexOutOfBoundsException: Index 25 out of bounds for length 2 (("" (expand "cauchy_posreal?") (("" (inst + -declnumbers nil nil)) nil)) nil)) nil)) nil) nil) ((cauchy_real nonempty-type-eq-decl nil cauchy nil) (cauchy_real? const-decl "bool" cauchy nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (>= div_div1formula-eclnil real_props intnonempty--qdecl integers nil (integer_predconst"rational>boolean] nil) (rational-ypefromdecl nil rationalsniljava.lang.StringIndexOutOfBoundsException: I (rational_pred const-decl "[real -> boolean]" cauchy_sinh - " >int" ) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) ( type--decl nil number_fields nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (number nonempty-type-decl nil numbers nil) (NOT const-decl "[bool -> bool]" booleans nil (osh_lemma formuladecl nilhyperbolicx (bool nonempty-type-eq-decl nil booleans nil) (boolean nonempty-type-decl nil java.lang.StringIndexOutOfBoundsException: Range [0 (sech const-decl "posreal_le1" hyperbolic "lnexp_fnd/") (posreal_le1 nonempty-type-eq-decl nil hyperbolic "lnexp_fnd/") (<= const-decl " expand "" (posreal nonempty-type-eq-decl nil real_types nil) (> const-decl "bool" reals nil) -eq-ecl (cauchy_posreal? const-decl "bool" cauchy nil) (sech_lemma java.lang.StringIndexOutOfBoundsException: Range [0, 23) out of bound nil) (cauchy_ge1_TCC1 0 (cauchy_ge1_TCC1 (zreal nonempty-ype-qdeclnilnil) ("" (expand "cauchy_ge1?") (("" (inst + "1") (("" (rewrite" java.lang.StringIndexOutOfBoundsException: Index 49 o ((number nonempty-type-decl nil numbers nil) (boolean nonempty-type-decl nil booleans nil) (number_field_pred const-decl "[number -> boolean]" number_fields(=const- "ool java.lang java.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 9 (number_field nonempty-type-from-decl nil number_fields nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (real nonempty-java.lang.StringIndexOutOfBoundsException: Range [4, 1) out of bou (nonempty-eqnil java.lang.StringIndexOutOfBoundsException: Index 49 out of bounds (= const- "bool"reals nil) (posreal_ge1 nonempty-type-eq-decl nil hyperbolic "lnexp_fnd/") (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl number nonempty-decl nil numbers ) ( const- [ >boolean] nil) ((cauchy_cschconst-"nat->int] nil) (cauchy_ge1? const-decl "bool" (cauchy_sinh_type application-judgement"cauchy_real nil)java.lang.StringIndexOutOfBoundsException: Index 8 out of bounds for length (subtype_TCC1 0 (subtype_TCC1-1 nil 3394200357 ("" (skosimp) (("" (typepred "x!1") (("" (expand "cauchy_ge1?") )java.lang.StringIndexOutOfBoundsException: Index 12 ou (("" (auchy_tanh_type 0 (("" (expand "cauchy_posreal?") 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"y" x1) "cx "cy" "cauchy_sqrt(cauchy_add(cauchy_mul(cx!1, cx!1), cauchy_int(1)))")) (("1" (assert) (("1" (inst + "sqrt(1 + sq(x!1)) + x!1") (("1" (hide-all-but (-3 1))cauchy_addcauchy_mul!1,1,java.lang.StringIndexOutOfBoundsExce (("1" ( "" "sq_lt" "xjava.lang.StringIndexOutOfBoundsException: Index 38 out of bounds for length 3 "abs(x!1)" cauchy_int)" "sqrt(1 + sq(x!1))")) (x)!11 (rewrite((java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for (rewrite "sq_sqrt") (("" ) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (expand "cauchy_nnreal?") ("2"inst+"+x))nil nil nil)) nil) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((cauchy_real java.lang.StringIndexOutOfBoundsException: Index 25 out of bounds f ) n java.lang.StringIndexOutOfBoundsException: Range [18, 17) out of bounds for len (>= const-decl "bool" reals nil) (type--declnil integers ) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) realnonempty--- nilreals (real_pred const-decl "[ (real_pred const-decl "[number_field"[- boolean"reals) ((umber_field -ypefrom-nil nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (number nonempty-type-decl nil numbers nil) (NOT const-decl "[bool -> bool]" booleans(numbernonempty-type-decl nil numbers nil) (bool nonempty-type-eq-(java.lang.StringIndexOutOfBoundsException: Range [20, 19) (boolean nonempty-type-decl nil booleans nil) ( - nilmul ) (int_lemma formula-decl nil int nil) (posreal_plus_nnreal_is_posreal application-java.lang.StringIndexOutOfBoundsExcep real_types nil) (numfield nonempty-type-eq-decl nil number_fields nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (sqrt_pos application-judgement "posreal" sqrt "reals/") (sq_abs formula-decl nil sq "reals/") (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) "strict_total_order?real)"real_props nil (abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs nil) (- const-decl "[numfield -> numfield]" number_fields nil) (sq_lt formula-decl nil sq "reals/") (x!1 skolem-const-decl "real" hyperbolicx nil) (AND const-decl "[bool, bool -> bool]" booleans nil) (> const-decl "bool" reals nil) (posreal nonempty-type-eq-decl nil real_types nil) (real_plus_real_is_real application-judgement "real x1const"" ) (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (sqrt const-decl "{nnz: (sqrt const-decl "{nnz: nnrealnil real_types ) (* const-decl "[numfield, numfield -> numfield]" number_fields nil) (= const-decl "[T, T -> boolean]" equalities nil) (cauchy_sqrt const( {:nnreal |nnz nnx "eals"java.lang.StringIndexOutOfBoundsException (nnreal type-eq-decl nil real_types nil) (cauchy_add const-decl "cauchy_real" add nil) (cauchy_nnreal nonempty-type-eq-decl nil cauchy nil) (cauchy_nnreal? const-decl "bool" (cauchy_nnreal? const-decl "bool" cauchy) (sqrt_lemma formula-decl nil sqrtx nil) java.lang.StringIndexOutOfBoundsException: Range [20, 19) out of bounds for leng (cauchy_mul const-decl "cauchy_real" (""typepred "ge1xjava.lang.StringIndexOutOfBoun (cauchy_int const-decl "cauchy_real" int nil) ("tjava.lang.StringIndexOutOfBoundsExce (nonneg_real nonempty-type-eq("""sqjava.lang.StringIndexOutOfBoundsException: Ind (sq const-decl "nonneg_real" sq "reals/") (- nil sq "eals/) (cauchy_posreal? const-decl "bool" cauchy nil)) nil)) (cauchy_acosh_TCC1 0 (cauchy_acosh_TCC1-2 nil ("" (skosimp) ("( cge1x!"java.lang.StringIndexOutOfBoundsException: Index 29 out of bounds for (("" (expand "cauchy_ge1?") (("" (skosimp) (("" (typepred "x!1") (("" (lemma "sub_lemma" ("x" "sq(x!1)" )) "cauchy_mul(cge1x!1, cge1x!1)" "cy" "cauchy_int(1)")) (("" (rewrite "int_lemma") (("" (expand "sq" -1 1) ") (("" (expand "cauchy_nnreal?") (("" (inst + (nonemptytype- nilintegersnil) (("" (lemma "sq_le" ("nna" "1" "nnb" "x!1")) ("( nil) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) nil)) nil) ((cauchy_ge1 nonempty-type-eq-decl nil hyperbolicx nil) (cauchy_ge1? const-decl "bool" hyperbolicx nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) > const-decl "ool reals ) (nt -ype-qdecl integersniljava.lang.StringIndexOutOfBoundsException: Index 48 out (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals ( name- "total_order[eal]" (eal nonemptytype-from-ecl 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) (umfieldnonempty-ype-qdeclnilnumber_fields) (OT const "[ool- bool] booleans nil) (bool nonempty-type-eq-decl nil booleans[eal)java.lang.StringIndexOutOfBoundsExcept (boolean nonempty-type-decl nil booleans java.lang.StringIndexOutOfBoundsException: sq -decl" sq"/java.lang.StringIndexOutOfBoundsException: Index 45 out of bounds fo (l) (cauchy_int const-decl "cauchy_real" int nil) (cauchy_mul const-decl "cauchy_real" mul nil) (cauchy_real nonempty-type-eq-decl nil cauchy nil) (cauchy_real? const-decl "bool" java.lang.StringIndexOutOfBoundsException: Index 39 (sub_lemma formula-decl nil sub nil) (cauchy_nnreal? const-decl "bool" cauchy nil) (sq_le formula-decl nil sq "reals/") (real_le_is_total_order name-judgement "(total_order?[real])" real_props nil) (sq_nz_pos application-judgement "posreal" sq "reals/") (sq_1 formula-decl nil sq "reals/") (x!1 skolem-const-decl "posreal_ge1" hyperbolicx nil) (nnreal type-eq-decl nil real_types nil) (numfield nonempty-type-eq-decl nil number_fields nil) (" (assertjava.lang.StringIndexOutOfBoundsException: Index 33 out of bounds for l (real_minus_real_is_real application-judgement "real" reals nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (mul_lemma formula-decl nil mul (int_lemma formula-decl nil int nil) (posreal_ge1 nonempty-type-eq-decl nil hyperbolic "lnexp_fnd/")) nil) (cauchy_acosh_TCC1-1 nil 3394200357 ("" (skosimp) (("" (typepred "cge1x!1") (("" (expand "cauchy_ge1?") (("" (skosimp) (("" (lemma "mul_lemma" ("x" "x!1" "cx" "cge1x!1" "y" "x!1" "cy" "cge1x!1")) (("" (rewrite "sq_rew") (("" (assert) (("" (lemma "sub_lemma" ("x" "sq(x!1)" "cx" )) "y" "1" "cy" "cauchy_int(1)")) (("" (rewrite "int_lemma") ((" ) (("" (expand "cauchy_nnreal?") (("" (inst + "sq(x!1)-1") (("" (hide-all-but 1) (("" (typepred "x!1") (("" (lemma "sq_le" ("nna" "1" "nnb" "x!1")) (("" (rewrite "sq_1") (("" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil) java.lang.StringIndexOutOfBoundsException: Index 24 out of bounds for length 21 nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) nil) ((sq_rew formula-decl nil sq "reals/") (sq const-decl "nonneg_real" sq "reals/") (cauchy_int const-decl "cauchy_real" int nil) (cauchy_mul const-decl "cauchy_real" mul nil) (sub_lemma formuladeclnilsub nil) (sq_1 formula-decl nil sq "reals/") (sq_le formula-decl nil sq "reals/") (? const-ecl""cauchy ) (int_lemma formula-decl nil int nil) (mul_lemma formula-decl nil mul java.lang.StringIndexOutOfBoundsException: Index 42 ("1" (cauchy_real nonempty-type-java.lang.StringIndexOutOfBoundsException: Range [68, (posreal_ge1 nonempty-type-eq-decl nil hyperbolic "lnexp_fnd/")) nil)) (nil (cauchy_acosh_TCC2- ("2 propax nil) ("" (skosimp) (("" (typepred "cge1x!1") (("" (expand "cauchy_ge1?") (("" (skosimp) (("" (typepred "x!1") (("" (lemma "sub_lemma" ("x" "sq(x!1)" "y" "1" "cx" "java.lang.StringIndexOutOfBoundsException: Range [69, 27) out of bounds for len (("" (rewrite "int_lemma") ( "q 1 ) (("" (rewrite "mul_lemma") (("" (case "sq(x!1)-1>=0") ( java.lang.StringIndexOutOfBoundsException: Range [19, 18) out of bounds for len (lemma number_fieldnonempty-ype-fromdecl nil java.lang.StringIndexOutOfBoundsExcept ("nnx" "sq(x!1)-1" "nncx" "cauchy_sub(cauchy_mul) (("1" (assert) (("1" (lemma "add_lemma" ("x" "x!1" "cx" "cge1x!1" "y" "sqrt(sq(x!1) - 1)" "cy" "cauchy_sqrt(cauchy_sub(cauchy_mul(cge1x!1, cge1x!1), ()))") 1"(ssert) (("1" (expand "cauchy_posreal?") (("1" (inst + ( constdecl "ool" reals nil nil ) ) nil)) nil)) nil) ("2" (propax) nil nil)) ( declbool nil ("2" (lemma " (cauchy_nnreal nonempty-type-eq-declnil cauchy ) (("2" (assert) nil nil)) nil)) nil) nil) ( application "osreal""eals"java.lang.StringIndexOutOfBoundsException: Index 5 ) nil)) nil)) nil)) nil)) nil)) java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 11 nil) ((cauchy_ge1 nonempty-type-eq-decl nil hyperbolicx nil) (cauchy_ge1? const-decl "bool" hyperbolicx nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (>= const-decl "bool" reals nil) (int nonempty-type-eq-decl nil (" (nteger_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) r nonempty-type-rom-decl 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) (number nonempty-type-decl nil numbers nil) (NOT const-decl "[bool -> bool]" booleans nil) (bool nonempty-type-eq-decl nil booleans nil) (boolean nonempty-ypedecl nilbooleans) (sq const-decl "nonneg_real" sq "reals/") nonneg_real nonempty-type-eq-decl nil real_types nil) (cauchy_int const-decl "(oolean- nil nil) (cauchy_mul const-decl "cauchy_real" mul nil) (cauchy_real nonempty-type-eq-decl nil cauchy nil) c const "bool nil) (sub_lemma formula-decl nil sub nil) (real_minus_real_is_real application-judgement "real" reals nil) (numfield nonempty-type-eq-decl nil number_fields nil) (- const-decl "[numfield, numfield -> numfieldstrict_total_order?real]" niljava.lang.St ((- const-decl[,numfield - numfield java.lang.StringIndexOutOfBoundsException: Index (real_gt_is_strict_total_order name-judgement (trict_total_order[] nil (+ const-decl "[(cauchy_nzreal? constdecl""cauchyjava.lang.StringIndexOutOfBoundsEx java.lang.StringIndexOutOfBoundsException: Range [15, 14) out of bounds for leng (> const-decl "bool" reals nil) (cauchy_posreal? const-decl "bool" cauchy nil) ( decl "nnz nnreal *nnz " "/java.lang.StringIndexOutOfBoundsException: Index 69 out of (* const-decl "[numfield, numfield -> numfield]" number_fields nil) (= const-decl "[T, T -> boolean]" java.lang.StringIndexOutOfBoundsException: Index 43 o (cauchy_sqrt const-decl "cauchy_nnreal" sqrtx nil) (add_lemma formula-decl nil add nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (sqrt_lemma formula-decl nil sqrtx nil) (cauchy_nnreal? const-decl "bool" cauchy nil) (cauchy_nnreal nonempty-type-eq-decl nil cauchy nil) (cauchy_sub const-decl "cauchy_real" sub nil) (nnreal type-eq-decl nil real_types nil) (sq_1 -ecl "eals"java.lang.StringIndexOutOfBoundsException: Index 39 out of bounds (sq_nz_pos application-judgement "posreal" sq "reals/") (real_le_is_total_order ("x 1 "x cauchy_int() y "1 c" real_props nil) (sq_le formula-decl("( " mul_lemma- mulnil (int_lemma formula-decl nil int nil) (posreal_ge1 nonempty-type-eq-decl nil hyperbolic "lnexp_fnd/")) nil)) (cauchy_atanh_TCC1 0 (cauchy_atanh_TCC1-1 nil 3394199209 ("" (skosimp) (("" (typepredcauchy_int() !))java.lang.StringIndexOutOfBoundsException: Index 60 (("" (expand "cauchy_smallreal?") (("" (skosimp) (("" (typepred("/( -sx1" (("" s" ("x" "1" "cx" "cauchy_int(1)" "y" "sx!1" "cy" "csx!1")) (("" (rewrite " "posrea" (" assert) (("" (expand "cauchy_nzreal?") (("" (inst + "1-sx!1") nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) java.lang.StringIndexOutOfBoundsException: Range [25, 8) out of bounds for lengt nil) ((cauchy_smallreal nonempty-type-eq (cauchy_smallreal? const-decl "bool" cauchy nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (int nonempty-type (integer_prednil (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) r type-fromdecl ) (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) (NOT const-decl "[bool -> bool]" booleans nil) (bool nonempty-type-eq-decl nil booleans nil) (boolean nonempty-type-decl nil booleans nil) (cauchy_int const-decl "cauchy_real" int nil) (cauchy_real nonempty-type-eq-decl nil cauchy nil) (cauchy_real? const-decl "bool" cauchy nil) (sub_lemma formula-decl nil sub nil) (real_lt_is_strict_total_order name-judgement "?[real) nil) (real_minus_real_is_real application-judgement "real" reals nil) (- const-decljava.lang.StringIndexOutOfBoundsException: Index 49 out of bounds fo (nzreal nonempty-type-eq-decl nil reals nil) (/= const-decl "boolean" notequal nil) (cauchy_nzreal? const-decl "bool" cauchy nil) (minus_odd_is_odd application-judgement "odd_int" integers nil) (int_lemma formula-decl nil int nil) (smallreal nonempty-type-eq-decl nil prelude_aux nil) (AND const-decl "[bool, bool -> bool]" booleans nil) (-decl"[umfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (< const-decl "bool" reals nil)) ) (cauchy_atanh_TCC2 0 (cauchy_atanh_TCC2-1 nil 3394199209 ("" ((real_gt_is_strict_total_order name-judgement (("" (typepred "csx!1") (("" (expand "cauchy_smallreal?") (("" (skosimp) (("" (typepred "sx!1") (("" (lemma "add_lemma" """1""c1) y""!1 "y csx") (("" (lemma "sub_lemma" ("x" "1" "cx" "cauchy_int(1)" "y" "sx!1" "cy" "csx!1")) ("(ewritei" (("" (assert) (("" (lemma "div_lemma" assert) ("x" "1+sx!1" "cx" "cauchy_add(cauchy_int(1), csx!1)" "nzy" "" "cauchy_sub(cauchy_int(1), csx!1)")) (("" (assert) (((("(ssert) (("(("java.lang.StringIndexOutOfBoundsException: Index 24 out of bounds for leng (("" (assert) (("" "cauchy_add(cauchy_mul(cx!1, cx!), cauchy_int(1))")) "posreal_div_posreal_is_posreal" ("px" "1 + sx!1" "py" "1 - sx!1")) (("" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((cauchy_smallreal nonempty-type-eq-decl nil cauchy nil) (cauchy_smallreal? const-decl "bool" cauchy nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (>= const-decl "bool" reals nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) lemma"ln_lemma" (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) -> boolean"reals ) (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) (bool nonempty-type-eq-decl nil booleans nil) boolean (cauchy_int const-decl "cauchy_real" int nil) (cauchy_real nonempty-type-eq-decl nil cauchy nil) (cauchy_realjava.lang.StringIndexOutOfBoundsException: Index 37 out of bounds fo (add_lemma formula-decl nil add nil) (int_lemma formula-decl nil int nil) (minus_odd_is_odd application-judgement "odd_int" integers nil) +const- "numfieldnumfield - ]"number_fields niljava.lang.StringIndexOutOfBoundsExcep -const-ecl"numfield,numfield ->numfield] ) (nonzero_real nonempty-type-eq-decl nil reals nil) (/= const-decl "boolean" notequal nil) (cauchy_sub const-decl "cauchy_real" sub nil) (cauchy_nzreal nonempty-type-eq-decl nil cauchy nil) (cauchy_nzreal? const-decl "bool" cauchy nil) (cauchy_add const-decl "cauchy_real" add nil) (div_lemma formula-decl nil div nil) (real_plus_real_is_real application- "" (real_minus_real_is_real application-judgement "real" reals nil) (cauchy_posreal? const-decl "bool" cauchy nil) (posreal_div_posreal_is_posreal judgement-java.lang.StringIndexOutOfBoundsExcepti (sx!1 skolem-const-decl "smallreal" hyperbolicx nil) (nonneg_real nonempty- ) (> const-decl "bool" reals nil) (posreal nonempty-type-eq-decl nil real_types nil) nonempty-ypeeqdecl number_fields nil) (/ constnil)) (real_div_nzreal_is_real application-judgement "real" reals java.lang.StringIndexOut (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (real_lt_is_strict_total_order name-judgement (strict_total_order?real]"real_propsniljava.lang.StringIndexOutOfBoundsException (sub_lemma formula-decl nil sub nil) (smallreal nonempty-type-eq-decl nil prelude_aux nil) (AND const-decl "[bool, bool -> bool]" booleans nil) (cauchy_asinh const"nat->int] nil) (" number_fieldsnil) (numfield nonempty-type-eq-decl nil number_fields nil) (< const-decl "bool" reals nil)) nil)) 0 (asinh_lemma-1 nil 3394201044 ("" (skosimp) expand "cauchy_asinh") (("" (expand "asinh") (("" (lemma "mul_lemma" ("x" "x!1" "cx" "cx!1" "y" "x!1" "cy" "cx!1")) ("( (("" (rewrite "sq_rew") (("" (lemma "add_lemma" ("x" "sq(x!1)" "cx" "cauchy_mul(cx!1, cx!1)" "y" "1" nonemptydeclnil nil) (("" (rewrite "int_lemma") ("" (assert) (("" (lemma "sqrt_lemma" nnx 1+sqx!"" "cauchy_add(cauchy_mul(cx!1, cx!1), cauchy_int(1))")) (("1" (assert) (("1" (lemma "add_lemma" ("x" "x!1" "cx" "cx!1" "y" =constdecl [T Tboolean"equalities nil) "cauchy_sqrt( *const-decl "numfield,numfield -> numfield]" number_fields nil) cauchy_int(1)))")) (("1" (assert) (("1" (lemma "ln_lemma" ("px" "sqrt(1 + sq(x!1)) + x!1" "pcx" cx! cauchy_sqrt(cauchy_add (cauchy_mul(cx!1, cx!1), ())") ((" applicationjudgement "reals ("2" (hide-all-but 1) (("2" ( "sqrt_lt" ("nny" "sq(x!1)" "nnz" "1+sq(x!1)")) (("2" (case "x!1>=0") (("1" (rewrite "sqrt_sq") ((" (acosh_lemma 0 nil) ("2" (rewrite "sqrt_sq_neg") (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (expand "cauchy_nnreal lemma "sqrt_lemma" "1+sq(x!1" java.lang.StringIndexOutOfBoundsException: Range [55, 54) out of bound nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((cauchy_asinh const-decl "[nat -> int]" hyperbolicx nil) (cauchy_real nonempty ())) (cauchy_real? const-decl "bool" cauchy nil) (nat ---decl naturalnumbersnil) (>= 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) (number nonempty-type-decl nil numbers niljava.lang.StringIndexOutOfBoundsException: (mul_lemma formula-decl nil mul nil) (sq_rew formula-decl nil sq "reals/") (int_lemma formula-decl nil int nil) (sqrt_lemma formula-decl nil sqrtx nil) (cauchy_nnreal? const-decl "bool" cauchy nil) (cauchy_nnreal nonempty-type-eq-decl nil cauchy nil) (cauchy_add const-decl "cauchy_real" add nil) (nnreal type-eq-decl nil real_types nil) (numfield nonempty-type-eq-decl nil number_fields nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (cauchy_sqrt const-decl "cauchy_nnreal(cauchy_acosh const- "nat >int] nil (= const-decl "[T, T -> boolean]" equalities nil) (* const-decl "[numfield, numfield -> numfield]" number_fields nil) (java.lang.StringIndexOutOfBoundsException: Range [4, 1) out of bounds for lengt (ln_lemma formula-decl nil log nil) (cauchy_posreal? (nat nonempty-type-eq naturalnumbers (cauchy_posreal nonempty-java.lang.StringIndexOutOfBoundsException: Range [4, 1) >decl b" ) (posreal nonempty-(java.lang.StringIndexOutOfBoundsException: Index 48 out of bou (real_ge_is_total_order name-judgement " rational -type-- nil ) real_props nil) (sqrt_lt formula-decl nil sqrt "reals/") (sqrt_sq_neg formula-decl nil sqrt "reals/") (minus_real_is_realnjava.lang.StringIndexOutOfBoundsException: Range [27, 26) ou (real_lt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (sqrt_sq formula-decl nil sqrt "reals/") (sq const-decl "nonneg_real" sq "reals/") (nonneg_real nonempty-type-eq-decl nil real_types nil) (cauchy_int const-decl "cauchy_real" int nil) (cauchy_mul const-decl "cauchy_real" mul nil) (add_lemma formula-decl nil add nil) (real_plus_real_is_real application-judgement "real" reals nil) (sqrt_pos application-judgement "posreal" sqrt "reals/") (posreal_plus_nnreal_is_posreal application-judgement "posreal" real_types nil) (asinh const-decl "real" hyperbolic "lnexp_fnd/")) ) (acosh_lemma 0 (acosh_lemma-1 nil 3394201403 ("" (skosimp) (("" (expand "cauchy_acosh") ((java.lang.StringIndexOutOfBoundsException: Range [15, 14) out of bounds for le (("" (lemma "mul_lemma" ("x" "ge1x!1" "cx" "cge1x!1" "y" "ge1x!1" "cy" "cge1x!1")) (("" (rewrite "sq_rew")( const[ - java.lang.StringIndexOutOfBoundsException: Range [5 (("" (assert) (("" (lemma "sub_lemma" ("x" "sq(ge1x!1)" "cx" "cauchy_mul(cge1x!1, cge1x!1)" " (osreal nonempty-eqdeclnil nil) (("" (rewrite "int_lemma") (("(java.lang.StringIndexOutOfBoundsException: Index 31 out of bounds for length (("" ( "sqrt_lemma" ("nnx" "sq(ge1x! (auchy_mulconst-decl "" nil "cauchy_sub(cauchy_mul(ge1x!1, cge1x!1) cauchy_int())") (("1" (assert) (("1" (lemma "add_lemma" ("x" "ge1x!1" "cx" "cge1x!1" "y" "sqrt(sq(ge1x!1) - 1)" "cy" "cauchy_sqrt(cauchy_sub (cauchy_mul(cge1x!1, cge1x("x""""java.lang.StringIndexOutOfBoundsException: Range cauchy_int(1)))")) (("1" (assert) (("1" (lemma "ln_lemma" ("px" "sqrt(sq(ge1x!1) - 1) + ge1x!1" "pcx" "cauchy_add(cge1x!1, cauchy_sqrt(cauchy_sub cauchy_mul(cge1x!1,!)java.lang.StringIndexOutOfBoundsException: Index 71 out of cauchy_int(1))))")) (("1" (assert) nil nil)) nil)) nil)) )java.lang.StringIndexOutOfBoundsException: Index 31 out of bounds for length 31 nil) ("2" (expand "cauchy_nnreal?") (2"( + sqge1x!)- 1" nil) nil)java.lang.StringIndexOutOfBoundsException: Index 71 out )) nil)) nil)) nil)) nil)) nil)) ) nil)) nil)) niljava.lang.StringIndexOutOfBoundsException: Index 8 out of bounds for length 8 ((cauchy_acosh"cauchy_ln(((auchy_int(1,!), (posreal_ge1 cauchy_sub(auchy_int() !)" (cauchy_ge1 nonempty-type-eq-decl nil hyperbolicx nil) (cauchy_ge1? const-decl "bool" hyperbolicx nil) (cauchy_real nonempty-type-eq-decl nil cauchy nil) (cauchy_real? const-decl "bool" cauchy 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) (mul_lemma formula-decl nil mul nil) (real_minus_real_is_real application-judgement "real" reals nil) (real_plus_real_is_real application-judgement "real" reals nil) (int_lemma formula-decl nil int nil) (sqrt_lemma formula-decl nil sqrtx nil) (cauchy_nnreal? const-decl "bool" cauchy nil) (cauchy_nnreal nonempty-type-eq-decl nil cauchy nil) (cauchy_sub const-decl "cauchy_real" sub nil) (nnreal type-eq-decl nil real_types nil) (numfield nonempty-type-eq-decl nil number_fields nil) (- const-decl "[numfield, numfield -> numfield]" number_fields nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (dd_lemmaformula- niladd ) (cauchy_sqrt const-decl "cauchy_nnreal" sqrtx nil) (= const-decl "[T,java.lang.StringIndexOutOfBoundsException: Index 49 out of bound *-decl[umfield, numfield -> numfield"number_fields nil (sqrt const real_props nil l - logjava.lang.StringIndexOutOfBoundsException: Index 39 out of bounds for lengt (cauchy_posreal? const-decl "bool" cauchy nil) (cauchy_posreal nonempty-type-eq-decl nil cauchy nil) (cauchy_add const-decl "cauchy_real" add nil) (> const-decl "bool" reals nil) (posreal nonempty-type-eq-decl nil real_types nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (sq const-decl "nonneg_real" sq "reals/") (nonneg_real nonempty-type-eq-decl nil real_types nil) (cauchy_int const-decl "cauchy_real" int nil) (cauchy_mul const-decl "cauchy_real" mul nil) (sub_lemma formula-decl nil sub nil) (sq_rew formula-decl nil sq "reals/") (acosh const-decl "nnreal" hyperbolic "lnexp_fnd/")) shostak)) (java.lang.StringIndexOutOfBoundsException: Range [3, 1) out of bounds for lengt (atanh_lemma-1 nil 3394201853 ("" (skosimp) (("" (expand "cauchy_atanh") (("" (expand "atanh") (("" (lemma "add_lemma" ("x" "1" "cx" "cauchy_int(1)" "y" "sx!1" "cy" "csx!1")) (("" (lemma "sub_lemma" (("" (rewrite "int_lemma") (("" (assert) (("" "iv_lemma" ("x" "1 + sx!1" "cx" (=const-""reals ) "nzcy" "cauchy_sub(cauchy_int(1), csx!1)")) (("" (assert) (("" ( (rational_pred const-decreal>boolean"rationals nil) ("px" "(1 + sx!1) / (1 - sx!1)" "pcx" "cauchy_div(java.lang.StringIndexOutOfBoundsException: Range [47, 46) out of bou cauchy_sub(cauchy_int(1,csx!)") (("1" (assert) (("1" (hide-all-but (- (("1" (lemma "lemma_div2n" (" booleannonemptytypedecl nil) "cauchy_ln(cauchy_div(cauchy_add(cauchy_int(1), cauchy_sub(cauchy_int(1), csx!1)))" "n" "1")) (("1" (assert) (("1" (expand (" skosimp) (("1" (rewrite "expt_x1") nil nil)) nil)) nil)) nil)) nil)) nil) ("2" (hide-all-but 1) nil)java.lang.StringIndexOutOfBoundsException: Index 17 out of bounds for length (lemma "posreal_div_posreal_is_posreal" ("px" "1+sx!1" "py" "1-sx!1")) (("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((cauchy_atanh const-decl "[nat -> int]" hyperbolicx nil) (eal --from-declrealsnil) (- const-decl "[numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (< const-decl "bool" reals nil) ANDdecl [,bool - bool"booleans java.lang.StringIndexOutOfBoundsException: Index 56 o (cauchy_smallreal nonempty-type-eq-decl nil cauchy nil) (cauchy_smallreal? const-decl "bool" cauchy nil) (cauchy_int const-decl "cauchy_real" int nil) (cauchy_real nonempty-type-eq-decl nil cauchy nil) (cauchy_real? const-decl "bool" cauchy nil) (natnonempty--eq- 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) (add_lemma formula-decl nil add nil) (int_lemma formula-decl nil int nil) (minus_odd_is_odd application-judgement "odd_int" integers nil) (real_plus_real_is_real application-judgement "real" reals nil) (real_minus_real_is_real application-judgement "real" reals nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (- const-decl "[numfield, numfield -> numfield]" number_fields nil) (nonzero_real nonempty-type-eq-decl nil reals nil) (/= const-decl "boolean" notequal nil) (cauchy_sub const-decl "cauchy_real" sub nil) (cauchy_nzreal nonempty-type-eq-decl nil cauchy nil) (cauchy_nzreal? const-decl "bool" cauchy nil) (cauchy_add const-decl "cauchy_real" add nil) (div_lemma formula-decl nil div nil) nil log ) (cauchy_posreal? const-decl "bool" cauchy nil) (cauchy_posreal nonempty-type-eq-decl nil cauchy nil) (cauchy_div const-decl "cauchy_real" div nil) (nonneg_real nonempty-type-eq-decl nil real_types nil) (> const-decl "bool" reals nil) (posreal nonempty-type-eq-decl nil real_types nil) (nznum nonempty-type-eq-decl nil number_fields nil) (/ const-decl "[numfield, nznum -> numfield]" number_fields nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (posint_exp application-judgement "posint" exponentiation nil) (expt_x1 formula-decl nil exponentiation nil) ( (nat nonemptynat -type--declnil ) (ln const-decl "real" ln_exp "lnexp_fnd/") (cauchy_ln const-decl "cauchy_real" log nil) (emma_div2n formula-decl nil nil) (posreal_div_posreal_is_posreal judgement-tcc nil real_types nil) (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (real_div_nzreal_is_real application-judgement "real" reals nil) (sub_lemma formula-decl nil sub nil) (atanh const-decl "real" hyperbolic "lnexp_fnd/")) shostak)) (cauchy_asinh_type 0 (cauchy_asinh_type-1 nil 3394202275 ("" (skosimp) (("" (typepred "cx!1") (("" (expand "cauchy_real?") (("" (skosimp) (("" (lemma "asinh_lemma" ("x" "x!1" "cx" "cx!1")) (("" (inst + "asinh(x!1)") (("" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil) ((cauchy_real nonempty-type-eq-decl nil cauchy nil) (cauchy_real? const-decl "bool" cauchy nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (>= const-decl "bool" reals nil) (int nonempty-type-eq-decl nil integers nil) integer_pred -decl"rational - 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) (number nonempty-type-decl nil numbers nil) (NOT const-decl "[bool -> bool]" booleans nil) (bool nonempty-type-eq-decl nil booleans nil) (boolean nonempty-type-decl nil booleans nil) (asinh const-decl "real" hyperbolic "lnexp_fnd/") (asinh_lemma formula-decl nil hyperbolicx nil)) nil)) (cauchy_acosh_type 0 (cauchy_acosh_type-1 nil 3394202275 ("" (skosimp) (("" (typepred "cge1x!1") (("" (expand "cauchy_ge1?") 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(("" (inst + "acosh(x!1)") (("" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((cauchy_ge1 nonempty-type-eq-decl nil hyperbolicx nil) (cauchy_ge1? const-decl "bool" hyperbolicx nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (>= const-decl "bool" reals 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) (number nonempty-type-decl nil numbers nil) (NOT const-decl "[bool -> bool]" booleans nil) (bool nonempty-type-eq-decl nil booleans nil) (boolean nonempty-type-decl nil booleans nil) (cauchy_nnreal? const-decl "bool" cauchy nil) (nnreal type-eq-decl nil real_types nil) (acosh const-decl "nnreal" hyperbolic "lnexp_fnd/") (acosh_lemma formula-decl nil hyperbolicx nil) (posreal_ge1 nonempty-type-eq-decl nil hyperbolic "lnexp_fnd/")) nil)) (cauchy_atanh_type 0 (cauchy_atanh_type-1 nil 3394202275 ("" (skosimp) (("" (typepred "csx!1") (("" (expand "cauchy_smallreal?") 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2026-10-11