| products/sources/formale sprachen/PVS/exact_real_arith/ |
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Quellcode-Bibliothek© Kompilation durch diese Firma[Weder Korrektheit noch Funktionsfähigkeit der Software werden zugesichert.]Datei: planner.vdmsl Sprache: LispOriginal von: PVS© |
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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]" 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) (cosh_lemma formula-decl nil hyperbolicx nil) (cosh const-decl "posreal_ge1" hyperbolic "lnexp_fnd/") (posreal_ge1 nonempty-type-eq-decl nil hyperbolic "lnexp_fnd/") (nzreal nonempty-type-eq-decl nil reals nil) (/= const-decl "boolean" notequal nil) (cauchy_cosh const-decl "[nat -> int]" hyperbolicx nil) (cauchy_nzreal nonempty-type-eq-decl nil cauchy nil) (cauchy_nzreal? const-decl "bool" cauchy nil) (inv_lemma formula-decl nil inv nil) (nzreal_div_nzreal_is_nzreal application-judgement "nzreal" real_types nil) (cauchy_cosh_type application-judgement "cauchy_posreal" hyperbolicx nil) (cauchy_sech const-decl "[nat -> int]" hyperbolicx nil)) shostak)) (coth_lemma 0 (coth_lemma-1 nil 3394198526 ("" (skosimp) (("" (expand "cauchy_coth") (("" (expand "coth") (("" (lemma "sinh_lemma" ("x" "nzx!1" "cx" "cnzx!1")) (("" (lemma "cosh_lemma" ("x" "nzx!1" "cx" "cnzx!1")) (("" (assert) (("" (expand "tanh") (("" (rewrite "div_div1") (("1" (assert) (("1" (lemma "div_lemma" ("x" "cosh(nzx!1)" "cx" "cauchy_cosh(cnzx!1)" "nzy" "sinh(nzx!1)" "nzcy" "cauchy_sinh(cnzx!1)")) (("1" (assert) nil nil)) nil)) nil) ("2" (hide-all-but 1) (("2" (lemma "sinh_0") (("2" (lemma "sinh_strict_increasing") (("2" (expand "strict_increasing?") (("2" (lemma "trichotomy" ("x" "nzx!1")) (("2" (split -1) (("1" (inst - "0" "nzx!1") (("1" (assert) nil nil)) nil) ("2" (assert) nil nil) ("3" (inst - "nzx!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 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_sinh_type application-judgement "cauchy_real" hyperbolicx nil) (cauchy_cosh_type application-judgement "cauchy_posreal" hyperbolicx nil) (nzreal_div_nzreal_is_nzreal application-judgement "nzreal" real_types nil) (cosh const-decl "posreal_ge1" hyperbolic "lnexp_fnd/") (posreal_ge1 nonempty-type-eq-decl nil hyperbolic "lnexp_fnd/") (sinh const-decl "real" hyperbolic "lnexp_fnd/") (nonzero_real nonempty-type-eq-decl nil reals nil) (div_div1 formula-decl nil real_props nil) (real_div_nzreal_is_real application-judgement "real" reals nil) (real_times_real_is_real application-judgement "real" reals nil) (div_lemma formula-decl nil div nil) (cauchy_cosh const-decl "[nat -> int]" hyperbolicx nil) (cauchy_sinh const-decl "[nat -> int]" hyperbolicx nil) (sinh_0 formula-decl nil hyperbolic "lnexp_fnd/") (strict_increasing? const-decl "bool" real_fun_preds "reals/") (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) (trichotomy formula-decl nil real_axioms nil) (sinh_strict_increasing formula-decl nil hyperbolic "lnexp_fnd/") (tanh const-decl "real_abs_lt1" hyperbolic "lnexp_fnd/") (cosh_lemma formula-decl nil hyperbolicx nil) (coth const-decl "real_abs_gt1" hyperbolic "lnexp_fnd/")) shostak)) (csch_lemma 0 (csch_lemma-1 nil 3394198422 ("" (skosimp) (("" (lemma "sinh_lemma" ("x" "nzx!1" "cx" "cnzx!1")) (("" (assert) (("" (expand "cauchy_csch") (("" (expand "csch") (("" (lemma "inv_lemma" ("nzx" "sinh(nzx!1)" "nzcx" "cauchy_sinh(cnzx!1)")) (("" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) 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 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_csch const-decl "[nat -> int]" hyperbolicx nil) (cauchy_sinh_type application-judgement "cauchy_real" hyperbolicx nil) (inv_lemma formula-decl nil inv nil) (cauchy_sinh const-decl "[nat -> int]" hyperbolicx nil) (sinh const-decl "real" hyperbolic "lnexp_fnd/") (nzreal_div_nzreal_is_nzreal application-judgement "nzreal" real_types nil) (csch const-decl "real" hyperbolic "lnexp_fnd/")) shostak)) (cauchy_tanh_type 0 (cauchy_tanh_type-1 nil 3394196253 ("" (skosimp) (("" (typepred "cx!1") (("" (expand "cauchy_real?") (("" (skosimp) (("" (lemma "tanh_lemma" ("x" "x!1" "cx" "cx!1")) (("" (assert) (("" (typepred "tanh(x!1)") (("" (expand "cauchy_smallreal?") (("" (inst + "tanh(x!1)") 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_smallreal? const-decl "bool" cauchy nil) (smallreal nonempty-type-eq-decl nil prelude_aux nil) (tanh const-decl "real_abs_lt1" hyperbolic "lnexp_fnd/") (real_abs_lt1 nonempty-type-eq-decl nil hyperbolic "lnexp_fnd/") (AND const-decl "[bool, bool -> bool]" booleans nil) (- const-decl "[numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (< const-decl "bool" reals nil) (tanh_lemma formula-decl nil hyperbolicx nil)) nil)) (cauchy_coth_type 0 (cauchy_coth_type-1 nil 3394196253 ("" (skosimp) (("" (typepred "cnzx!1") (("" (expand "cauchy_nzreal?") 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