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© Kompilation durch diese Firma

[Weder Korrektheit noch Funktionsfähigkeit der Software werden zugesichert.]

Datei: ci-unimath.sh   Sprache: Lisp

Original von: PVS©

(hyperbolic
 (cosh_TCC1 0
  (cosh_TCC1-1 nil 3253390561
   ("" (skosimp*)
    (("" (lemma "trichotomy" ("x" "x!1"))
      (("" (lemma "exp_diff" ("x" "0" "y" "x!1"))
        (("" (rewrite "exp_0")
          (("" (replace -1 1)
            (("" (lemma "div_mult_pos_ge1")
              (("" (inst - "2" "1" "exp(x!1) + 1 / exp(x!1)")
                (("" (replace -1 1)
                  (("" (split -3)
                    (("1" (lemma "exp_strict_increasing")
                      (("1" (expand "strict_increasing?")
                        (("1" (inst - "0" "x!1")
                          (("1" (rewrite "exp_0")
                            (("1" (assert)
                              (("1"
                                (lemma
                                 "sq_lt"
                                 ("nnb" "exp(x!1)-1" "nna" "0"))
                                (("1"
                                  (expand "sq")
                                  (("1"
                                    (lemma
                                     "div_mult_pos_lt1"
                                     ("z"
                                      "-1"
                                      "py"
                                      "exp(x!1)"
                                      "x"
                                      "exp(x!1)-2"))
                                    (("1" (assertnil nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil)
                     ("2" (replace -1)
                      (("2" (rewrite "exp_0") (("2" (assertnil nil))
                        nil))
                      nil)
                     ("3" (lemma "exp_strict_increasing")
                      (("3" (expand "strict_increasing?")
                        (("3" (inst - "x!1" "0")
                          (("3" (rewrite "exp_0")
                            (("3" (assert)
                              (("3"
                                (lemma
                                 "sq_lt"
                                 ("nna" "0" "nnb" "1-exp(x!1)"))
                                (("3"
                                  (expand "sq")
                                  (("3"
                                    (lemma
                                     "div_mult_pos_lt1"
                                     ("py"
                                      "exp(x!1)"
                                      "z"
                                      "-1"
                                      "x"
                                      "exp(x!1)-2"))
                                    (("3" (assertnil nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    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)
    (trichotomy formula-decl nil real_axioms nil)
    (exp_0 formula-decl nil ln_exp nil)
    (minus_odd_is_odd application-judgement "odd_int" integers nil)
    (posreal_plus_nnreal_is_posreal application-judgement "posreal"
     real_types nil)
    (div_mult_pos_ge1 formula-decl nil real_props nil)
    (posrat_div_posrat_is_posrat application-judgement "posrat"
     rationals nil)
    (posrat_plus_nnrat_is_posrat application-judgement "posrat"
     rationals nil)
    (exp_strict_increasing formula-decl nil ln_exp nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (mult_divides2 application-judgement "(divides(m))" divides nil)
    (mult_divides1 application-judgement "(divides(n))" divides nil)
    (int_times_even_is_even application-judgement "even_int" integers
     nil)
    (posint_times_posint_is_posint application-judgement "posint"
     integers nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (posreal_times_posreal_is_posreal application-judgement "posreal"
     real_types nil)
    (sq const-decl "nonneg_real" sq "reals/")
    (nzreal_div_nzreal_is_nzreal application-judgement "nzreal"
     real_types nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (- const-decl "[numfield -> numfield]" number_fields nil)
    (div_mult_pos_lt1 formula-decl nil real_props nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (sq_lt formula-decl nil sq "reals/")
    (posreal_div_posreal_is_posreal application-judgement "posreal"
     real_types nil)
    (strict_increasing? const-decl "bool" real_fun_preds "reals/")
    (/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
    (nznum nonempty-type-eq-decl nil number_fields nil)
    (/= const-decl "boolean" notequal nil)
    (exp const-decl "{py | x = ln(py)}" ln_exp nil)
    (ln const-decl "real" ln_exp nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (> const-decl "bool" reals nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (>= const-decl "bool" reals nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (exp_diff formula-decl nil ln_exp nil))
   shostak))
 (tanh_TCC1 0
  (tanh_TCC1-1 nil 3253429443
   ("" (skosimp*)
    (("" (typepred "cosh(x!1)") (("" (assertnil nil)) nil)) nil)
   ((cosh const-decl "posreal_ge1" hyperbolic nil)
    (posreal_ge1 nonempty-type-eq-decl nil hyperbolic nil)
    (>= const-decl "bool" reals 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)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil))
   shostak))
 (tanh_TCC2 0
  (tanh_TCC2-1 nil 3253429443
   ("" (skosimp*)
    (("" (lemma "div_mult_pos_lt1")
      (("" (inst - "cosh(x!1)" "1" "sinh(x!1)")
        (("1" (lemma "div_mult_pos_lt2")
          (("1" (inst - "cosh(x!1)" "-1" "sinh(x!1)")
            (("1" (replace -1)
              (("1" (replace -2)
                (("1" (hide (-1 -2))
                  (("1" (expand "cosh")
                    (("1" (expand "sinh")
                      (("1" (typepred "exp(x!1)")
                        (("1" (typepred "exp(-x!1)")
                          (("1" (name-replace "EPX" "exp(x!1)")
                            (("1" (name-replace "EMX" "exp(-x!1)")
                              (("1"
                                (hide -3 -6)
                                (("1" (grind) nil nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil)
             ("2" (typepred "cosh(x!1)") (("2" (assertnil nil)) nil))
            nil))
          nil)
         ("2" (typepred "cosh(x!1)") (("2" (assertnil nil)) nil))
        nil))
      nil))
    nil)
   ((div_mult_pos_lt1 formula-decl nil real_props nil)
    (div_mult_pos_lt2 formula-decl nil real_props nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (minus_real_is_real application-judgement "real" reals nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_div_nzreal_is_real application-judgement "real" reals nil)
    (posreal_times_posreal_is_posreal application-judgement "posreal"
     real_types nil)
    (nzreal_times_nzreal_is_nzreal application-judgement "nzreal"
     real_types nil)
    (exp const-decl "{py | x = ln(py)}" ln_exp nil)
    (ln const-decl "real" ln_exp nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (posreal_div_posreal_is_posreal application-judgement "posreal"
     real_types nil)
    (posreal_plus_nnreal_is_posreal application-judgement "posreal"
     real_types nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (- const-decl "[numfield -> numfield]" number_fields nil)
    (minus_odd_is_odd application-judgement "odd_int" integers nil)
    (sinh const-decl "real" hyperbolic nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (>= const-decl "bool" reals nil)
    (posreal_ge1 nonempty-type-eq-decl nil hyperbolic nil)
    (cosh const-decl "posreal_ge1" hyperbolic nil)
    (x!1 skolem-const-decl "real" hyperbolic nil)
    (> const-decl "bool" reals 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))
   shostak))
 (csch_TCC1 0
  (csch_TCC1-1 nil 3253429443
   ("" (skosimp*)
    (("" (expand "sinh")
      (("" (lemma "exp_diff" ("x" "0" "y" "n0x!1"))
        (("" (lemma "exp_0")
          (("" (replace -1 -2)
            (("" (replace -2 -3)
              (("" (rewrite "div_cancel3" -3)
                ((""
                  (lemma "minus_div1"
                   ("x" "exp(n0x!1)" "y" "1" "n0x" "1" "n0y"
                    "exp(n0x!1)"))
                  (("" (replace -1 -4)
                    (("" (rewrite "div_cancel3" -4)
                      (("" (lemma "exp_strict_increasing")
                        (("" (expand "strict_increasing?")
                          (("" (lemma "trichotomy" ("x" "2*n0x!1"))
                            ((""
                              (lemma "exp_sum"
                               ("x" "n0x!1" "y" "n0x!1"))
                              ((""
                                (replace -1 -7 rl)
                                ((""
                                  (split -2)
                                  (("1"
                                    (inst - "0" "2*n0x!1")
                                    (("1" (assertnil nil))
                                    nil)
                                   ("2" (assertnil nil)
                                   ("3"
                                    (inst - "n0x!1" "0")
                                    (("3"
                                      (replace -2)
                                      (("3"
                                        (hide -2)
                                        (("3"
                                          (assert)
                                          (("3"
                                            (replace -6)
                                            (("3"
                                              (assert)
                                              (("3"
                                                (hide -5)
                                                (("3"
                                                  (move-terms -3 l 2)
                                                  (("3"
                                                    (assert)
                                                    (("3"
                                                      (replace -3 * rl)
                                                      (("3"
                                                        (hide -1 -2 -3)
                                                        (("3"
                                                          (lemma
                                                           "exp_neg")
                                                          (("3"
                                                            (inst?)
                                                            (("3"
                                                              (grind-reals)
                                                              nil
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((sinh const-decl "real" hyperbolic nil)
    (exp_0 formula-decl nil ln_exp nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (minus_div1 formula-decl nil real_props nil)
    (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (posreal_times_posreal_is_posreal application-judgement "posreal"
     real_types nil)
    (nnreal_times_nnreal_is_nnreal application-judgement "nnreal"
     real_types nil)
    (odd_times_odd_is_odd application-judgement "odd_int" integers nil)
    (posint_times_posint_is_posint application-judgement "posint"
     integers nil)
    (strict_increasing? const-decl "bool" real_fun_preds "reals/")
    (exp_sum formula-decl nil ln_exp nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_div_nzreal_is_real application-judgement "real" reals nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (nnreal_div_posreal_is_nnreal application-judgement "nnreal"
     real_types nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (IFF const-decl "[bool, bool -> bool]" booleans nil)
    (nnreal_plus_posreal_is_posreal application-judgement "posreal"
     real_types nil)
    (exp_neg formula-decl nil ln_exp nil)
    (div_cancel4 formula-decl nil real_props nil)
    (minus_nzreal_is_nzreal application-judgement "nzreal" real_types
     nil)
    (trichotomy formula-decl nil real_axioms nil)
    (nzreal_times_nzreal_is_nzreal application-judgement "nzreal"
     real_types nil)
    (exp_strict_increasing formula-decl nil ln_exp nil)
    (posreal_div_posreal_is_posreal application-judgement "posreal"
     real_types nil)
    (nnint_times_nnint_is_nnint application-judgement "nonneg_int"
     integers nil)
    (even_times_int_is_even application-judgement "even_int" integers
     nil)
    (mult_divides1 application-judgement "(divides(n))" divides nil)
    (mult_divides2 application-judgement "(divides(m))" divides nil)
    (/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
    (nznum nonempty-type-eq-decl nil number_fields nil)
    (exp const-decl "{py | x = ln(py)}" ln_exp nil)
    (ln const-decl "real" ln_exp nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (> const-decl "bool" reals nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (>= const-decl "bool" reals nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (nonzero_real nonempty-type-eq-decl nil reals nil)
    (div_cancel3 formula-decl nil real_props nil)
    (minus_odd_is_odd application-judgement "odd_int" integers nil)
    (exp_diff formula-decl nil ln_exp nil)
    (number nonempty-type-decl nil numbers nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (/= const-decl "boolean" notequal nil)
    (nzreal nonempty-type-eq-decl nil reals nil))
   shostak))
 (sech_TCC1 0
  (sech_TCC1-1 nil 3253429443
   ("" (skosimp*)
    (("" (typepred "cosh(x!1)")
      ((""
        (lemma "both_sides_div_pos_ge2"
         ("py" "cosh(x!1)" "px" "1" "pz" "1"))
        (("1"
          (lemma "posreal_div_posreal_is_posreal"
           ("px" "1" "py" "cosh(x!1)"))
          (("1" (assertnil nil)) nil)
         ("2" (assertnil nil))
        nil))
      nil))
    nil)
   ((cosh const-decl "posreal_ge1" hyperbolic nil)
    (posreal_ge1 nonempty-type-eq-decl nil hyperbolic nil)
    (>= const-decl "bool" reals 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)
    (posreal_div_posreal_is_posreal judgement-tcc nil real_types nil)
    (nzreal_div_nzreal_is_nzreal application-judgement "nzreal"
     real_types nil)
    (posrat_div_posrat_is_posrat application-judgement "posrat"
     rationals nil)
    (AND const-decl "[bool, bool -> bool]" booleans 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_div_pos_ge2 formula-decl nil real_props 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))
   shostak))
 (coth_TCC1 0
  (coth_TCC1-1 nil 3253429443
   ("" (skosimp*)
    (("" (expand "tanh")
      (("" (expand "sinh")
        (("" (lemma "exp_diff" ("x" "0" "y" "n0x!1"))
          (("" (lemma "exp_0")
            (("" (replace -1 -2)
              (("" (replace -2 -3)
                (("" (rewrite "div_div2" -3)
                  ((""
                    (lemma "minus_div1"
                     ("x" "exp(n0x!1)" "n0x" "1" "y" "1" "n0y"
                      "exp(n0x!1)"))
                    (("" (replace -1 -4)
                      (("" (rewrite "div_div2" -4)
                        ((""
                          (lemma "exp_sum" ("x" "n0x!1" "y" "n0x!1"))
                          (("" (replace -1 -5 rl)
                            (("" (hide -1 -2 -4)
                              ((""
                                (lemma "exp_strict_increasing")
                                ((""
                                  (expand "strict_increasing?")
                                  ((""
                                    (lemma
                                     "trichotomy"
                                     ("x" "2*n0x!1"))
                                    ((""
                                      (split -1)
                                      (("1"
                                        (inst - "0" "2*n0x!1")
                                        (("1" (assertnil nil))
                                        nil)
                                       ("2" (assertnil nil)
                                       ("3"
                                        (inst - "2*n0x!1" "0")
                                        (("3" (assertnil nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((tanh const-decl "real_abs_lt1" hyperbolic nil)
    (nzreal nonempty-type-eq-decl nil reals nil)
    (/= const-decl "boolean" notequal 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_diff formula-decl nil ln_exp nil)
    (minus_odd_is_odd application-judgement "odd_int" integers nil)
    (div_div2 formula-decl nil real_props nil)
    (nonzero_real nonempty-type-eq-decl nil reals nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (>= const-decl "bool" reals nil)
    (posreal_ge1 nonempty-type-eq-decl nil hyperbolic nil)
    (cosh const-decl "posreal_ge1" hyperbolic nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields 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 nil)
    (exp const-decl "{py | x = ln(py)}" ln_exp nil)
    (nznum nonempty-type-eq-decl nil number_fields nil)
    (/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (posreal_div_posreal_is_posreal application-judgement "posreal"
     real_types nil)
    (exp_sum formula-decl nil ln_exp nil)
    (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_plus_real_is_real application-judgement "real" reals nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (trichotomy formula-decl nil real_axioms nil)
    (nzreal_times_nzreal_is_nzreal application-judgement "nzreal"
     real_types nil)
    (exp_strict_increasing formula-decl nil ln_exp nil)
    (posint_times_posint_is_posint application-judgement "posint"
     integers nil)
    (odd_times_odd_is_odd application-judgement "odd_int" integers nil)
    (mult_divides1 application-judgement "(divides(n))" divides nil)
    (posreal_times_posreal_is_posreal application-judgement "posreal"
     real_types nil)
    (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (minus_div1 formula-decl nil real_props nil)
    (real_div_nzreal_is_real application-judgement "real" reals nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (exp_0 formula-decl nil ln_exp nil)
    (sinh const-decl "real" hyperbolic nil))
   shostak))
 (coth_TCC2 0
  (coth_TCC2-1 nil 3253429443
   ("" (skosimp*)
    (("" (typepred "tanh(n0x!1)")
      (("" (lemma "coth_TCC1" ("nzx" "n0x!1"))
        (("" (lemma "trichotomy" ("x" "n0x!1"))
          (("" (case "strict_increasing?(sinh)")
            (("1" (expand "strict_increasing?")
              (("1" (case "sinh(0)=0")
                (("1" (expand "tanh")
                  (("1" (typepred "cosh(n0x!1)")
                    (("1" (split -4)
                      (("1" (inst - "0" "n0x!1")
                        (("1" (rewrite "div_div1")
                          (("1" (assert)
                            (("1" (replace -3 -4)
                              (("1"
                                (lemma "div_mult_pos_lt1")
                                (("1"
                                  (inst
                                   -
                                   "sinh(n0x!1)"
                                   "-1"
                                   "cosh(n0x!1)")
                                  (("1"
                                    (lemma "div_mult_pos_lt2")
                                    (("1"
                                      (inst
                                       -
                                       "sinh(n0x!1)"
                                       "1"
                                       "cosh(n0x!1)")
                                      (("1"
                                        (replace -1)
                                        (("1"
                                          (replace -2)
                                          (("1"
                                            (hide -1 -2)
                                            (("1"
                                              (expand "cosh")
                                              (("1"
                                                (expand "sinh")
                                                (("1"
                                                  (assert)
                                                  nil
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil)
                       ("2" (assertnil nil)
                       ("3" (inst - "n0x!1" "0")
                        (("3" (replace -3 -4)
                          (("3" (assert)
                            (("3" (lemma "div_mult_neg_lt1")
                              (("3"
                                (rewrite "div_div1")
                                (("3"
                                  (inst
                                   -
                                   "sinh(n0x!1)"
                                   "-1"
                                   "cosh(n0x!1)")
                                  (("3"
                                    (lemma "div_mult_neg_lt2")
                                    (("3"
                                      (inst
                                       -
                                       "sinh(n0x!1)"
                                       "1"
                                       "cosh(n0x!1)")
                                      (("3"
                                        (replace -1)
                                        (("3"
                                          (replace -2)
                                          (("3"
                                            (hide (-1 -2))
                                            (("3"
                                              (expand "sinh")
                                              (("3"
                                                (expand "cosh")
                                                (("3"
                                                  (assert)
                                                  nil
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil)
                 ("2" (expand "sinh" 1)
                  (("2" (rewrite "exp_0") (("2" (assertnil nil))
                    nil))
                  nil))
                nil))
              nil)
             ("2" (hide-all-but 1)
              (("2" (lemma "exp_strict_increasing")
                (("2" (expand "strict_increasing?")
                  (("2" (expand "sinh")
                    (("2" (skosimp*)
                      (("2" (inst-cp - "x!1" "y!1")
                        (("2" (inst - "-y!1" "-x!1")
                          (("2" (assertnil nil)) nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((nzreal nonempty-type-eq-decl nil reals nil)
    (/= const-decl "boolean" notequal nil)
    (tanh const-decl "real_abs_lt1" hyperbolic nil)
    (real_abs_lt1 nonempty-type-eq-decl nil hyperbolic nil)
    (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)
    (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)
    (strict_increasing? const-decl "bool" real_fun_preds "reals/")
    (sinh const-decl "real" hyperbolic nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (>= const-decl "bool" reals nil)
    (posreal_ge1 nonempty-type-eq-decl nil hyperbolic nil)
    (cosh const-decl "posreal_ge1" hyperbolic nil)
    (div_mult_neg_lt2 formula-decl nil real_props nil)
    (<= const-decl "bool" reals nil)
    (nonpos_real nonempty-type-eq-decl nil real_types nil)
    (negreal nonempty-type-eq-decl nil real_types nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (div_mult_neg_lt1 formula-decl nil real_props nil)
    (div_mult_pos_lt1 formula-decl nil real_props nil)
    (div_mult_pos_lt2 formula-decl nil real_props nil)
    (posreal_div_posreal_is_posreal application-judgement "posreal"
     real_types nil)
    (posreal_plus_nnreal_is_posreal application-judgement "posreal"
     real_types nil)
    (minus_nzreal_is_nzreal application-judgement "nzreal" real_types
     nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (minus_even_is_even application-judgement "even_int" integers nil)
    (exp_0 formula-decl nil ln_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)
    (real_times_real_is_real application-judgement "real" reals nil)
    (nzreal_div_nzreal_is_nzreal application-judgement "nzreal"
     real_types nil)
    (real_div_nzreal_is_real application-judgement "real" reals nil)
    (minus_odd_is_odd application-judgement "odd_int" integers nil)
    (real_lt_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)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (div_div1 formula-decl nil real_props nil)
    (nonzero_real nonempty-type-eq-decl nil reals nil)
    (rat_div_nzrat_is_rat application-judgement "rat" rationals nil)
    (odd_minus_odd_is_even application-judgement "even_int" integers
     nil)
    (exp_strict_increasing formula-decl nil ln_exp nil)
    (minus_real_is_real application-judgement "real" reals nil)
    (trichotomy formula-decl nil real_axioms nil))
   shostak))
 (posreal_csch_TCC1 0
  (posreal_csch_TCC1-1 nil 3253435075
   ("" (skosimp*)
    (("" (expand "csch")
      ((""
        (lemma "div_mult_pos_lt2" ("z" "1" "x" "0" "py" "sinh(px!1)"))
        (("1" (assertnil nil)
         ("2" (hide 2)
          (("2" (expand "sinh")
            (("2" (lemma "exp_diff" ("x" "0" "y" "px!1"))
              (("2" (rewrite "exp_0")
                (("2" (rewrite -1)
                  (("2" (lemma "div_mult_pos_lt2")
                    (("2" (inst - "2" "0" "exp(px!1)-1/exp(px!1)")
                      (("2"
                        (lemma "minus_div1"
                         ("x" "exp(px!1)" "n0x" "1" "y" "1" "n0y"
                          "exp(px!1)"))
                        (("2" (lemma "exp_strict_increasing")
                          (("2" (expand "strict_increasing?")
                            (("2" (inst - "0" "2*px!1")
                              (("2"
                                (rewrite "exp_0")
                                (("2"
                                  (lemma
                                   "exp_sum"
                                   ("x" "px!1" "y" "px!1"))
                                  (("2"
                                    (replace -1 -3 rl)
                                    (("2"
                                      (expand ">=" 1)
                                      (("2"
                                        (expand ">" 1)
                                        (("2"
                                          (expand "<=" 1)
                                          (("2"
                                            (assert)
                                            (("2"
                                              (replace -4 1)
                                              (("2"
                                                (replace -3 1)
                                                (("2"
                                                  (lemma
                                                   "posreal_div_posreal_is_posreal"
                                                   ("px"
                                                    "exp(2*px!1)-1"
                                                    "py"
                                                    "exp(px!1)"))
                                                  (("2"
                                                    (assert)
                                                    nil
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((csch const-decl "real" hyperbolic nil)
    (exp_diff formula-decl nil ln_exp nil)
    (posreal_div_posreal_is_posreal application-judgement "posreal"
     real_types nil)
    (/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
    (nznum nonempty-type-eq-decl nil number_fields nil)
    (/= const-decl "boolean" notequal nil)
    (exp const-decl "{py | x = ln(py)}" ln_exp nil)
    (ln const-decl "real" ln_exp nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (exp_strict_increasing formula-decl nil ln_exp nil)
    (posreal_times_posreal_is_posreal application-judgement "posreal"
     real_types nil)
    (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (exp_sum formula-decl nil ln_exp nil)
    (<= const-decl "bool" reals nil)
    (posreal_div_posreal_is_posreal judgement-tcc nil real_types nil)
    (posreal_plus_nnreal_is_posreal application-judgement "posreal"
     real_types nil)
    (real_div_nzreal_is_real application-judgement "real" reals nil)
    (nnint_times_nnint_is_nnint application-judgement "nonneg_int"
     integers nil)
    (even_times_int_is_even application-judgement "even_int" integers
     nil)
    (mult_divides2 application-judgement "(divides(m))" divides nil)
    (mult_divides1 application-judgement "(divides(n))" divides nil)
    (odd_times_odd_is_odd application-judgement "odd_int" integers nil)
    (posint_times_posint_is_posint application-judgement "posint"
     integers nil)
    (strict_increasing? const-decl "bool" real_fun_preds "reals/")
    (nonzero_real nonempty-type-eq-decl nil reals nil)
    (minus_div1 formula-decl nil real_props nil)
    (minus_odd_is_odd application-judgement "odd_int" integers nil)
    (exp_0 formula-decl nil ln_exp nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (nzreal_div_nzreal_is_nzreal application-judgement "nzreal"
     real_types nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (AND const-decl "[bool, bool -> bool]" booleans 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)
    (div_mult_pos_lt2 formula-decl nil real_props nil)
    (number nonempty-type-decl nil numbers nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (>= const-decl "bool" reals 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)
    (sinh const-decl "real" hyperbolic nil))
   shostak))
 (posreal_coth_TCC1 0
  (posreal_coth_TCC1-1 nil 3253435075
   ("" (expand "coth")
    (("" (skosimp*)
      (("" (typepred "tanh(px!1)")
        (("" (case "strict_increasing?(tanh)")
          (("1" (expand "strict_increasing?")
            (("1" (inst - "0" "px!1")
              (("1" (assert)
                (("1" (expand "tanh" -1 1)
                  (("1" (expand "sinh" -1 1)
                    (("1" (expand "cosh" -1 1)
                      (("1" (rewrite "exp_0")
                        (("1" (rewrite "div_div2")
                          (("1" (grind-reals)
                            (("1" (cross-mult 1) nil nil)) nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil)
           ("2" (hide-all-but 1)
            (("2" (expand "strict_increasing?")
              (("2" (skosimp*)
                (("2" (expand "tanh")
                  (("2" (rewrite "div_mult_pos_lt1" 1)
                    (("2"
                      (lemma "div_mult_pos_lt2"
                       ("z" "sinh(y!1)*cosh(x!1)" "py" "cosh(y!1)" "x"
                        "sinh(x!1)"))
                      (("2" (replace -1)
                        (("2" (hide -1)
                          (("2" (expand "sinh")
                            (("2" (expand "cosh")
                              (("2"
                                (assert)
                                (("2"
                                  (lemma
                                   "both_sides_times_pos_lt1"
                                   ("pz"
                                    "4"
                                    "x"
                                    "(exp(x!1) - exp(-x!1)) / 2 * ((exp(-y!1) + exp(y!1)) / 2)"
                                    "y"
                                    "(exp(y!1) - exp(-y!1)) / 2 * ((exp(-x!1) + exp(x!1)) / 2)"))
                                  (("2"
                                    (replace -1 1 rl)
                                    (("2"
                                      (hide -1)
                                      (("2"
                                        (case-replace
                                         "(exp(x!1) - exp(-x!1)) / 2 * ((exp(-y!1) + exp(y!1)) / 2) * 4 = (exp(x!1) - exp(-x!1))*(exp(-y!1) + exp(y!1))")
                                        (("1"
                                          (case-replace
                                           "(exp(y!1) - exp(-y!1)) / 2 * ((exp(-x!1) + exp(x!1)) / 2) * 4 = (exp(y!1) - exp(-y!1))*(exp(-x!1) + exp(x!1))")
                                          (("1"
                                            (hide -1 -2)
                                            (("1"
                                              (assert)
                                              (("1"
                                                (name-replace
                                                 "K1"
                                                 "-1 * (exp(-x!1) * exp(-y!1))")
                                                (("1"
                                                  (name-replace
                                                   "K2"
                                                   "exp(x!1) * exp(y!1)")
                                                  (("1"
                                                    (lemma
                                                     "exp_sum"
                                                     ("x"
                                                      "-x!1"
                                                      "y"
                                                      "y!1"))
                                                    (("1"
                                                      (replace -1 1 rl)
                                                      (("1"
                                                        (lemma
                                                         "exp_sum"
                                                         ("x"
                                                          "-y!1"
                                                          "y"
                                                          "x!1"))
                                                        (("1"
                                                          (replace
                                                           -1
                                                           1
                                                           rl)
                                                          (("1"
                                                            (case-replace
                                                             "K1 - exp(-x!1 + y!1) + (exp(-y!1 + x!1) + K2) <
                       K1 - exp(-y!1 + x!1) + (exp(-x!1 + y!1) + K2) IFF exp(-y!1 + x!1) < exp(-x!1+y!1)")
                                                            (("1"
                                                              (hide
                                                               -1
                                                               -2
                                                               -3)
                                                              (("1"
                                                                (lemma
                                                                 "exp_strict_increasing")
                                                                (("1"
                                                                  (expand
                                                                   "strict_increasing?")
                                                                  (("1"
                                                                    (inst
                                                                     -
                                                                     "x!1-y!1"
                                                                     "y!1-x!1")
                                                                    (("1"
                                                                      (assert)
                                                                      nil
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil)
                                                             ("2"
                                                              (hide
                                                               -1
                                                               -2
                                                               2)
                                                              (("2"
                                                                (lemma
                                                                 "both_sides_times_pos_lt1"
                                                                 ("x"
                                                                  "exp(-y!1 + x!1)"
                                                                  "y"
                                                                  "exp(-x!1 + y!1)"
                                                                  "pz"
                                                                  "2"))
                                                                (("2"
                                                                  (replace
                                                                   -1
                                                                   1
                                                                   rl)
                                                                  (("2"
                                                                    (assert)
                                                                    (("2"
                                                                      (name-replace
                                                                       "K3"
                                                                       "exp(-y!1 + x!1)")
                                                                      (("2"
                                                                        (name-replace
                                                                         "K4"
                                                                         "exp(-x!1 + y!1)")
                                                                        (("2"
                                                                          (hide
                                                                           -1
                                                                           -2)
                                                                          (("2"
                                                                            (grind)
                                                                            nil
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil)
                                           ("2"
                                            (hide -1 -2 2)
                                            (("2"
                                              (name-replace
                                               "EXPX"
                                               "(exp(-x!1) + exp(x!1))")
                                              (("2"
                                                (name-replace
                                                 "EXPY"
                                                 "(exp(y!1)-exp(-y!1))")
                                                (("2"
                                                  (assert)
                                                  nil
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil)
                                         ("2"
                                          (hide -1 2)
                                          (("2"
                                            (name-replace
                                             "EXPY"
                                             "(exp(-y!1)+exp(y!1))")
                                            (("2"
                                              (name-replace
                                               "EXPX"
                                               "(exp(x!1)-exp(-x!1))")
                                              (("2" (assertnil nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((strict_increasing? const-decl "bool" real_fun_preds "reals/")
    (cosh const-decl "posreal_ge1" hyperbolic nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (nonzero_real nonempty-type-eq-decl nil reals nil)
    (/= const-decl "boolean" notequal nil)
    (div_div2 formula-decl nil real_props nil)
    (odd_minus_odd_is_even application-judgement "even_int" 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)
    (posint_times_posint_is_posint application-judgement "posint"
     integers nil)
    (rat_div_nzrat_is_rat application-judgement "rat" rationals nil)
    (div_mult_pos_gt1 formula-decl nil extra_real_props nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (posreal_div_posreal_is_posreal application-judgement "posreal"
     real_types nil)
    (real_div_nzreal_is_real application-judgement "real" reals nil)
    (posreal_plus_nnreal_is_posreal application-judgement "posreal"
     real_types nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (exp_0 formula-decl nil ln_exp nil)
    (sinh const-decl "real" hyperbolic nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (minus_odd_is_odd application-judgement "odd_int" integers nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (nzreal_div_nzreal_is_nzreal application-judgement "nzreal"
     real_types nil)
    (div_mult_pos_lt2 formula-decl nil real_props nil)
    (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (both_sides_times_pos_lt1 formula-decl nil real_props nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (ln const-decl "real" ln_exp nil)
    (exp const-decl "{py | x = ln(py)}" ln_exp nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (nzreal_times_nzreal_is_nzreal application-judgement "nzreal"
     real_types nil)
    (posreal_times_posreal_is_posreal application-judgement "posreal"
     real_types nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (exp_strict_increasing formula-decl nil ln_exp nil)
    (IFF const-decl "[bool, bool -> bool]" booleans nil)
    (exp_sum formula-decl nil ln_exp nil)
    (nzreal nonempty-type-eq-decl nil reals nil)
    (minus_real_is_real application-judgement "real" reals nil)
    (div_mult_pos_lt1 formula-decl nil real_props nil)
    (posreal_ge1 nonempty-type-eq-decl nil hyperbolic nil)
    (nznum nonempty-type-eq-decl nil number_fields nil)
    (/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (< const-decl "bool" reals nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (- const-decl "[numfield -> numfield]" number_fields nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (real_abs_lt1 nonempty-type-eq-decl nil hyperbolic nil)
    (tanh const-decl "real_abs_lt1" hyperbolic nil)
    (>= const-decl "bool" reals 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)
    (coth const-decl "real_abs_gt1" hyperbolic nil))
   shostak))
 (sinh_strict_increasing 0
  (sinh_strict_increasing-1 nil 3253386551
   ("" (expand "strict_increasing?")
    (("" (expand "sinh")
      (("" (skosimp*)
        ((""
          (lemma "both_sides_div_pos_lt1"
           ("x" "exp(x!1)-exp(-x!1)" "y" "exp(y!1)-exp(-y!1)" "pz"
            "2"))
          (("" (lemma "exp_strict_increasing")
            (("" (expand "strict_increasing?")
              (("" (inst-cp - "x!1" "y!1")
                (("" (inst - "-y!1" "-x!1")
                  (("" (name-replace "EPX" "exp(x!1)")
                    (("" (name-replace "EMX" "exp(-x!1)")
                      (("" (name-replace "EMY" "exp(-y!1)")
                        (("" (name-replace "EPY" "exp(y!1)")
                          ((""
                            (lemma "both_sides_times_neg_lt1"
                             ("x" "y!1" "y" "x!1" "nz" "-1"))
                            (("" (assertnil nil)) nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((real_minus_real_is_real application-judgement "real" reals nil)
    (sinh const-decl "real" hyperbolic nil)
    (- const-decl "[numfield -> numfield]" number_fields nil)
    (exp const-decl "{py | x = ln(py)}" ln_exp nil)
    (ln const-decl "real" ln_exp nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (> const-decl "bool" reals nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (>= const-decl "bool" reals nil)
    (bool nonempty-type-eq-decl nil booleans 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)
    (both_sides_div_pos_lt1 formula-decl nil real_props nil)
    (minus_real_is_real application-judgement "real" reals nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (real_div_nzreal_is_real application-judgement "real" reals nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (negreal nonempty-type-eq-decl nil real_types nil)
    (< const-decl "bool" reals nil)
    (nonpos_real nonempty-type-eq-decl nil real_types nil)
    (<= const-decl "bool" reals nil)
    (both_sides_times_neg_lt1 formula-decl nil real_props nil)
    (minus_odd_is_odd application-judgement "odd_int" integers nil)
    (exp_strict_increasing formula-decl nil ln_exp nil)
    (strict_increasing? const-decl "bool" real_fun_preds "reals/"))
   shostak))
 (cosh_strict_increasing 0
  (cosh_strict_increasing-1 nil 3253395203
   ("" (expand "strict_increasing?")
    (("" (skosimp*)
      (("" (typepred "x!1")
        (("" (typepred "y!1")
          (("" (expand "nnreal_cosh")
            (("" (expand "cosh")
              ((""
                (lemma "both_sides_div_pos_lt1"
                 ("x" "exp(-x!1) + exp(x!1)" "y" "exp(-y!1) + exp(y!1)"
                  "pz" "2"))
                (("" (replace -1 1)
                  (("" (lemma "exp_diff" ("x" "0" "y" "x!1"))
                    (("" (rewrite "exp_0")
                      (("" (replace -1 1)
                        (("" (lemma "exp_diff" ("x" "0" "y" "y!1"))
                          (("" (rewrite "exp_0")
                            (("" (replace -1 1)
                              ((""
                                (lemma
                                 "both_sides_times_pos_lt1"
                                 ("x"
                                  "1/exp(x!1)+exp(x!1)"
                                  "y"
                                  "1/exp(y!1)+exp(y!1)"
                                  "pz"
                                  "exp(x!1)*exp(y!1)"))
                                ((""
                                  (replace -1 1 rl)
                                  ((""
                                    (simplify 1)
                                    ((""
                                      (lemma "div_cancel1")
                                      ((""
                                        (inst-cp - "exp(x!1)" "1")
                                        ((""
                                          (inst - "exp(y!1)" "1")
                                          ((""
                                            (lemma
                                             "exp_strict_increasing")
                                            ((""
                                              (expand
                                               "strict_increasing?")
                                              ((""
                                                (inst - "x!1" "y!1")
                                                ((""
                                                  (assert)
                                                  ((""
                                                    (lemma
                                                     "exp_increasing")
                                                    ((""
                                                      (expand
                                                       "increasing?")
                                                      ((""
                                                        (inst
                                                         -
                                                         "0"
                                                         "x!1")
                                                        ((""
                                                          (assert)
                                                          ((""
                                                            (rewrite
                                                             "exp_0")
                                                            ((""
                                                              (name-replace
                                                               "EPX"
                                                               "exp(x!1)")
                                                              ((""
                                                                (name-replace
                                                                 "EPY"
                                                                 "exp(y!1)")
                                                                ((""
                                                                  (hide
                                                                   (-5
                                                                    -6
                                                                    -7
                                                                    1))
                                                                  ((""
                                                                    (lemma
                                                                     "posreal_times_posreal_is_posreal"
                                                                     ("px"
                                                                      "EPX*EPY-1"
                                                                      "py"
                                                                      "EPY-EPX"))
                                                                    (("1"
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