Quelle acosx.prf Sprache: Lisp

(acosx
(acos_lemma 0
  (acos_lemma-1 nil 3288613766
   ("" (skosimp*)
    (("" (expand "acos")
      (("" (expand "cauchy_acos")
        (("" (lemma "pi_lemma")
          ((""
            (lemma "lemma_div2n" ("x" "pi" "cx" "cauchy_pi" "n" "1"))
            (("" (lemma "asin_lemma" ("x" "x!1" "cx" "cx!1"))
              (("" (assert)
                (("" (expand "div2n")
                  (("" (rewrite "expt_x1")
                    ((""
                      (lemma "sub_lemma"
                       ("x" "pi/2" "y" "asin(x!1)" "cx"
                        "cauchy_div2n(cauchy_pi, 1)" "cy"
                        "cauchy_asin(cx!1)"))
                      (("" (assert) nil nil)) nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((acos const-decl "nnreal_le_pi" acos "trig_fnd/")
    (pi_lemma formula-decl nil atanx nil)
    (asin_lemma formula-decl nil asinx nil)
    (cauchy_real_abs_le1? const-decl "bool" asinx nil)
    (cauchy_real_abs_le1 nonempty-type-eq-decl nil asinx nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (<= const-decl "bool" reals nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (- const-decl "[numfield -> numfield]" number_fields nil)
    (real_abs_le1 nonempty-type-eq-decl nil asin "trig_fnd/")
    (div2n const-decl "real" shift nil)
    (sub_lemma formula-decl nil sub nil)
    (cauchy_div2n const-decl "cauchy_real" shift nil)
    (cauchy_asin const-decl "cauchy_real" asinx nil)
    (/= const-decl "boolean" notequal nil)
    (nznum nonempty-type-eq-decl nil number_fields nil)
    (/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
    (real_abs_le_pi2 nonempty-type-eq-decl nil asin "trig_fnd/")
    (asin const-decl "real_abs_le_pi2" asin "trig_fnd/")
    (posint_exp application-judgement "posint" exponentiation nil)
    (expt_x1 formula-decl nil exponentiation nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (posreal_div_posreal_is_posreal application-judgement "posreal"
     real_types nil)
    (minus_nzreal_is_nzreal application-judgement "nzreal" real_types
     nil)
    (lemma_div2n formula-decl nil shift 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)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (int nonempty-type-eq-decl nil integers nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (>= const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (cauchy_real? const-decl "bool" cauchy nil)
    (cauchy_real nonempty-type-eq-decl nil cauchy nil)
    (cauchy_pi const-decl "cauchy_real" atanx 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)
    (pi const-decl "posreal" atan "trig_fnd/")
    (cauchy_acos const-decl "cauchy_real" acosx nil))
   shostak)))

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