Quelle trig_aux.prf Sprache: Lisp

(trig_aux
(sin_cos_eq_0 0
  (sin_cos_eq_0-1 nil 3385302546
   ("" (skosimp)
    (("" (rewrite "sin_eq_0")
      (("" (skosimp)
        (("" (replace -1)
          (("" (rewrite "cos_k_pi") (("" (assert) nil nil)) nil)) nil))
        nil))
      nil))
    nil)
   ((sin_eq_0 formula-decl nil trig_basic "trig/")
    (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)
    (real_times_real_is_real application-judgement "real" reals nil)
    (rat_exp application-judgement "rat" exponentiation nil)
    (nzreal_exp application-judgement "nzreal" exponentiation nil)
    (minus_odd_is_odd application-judgement "odd_int" integers nil)
    (int nonempty-type-eq-decl nil integers nil)
    (integer nonempty-type-from-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)
    (cos_k_pi formula-decl nil trig_basic "trig/"))
   shostak))
(eq_iff_periodic 0
  (eq_iff_periodic-1 nil 3385302828
   ("" (skosimp)
    (("" (split)
      (("1" (flatten)
        (("1" (lemma "cos_minus" ("a" "a!1" "b" "b!1"))
          (("1" (replace -2)
            (("1" (replace -3)
              (("1" (rewrite "sq_rew")
                (("1" (rewrite "sq_rew")
                  (("1" (lemma "sin2_cos2" ("a" "b!1"))
                    (("1" (assert)
                      (("1" (replace -1)
                        (("1" (rewrite "cos_eq_1" -2)
                          (("1" (skosimp)
                            (("1" (inst + "i!1")
                              (("1" (assert) nil nil)) nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil)
       ("2" (skosimp*)
        (("2" (replace -1)
          (("2" (rewrite "sin_period" 1 :dir rl)
            (("2" (rewrite "cos_period" 1 :dir rl) 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)
    (cos_minus formula-decl nil trig_basic "trig/")
    (minus_odd_is_odd application-judgement "odd_int" integers nil)
    (sin const-decl "real" trig_basic "trig/")
    (real_minus_real_is_real application-judgement "real" reals nil)
    (nnreal_plus_nnreal_is_nnreal application-judgement "nnreal"
     real_types nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (cos_eq_1 formula-decl nil trig_basic "trig/")
    (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_plus_real_is_real application-judgement "real" reals nil)
    (sin2_cos2 formula-decl nil trig_basic "trig/")
    (sq_rew formula-decl nil sq "reals/")
    (cos const-decl "real" trig_basic "trig/")
    (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)
    (real_times_real_is_real application-judgement "real" reals nil)
    (sin_range application-judgement "trig_range" trig_basic "trig/")
    (cos_range application-judgement "trig_range" trig_basic "trig/")
    (cos_period formula-decl nil trig_basic "trig/")
    (integer nonempty-type-from-decl nil integers nil)
    (sin_period formula-decl nil trig_basic "trig/"))
   shostak)))

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