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products/sources/formale Sprachen/PVS/reals/ (Beweissystem der NASA Version 6.0.9^©) Datei vom 28.9.2014 mit Größe 4 kB

SSL expt_rew.prf Interaktion und
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(expt_rew
(zero_hat 0
  (zero_hat-1 nil 3255279382 ("" (skosimp*) (("" (grind) nil nil)) nil)
   ((expt def-decl "real" exponentiation nil)
    (^ const-decl "real" exponentiation nil)
    (int_minus_int_is_int application-judgement "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)
    (nnint_times_nnint_is_nnint application-judgement "nonneg_int"
     integers nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (nzrat_div_nzrat_is_nzrat application-judgement "nzrat" rationals
     nil)
    (nat_expt application-judgement "nat" exponentiation nil)
    (nat_exp application-judgement "nat" exponentiation nil))
   shostak))
(mult_hat_TCC1 0
  (mult_hat_TCC1-1 nil 3255279661
   ("" (skosimp*) (("" (assert) nil nil)) nil) nil shostak))
(mult_hat_TCC2 0
  (mult_hat_TCC2-1 nil 3255279661
   ("" (skosimp*) (("" (assert) nil nil)) nil)
   ((nzreal_times_nzreal_is_nzreal application-judgement "nzreal"
     real_types nil))
   shostak))
(mult_hat 0
  (mult_hat-1 nil 3255279671
   ("" (skosimp*)
    (("" (lemma "mult_expt") (("" (inst?) (("" (assert) nil nil)) nil))
      nil))
    nil)
   ((mult_expt formula-decl nil exponentiation nil)
    (nzreal_times_nzreal_is_nzreal application-judgement "nzreal"
     real_types nil)
    (nzreal_exp application-judgement "nzreal" exponentiation nil)
    (nzreal nonempty-type-eq-decl nil reals nil)
    (/= const-decl "boolean" notequal 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))
   shostak))
(div_hat_TCC1 0
  (div_hat_TCC1-1 nil 3255279661
   ("" (skosimp*) (("" (assert) nil nil)) nil)
   ((nzreal_div_nzreal_is_nzreal application-judgement "nzreal"
     real_types nil))
   shostak))
(div_hat 0
  (div_hat-1 nil 3255279686
   ("" (skosimp*) (("" (rewrite "div_expt") nil nil)) nil)
   ((nzreal_div_nzreal_is_nzreal application-judgement "nzreal"
     real_types nil)
    (nzreal_exp application-judgement "nzreal" exponentiation nil)
    (div_expt formula-decl nil exponentiation 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)
    (/= const-decl "boolean" notequal nil)
    (nzreal nonempty-type-eq-decl nil reals nil))
   shostak))
(inv_hat 0
  (inv_hat-1 nil 3255279696
   ("" (skosimp*) (("" (rewrite "inv_expt") nil nil)) nil)
   ((nzreal_div_nzreal_is_nzreal application-judgement "nzreal"
     real_types nil)
    (nzreal_exp application-judgement "nzreal" exponentiation nil)
    (inv_expt formula-decl nil exponentiation 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)
    (/= const-decl "boolean" notequal nil)
    (nzreal nonempty-type-eq-decl nil reals nil))
   shostak)))

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