Quelle mixed_sigmas.prf Sprache: Lisp

(mixed_sigmas
(IMP_sigma_TCC1 0
  (IMP_sigma_TCC1-1 nil 3537537618
   ("" (lemma "connected_domain1") (("" (propax) nil nil)) nil)
   ((connected_domain1 formula-decl nil mixed_sigmas nil)) nil))
(IMP_sigma_TCC2 0
  (IMP_sigma_TCC2-1 nil 3537537618
   ("" (lemma "connected_domain2") (("" (propax) nil nil)) nil)
   ((connected_domain2 formula-decl nil mixed_sigmas nil)) nil))
(mixed_sigmas_const_eq_TCC1 0
  (mixed_sigmas_const_eq_TCC1-1 nil 3537536439
   ("" (skeep)
    (("" (lemma "T_pred_lem[T]")
      (("" (inst - thigh tlow _)
        (("" (skeep) (("" (inst?) (("" (assert) nil nil)) nil)) nil))
        nil))
      nil))
    nil)
   ((T formal-subtype-decl nil mixed_sigmas nil)
    (T_pred const-decl "[int -> boolean]" mixed_sigmas 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)
    (T_pred_lem formula-decl nil sigma nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (>= const-decl "bool" reals nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (int_plus_int_is_int application-judgement "int" integers nil)
    (T_low type-eq-decl nil sigma nil)
    (T_high type-eq-decl nil sigma nil)
    (<= const-decl "bool" reals nil)
    (OR const-decl "[bool, bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil))
   nil))
(mixed_sigmas_const_eq_TCC2 0
  (mixed_sigmas_const_eq_TCC2-1 nil 3537536439
   ("" (skeep)
    (("" (skeep)
      (("" (lemma "T_pred_lem[H]")
        (("" (inst - "hhigh" "hlow" _)
          (("" (inst?) (("" (assert) nil nil)) nil)) nil))
        nil))
      nil))
    nil)
   ((bool nonempty-type-eq-decl nil booleans nil)
    (OR const-decl "[bool, bool -> bool]" booleans nil)
    (<= const-decl "bool" reals nil)
    (T_high type-eq-decl nil sigma nil)
    (T_low type-eq-decl nil sigma nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (>= const-decl "bool" reals nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (int_plus_int_is_int application-judgement "int" integers nil)
    (T_pred_lem formula-decl nil sigma 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)
    (H_pred const-decl "[int -> boolean]" mixed_sigmas nil)
    (H formal-subtype-decl nil mixed_sigmas nil))
   nil))
(mixed_sigmas_const_eq 0
  (mixed_sigmas_const_eq-1 nil 3537536793
   (""
    (case "FORALL (F: [T -> real], G: [H -> real], hhigh: T_high[H],
                     hlow: T_low[H], thigh: T_high[T], tlow: T_low[T]):
               (thigh - tlow = hhigh - hlow AND
                 (FORALL (i: nat):
                    i <= thigh - tlow IMPLIES F(tlow + i) = G(hlow + i)))
                IMPLIES (FORALL (i: nat):
                    i <= thigh - tlow IMPLIES sigma[T](tlow, tlow+i, F) = sigma[H](hlow, hlow+i, G))")
    (("1" (skeep)
      (("1" (inst - "F" "G" "hhigh" "hlow" "thigh" "tlow")
        (("1" (assert)
          (("1" (replace -3)
            (("1" (inst - "thigh-tlow")
              (("1" (assert) nil nil)
               ("2" (assert)
                (("2" (expand "sigma" +) (("2" (propax) nil nil)) nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     ("2" (hide 2)
      (("2" (skeep)
        (("2" (induct "i")
          (("1" (assert)
            (("1" (flatten)
              (("1" (expand "sigma" +)
                (("1" (expand "sigma" +)
                  (("1" (inst - "0") (("1" (assert) nil nil)) nil))
                  nil))
                nil))
              nil))
            nil)
           ("2" (skeep)
            (("2" (assert)
              (("2" (expand "sigma" +)
                (("2" (inst - "1+j") (("2" (assert) nil nil)) nil))
                nil))
              nil))
            nil)
           ("3" (skeep)
            (("3" (lemma "T_pred_lem[H]")
              (("3" (inst - "hhigh" "hlow" "i+hlow")
                (("3" (assert) nil nil)) nil))
              nil))
            nil)
           ("4" (skeep)
            (("4" (lemma "T_pred_lem[T]")
              (("4" (inst - "thigh" "tlow" "i+tlow")
                (("4" (assert) nil nil)) nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     ("3" (hide 2)
      (("3" (skeep)
        (("3" (skeep)
          (("3" (lemma "T_pred_lem[H]")
            (("3" (inst - "hhigh" "hlow" "hlow + i1")
              (("3" (assert) nil nil)) nil))
            nil))
          nil))
        nil))
      nil)
     ("4" (hide 2)
      (("4" (skeep)
        (("4" (skeep)
          (("4" (lemma "T_pred_lem[T]")
            (("4" (inst - "thigh" "tlow" "i1+tlow")
              (("4" (assert) nil nil)) nil))
            nil))
          nil))
        nil))
      nil)
     ("5" (hide 2)
      (("5" (skeep)
        (("5" (skeep)
          (("5" (lemma "T_pred_lem[H]")
            (("5" (inst - "hhigh" "hlow" "hlow + i")
              (("5" (assert) nil nil)) nil))
            nil))
          nil))
        nil))
      nil)
     ("6" (hide 2)
      (("6" (skeep)
        (("6" (skeep)
          (("6" (lemma "T_pred_lem[T]")
            (("6" (inst - "thigh" "tlow" "i+tlow")
              (("6" (assert) nil nil)) nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((thigh skolem-const-decl "T_high[T]" mixed_sigmas nil)
    (tlow skolem-const-decl "T_low[T]" mixed_sigmas nil)
    (hlow skolem-const-decl "T_low[H]" mixed_sigmas nil)
    (pred type-eq-decl nil defined_types nil)
    (nat_induction formula-decl nil naturalnumbers nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (nnint_plus_posint_is_posint application-judgement "posint"
     integers nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (T_pred_lem formula-decl nil sigma nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (thigh skolem-const-decl "T_high[T]" mixed_sigmas nil)
    (tlow skolem-const-decl "T_low[T]" mixed_sigmas nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (int_plus_int_is_int application-judgement "int" integers 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)
    (T_pred const-decl "[int -> boolean]" mixed_sigmas nil)
    (T formal-subtype-decl nil mixed_sigmas nil)
    (H_pred const-decl "[int -> boolean]" mixed_sigmas nil)
    (H formal-subtype-decl nil mixed_sigmas nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (OR const-decl "[bool, bool -> bool]" booleans nil)
    (<= const-decl "bool" reals nil)
    (T_high type-eq-decl nil sigma nil)
    (T_low type-eq-decl nil sigma nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (>= const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (sigma def-decl "real" sigma nil))
   shostak))
(mixed_sigmas_eq 0
  (mixed_sigmas_eq-1 nil 3537537619
   ("" (lemma "mixed_sigmas_const_eq")
    (("" (inst - _ _ _ _ _ _ 1)
      (("" (assert)
        (("" (case "FORALL (aa:real): 1*aa = aa")
          (("1" (rewrite -1) (("1" (rewrite -1) nil nil)) nil)
           ("2" (hide-all-but 1) (("2" (assert) nil nil)) nil))
          nil))
        nil))
      nil))
    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 "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (mixed_sigmas_const_eq formula-decl nil mixed_sigmas nil))
   shostak)))

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