Quelle interval_chain.prf Sprache: Lisp

(interval_chain
(IMP_chain_rule_TCC1 0
  (IMP_chain_rule_TCC1-1 nil 3304701211
   ("" (lemma "deriv_domain_Xt[X]") (("" (propax) nil nil)) nil)
   ((deriv_domain_Xt formula-decl nil interval_deriv nil)
    (real nonempty-type-from-decl nil reals nil)
    (Interval type-eq-decl nil interval nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (StrictInterval? const-decl "bool" interval nil)
    (X formal-const-decl "(StrictInterval?)" interval_chain nil))
   shostak))
(IMP_chain_rule_TCC2 0
  (IMP_chain_rule_TCC2-2 nil 3304701423
   ("" (expand "not_one_element?")
    (("" (skeep)
      (("" (typepred "x")
        (("" (typepred "X")
          (("" (expand "StrictlyProper?")
            (("" (inst 1 "if x=lb(X) then ub(X) else lb(X) endif")
              (("1" (grind) nil nil) ("2" (grind) nil nil)
               ("3" (grind) nil nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (/= const-decl "boolean" notequal nil)
    (IF const-decl "[boolean, T, T -> T]" if_def nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (x skolem-const-decl "XT" interval_chain 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)
    (Interval type-eq-decl nil interval nil)
    (|##| const-decl "bool" interval nil)
    (StrictInterval? const-decl "bool" interval nil)
    (X formal-const-decl "(StrictInterval?)" interval_chain nil)
    (XT type-eq-decl nil interval_chain nil)
    (not_one_element? const-decl "bool" deriv_domain_def "analysis/"))
   nil))
(IMP_chain_rule_TCC3 0
  (IMP_chain_rule_TCC3-1 nil 3304701483
   ("" (lemma "deriv_domain_Xt[Y]") (("" (propax) nil nil)) nil)
   ((deriv_domain_Xt formula-decl nil interval_deriv nil)
    (real nonempty-type-from-decl nil reals nil)
    (Interval type-eq-decl nil interval nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (StrictInterval? const-decl "bool" interval nil)
    (Y formal-const-decl "(StrictInterval?)" interval_chain nil))
   shostak))
(IMP_chain_rule_TCC4 0
  (IMP_chain_rule_TCC4-1 nil 3304701436
   ("" (expand "not_one_element?")
    (("" (skeep)
      (("" (typepred "x")
        (("" (typepred "Y")
          (("" (expand "StrictlyProper?")
            (("" (inst 1 "if x=lb(Y) then ub(Y) else lb(Y) endif")
              (("1" (grind) nil nil) ("2" (grind) nil nil)
               ("3" (grind) nil nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (/= const-decl "boolean" notequal nil)
    (IF const-decl "[boolean, T, T -> T]" if_def nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (x skolem-const-decl "YT" interval_chain 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)
    (Interval type-eq-decl nil interval nil)
    (|##| const-decl "bool" interval nil)
    (StrictInterval? const-decl "bool" interval nil)
    (Y formal-const-decl "(StrictInterval?)" interval_chain nil)
    (YT type-eq-decl nil interval_chain nil)
    (not_one_element? const-decl "bool" deriv_domain_def "analysis/"))
   nil))
(Diff_comp_TCC1 0
  (Diff_comp_TCC1-1 nil 3319158888
   ("" (skosimp :preds? t) (("" (inst -2 "t!1") nil nil)) 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)
    (Interval type-eq-decl nil interval nil)
    (|##| const-decl "bool" interval nil)
    (StrictInterval? const-decl "bool" interval nil)
    (X formal-const-decl "(StrictInterval?)" interval_chain nil)
    (Xt type-eq-decl nil interval_deriv nil)
    (Diff? const-decl "bool" interval_deriv nil)
    (XT type-eq-decl nil interval_chain nil)
    (Y formal-const-decl "(StrictInterval?)" interval_chain nil))
   nil))
(Diff_comp 0
  (Diff_comp-1 nil 3319159473
   ("" (skosimp :preds? t)
    (("" (expand "Diff?")
      (("" (lemma "composition_derivable_fun")
        (("" (inst -1 "f!1" "g!1")
          (("" (assert) (("" (expand "o") (("" (propax) nil nil)) nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((f!1 skolem-const-decl
     "(LAMBDA (f: (Diff?[X])): FORALL (t: XT): f(t) ## Y)"
     interval_chain nil)
    (O const-decl "T3" function_props nil)
    (YT type-eq-decl nil interval_chain nil)
    (composition_derivable_fun formula-decl nil chain_rule "analysis/")
    (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)
    (Interval type-eq-decl nil interval nil)
    (|##| const-decl "bool" interval nil)
    (StrictInterval? const-decl "bool" interval nil)
    (X formal-const-decl "(StrictInterval?)" interval_chain nil)
    (Xt type-eq-decl nil interval_deriv nil)
    (Diff? const-decl "bool" interval_deriv nil)
    (XT type-eq-decl nil interval_chain nil)
    (Y formal-const-decl "(StrictInterval?)" interval_chain nil))
   nil))
(Deriv_comp_TCC1 0
  (Deriv_comp_TCC1-1 nil 3319158888
   ("" (skosimp :preds? t) (("" (rewrite "Diff_comp") nil nil)) nil)
   ((Diff_comp formula-decl nil interval_chain 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)
    (Interval type-eq-decl nil interval nil)
    (|##| const-decl "bool" interval nil)
    (StrictInterval? const-decl "bool" interval nil)
    (X formal-const-decl "(StrictInterval?)" interval_chain nil)
    (Xt type-eq-decl nil interval_deriv nil)
    (Diff? const-decl "bool" interval_deriv nil)
    (XT type-eq-decl nil interval_chain nil)
    (Y formal-const-decl "(StrictInterval?)" interval_chain nil))
   nil))
(Deriv_comp 0
  (Deriv_comp-1 nil 3319159512
   ("" (skosimp :preds? t)
    (("" (expand* "Diff?" "D")
      (("" (lemma "deriv_comp_fun")
        (("" (inst -1 "f!1" "g!1")
          (("1" (expand "o")
            (("1" (assert)
              (("1" (expand "*") (("1" (propax) nil nil)) nil)) nil))
            nil)
           ("2" (assert) nil nil))
          nil))
        nil))
      nil))
    nil)
   ((D const-decl "[Xt -> real]" interval_deriv nil)
    (derivable? const-decl "bool" derivatives "analysis/")
    (g!1 skolem-const-decl "(Diff?[Y])" interval_chain nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (f!1 skolem-const-decl
     "(LAMBDA (f: (Diff?[X])): FORALL (t: XT): f(t) ## Y)"
     interval_chain nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (* const-decl "[T -> real]" real_fun_ops "reals/")
    (O const-decl "T3" function_props nil)
    (YT type-eq-decl nil interval_chain nil)
    (deriv_comp_fun formula-decl nil chain_rule "analysis/")
    (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)
    (Interval type-eq-decl nil interval nil)
    (|##| const-decl "bool" interval nil)
    (StrictInterval? const-decl "bool" interval nil)
    (X formal-const-decl "(StrictInterval?)" interval_chain nil)
    (Xt type-eq-decl nil interval_deriv nil)
    (Diff? const-decl "bool" interval_deriv nil)
    (XT type-eq-decl nil interval_chain nil)
    (Y formal-const-decl "(StrictInterval?)" interval_chain nil))
   nil)))

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