products/sources/formale sprachen/PVS/trig image not shown  

Quellcode-Bibliothek

© Kompilation durch diese Firma

[Weder Korrektheit noch Funktionsfähigkeit der Software werden zugesichert.]

Datei:   Sprache: Lisp

Original von: PVS©

(asin (real_abs_le_pi2_TCC1 0
       (real_abs_le_pi2_TCC1-1 nil 3323019118
        ("" (subtype-tcc) nil nil)
        ((minus_nzreal_is_nzreal application-judgement "nzreal"
          real_types nil)
         (nzreal_div_nzreal_is_nzreal application-judgement "nzreal"
          real_types nil)
         (posreal_div_posreal_is_posreal application-judgement
          "posreal" real_types nil)
         (real_le_is_total_order name-judgement "(total_order?[real])"
          real_props nil))
        nil))
      (asin_TCC1 0
       (asin_TCC1-1 nil 3262199128
        ("" (skolem 1 ("x"))
         (("" (flatten)
           (("" (typepred "x")
             (("" (expand "abs")
               (("" (assert)
                 ((""
                   (lemma "le_times_le_pos"
                    ("nnx" "-x" "y" "1" "nnz" "-x" "w" "1"))
                   (("" (assertnil nil)) nil))
                 nil))
               nil))
             nil))
           nil))
         nil)
        ((minus_nzreal_is_nzreal application-judgement "nzreal"
          real_types nil)
         (nzreal_div_nzreal_is_nzreal application-judgement "nzreal"
          real_types nil)
         (minus_odd_is_odd application-judgement "odd_int" integers
          nil)
         (real_le_is_total_order name-judgement "(total_order?[real])"
          real_props 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)
         (<= const-decl "bool" reals nil)
         (numfield nonempty-type-eq-decl nil number_fields nil)
         (- const-decl "[numfield -> numfield]" number_fields nil)
         (AND const-decl "[bool, bool -> bool]" booleans nil)
         (real_abs_le1 nonempty-type-eq-decl nil asin nil))
        shostak))
      (asin_TCC2 0
       (asin_TCC2-1 nil 3262199262
        ("" (grind)
         (("1" (lemma "sq_lt_abs" ("a" "-x!1" "b" "1"))
           (("1" (grind) nil nil)) nil)
          ("2" (rewrite "sq_rew")
           (("2" (lemma "sq_lt" ("nna" "x!1" "nnb" "1"))
             (("2" (grind) nil nil)) nil))
           nil))
         nil)
        ((minus_real_is_real application-judgement "real" reals nil)
         (sq_lt_abs formula-decl nil sq "reals/")
         (nzrat_abs_is_pos application-judgement "{r: posrat | r >= q}"
          real_defs nil)
         (int_abs_is_nonneg application-judgement
          "{j: nonneg_int | j >= i}" real_defs nil)
         (nzint_abs_is_pos application-judgement "{j: posint | j >= i}"
          real_defs nil)
         (abs const-decl "{n: nonneg_real | n >= m AND n >= -m}"
              real_defs nil)
         (sq const-decl "nonneg_real" sq "reals/")
         (sq_nz_pos application-judgement "posreal" sq "reals/")
         (real_minus_real_is_real application-judgement "real" reals
          nil)
         (real_ge_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)
         (minus_odd_is_odd application-judgement "odd_int" integers
          nil)
         (real_le_is_total_order name-judgement "(total_order?[real])"
          real_props 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)
         (<= const-decl "bool" reals nil)
         (numfield nonempty-type-eq-decl nil number_fields nil)
         (- const-decl "[numfield -> numfield]" number_fields nil)
         (AND const-decl "[bool, bool -> bool]" booleans nil)
         (real_abs_le1 nonempty-type-eq-decl nil asin nil)
         (real_times_real_is_real application-judgement "real" reals
          nil))
        shostak))
      (asin_TCC3 0
       (asin_TCC3-1 nil 3262199449
        ("" (skolem 1 ("x"))
         (("" (flatten)
           (("" (typepred "x")
             (("" (expand "abs")
               (("" (case "x < 0")
                 (("1" (assert)
                   (("1"
                     (lemma "lt_times_lt_pos1"
                      ("px" "-x" "y" "1" "nnz" "-x" "w" "1"))
                     (("1" (assertnil nil)) nil))
                   nil)
                  ("2" (assert)
                   (("2"
                     (lemma "lt_times_lt_pos1"
                      ("px" "x" "y" "1" "nnz" "x" "w" "1"))
                     (("2" (assertnil nil)) nil))
                   nil))
                 nil))
               nil))
             nil))
           nil))
         nil)
        ((< const-decl "bool" reals nil)
         (minus_real_is_real application-judgement "real" reals nil)
         (lt_times_lt_pos1 formula-decl nil real_props nil)
         (>= const-decl "bool" reals 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)
         (real_ge_is_total_order name-judgement "(total_order?[real])"
          real_props nil)
         (real_gt_is_strict_total_order name-judgement
          "(strict_total_order?[real])" real_props nil)
         (real_lt_is_strict_total_order name-judgement
          "(strict_total_order?[real])" real_props nil)
         (real_le_is_total_order name-judgement "(total_order?[real])"
          real_props nil)
         (minus_odd_is_odd application-judgement "odd_int" integers
          nil)
         (real_minus_real_is_real application-judgement "real" reals
          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)
         (<= const-decl "bool" reals nil)
         (numfield nonempty-type-eq-decl nil number_fields nil)
         (- const-decl "[numfield -> numfield]" number_fields nil)
         (AND const-decl "[bool, bool -> bool]" booleans nil)
         (real_abs_le1 nonempty-type-eq-decl nil asin nil)
         (real_times_real_is_real application-judgement "real" reals
          nil))
        shostak))
      (asin_TCC4 0
       (asin_TCC4-1 nil 3262199280
        ("" (skolem 1 ("x"))
         (("" (flatten)
           (("" (typepred "x")
             (("" (assert)
               (("" (typepred "atan(x / sqrt(1 - x * x))")
                 (("1" (rewrite "pi_value" 2)
                   (("1" (expand "atan" 2 4)
                     (("1" (assert)
                       (("1" (expand "atan" -2 2)
                         (("1" (assertnil nil)) nil))
                       nil))
                     nil))
                   nil)
                  ("2" (hide 3)
                   (("2" (lemma "sqrt_pos" ("px" "1-x*x"))
                     (("1" (assertnil nil)
                      ("2" (hide 2)
                       (("2" (lemma "sq_lt_abs" ("a" "x" "b" "1"))
                         (("2" (grind) nil nil)) nil))
                       nil))
                     nil))
                   nil))
                 nil))
               nil))
             nil))
           nil))
         nil)
        ((real_minus_real_is_real application-judgement "real" reals
          nil)
         (real_div_nzreal_is_real application-judgement "real" reals
          nil)
         (minus_nzreal_is_nzreal application-judgement "nzreal"
          real_types nil)
         (nzreal_div_nzreal_is_nzreal application-judgement "nzreal"
          real_types nil)
         (real_lt_is_strict_total_order name-judgement
          "(strict_total_order?[real])" real_props nil)
         (minus_odd_is_odd application-judgement "odd_int" integers
          nil)
         (real_le_is_total_order name-judgement "(total_order?[real])"
          real_props nil)
         (sq_nz_pos application-judgement "posreal" sq "reals/")
         (nzint_abs_is_pos application-judgement "{j: posint | j >= i}"
          real_defs nil)
         (int_abs_is_nonneg application-judgement
          "{j: nonneg_int | j >= i}" real_defs nil)
         (nzrat_abs_is_pos application-judgement "{r: posrat | r >= q}"
          real_defs nil)
         (abs const-decl "{n: nonneg_real | n >= m AND n >= -m}"
              real_defs nil)
         (sq const-decl "nonneg_real" sq "reals/")
         (sq_lt_abs formula-decl nil sq "reals/")
         (real_gt_is_strict_total_order name-judgement
          "(strict_total_order?[real])" real_props nil)
         (sqrt_pos judgement-tcc nil sqrt "reals/")
         (pi_value formula-decl nil atan nil)
         (minus_real_is_real application-judgement "real" reals nil)
         (real_ge_is_total_order name-judgement "(total_order?[real])"
          real_props nil)
         (< const-decl "bool" reals nil)
         (/= const-decl "boolean" notequal nil)
         (nznum nonempty-type-eq-decl nil number_fields nil)
         (/ const-decl "[numfield, nznum -> numfield]" number_fields
            nil)
         (>= const-decl "bool" reals 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_lb const-decl "posreal" trig_basic nil)
         (pi_ub const-decl "posreal" trig_basic nil)
         (pi const-decl "{r: posreal | r > pi_lb AND r < pi_ub}"
          trig_basic nil)
         (real_abs_lt_pi2 nonempty-type-eq-decl nil atan nil)
         (atan const-decl "real_abs_lt_pi2" atan nil)
         (nnreal type-eq-decl nil real_types nil)
         (= const-decl "[T, T -> boolean]" equalities nil)
         (* const-decl "[numfield, numfield -> numfield]" number_fields
            nil)
         (sqrt const-decl "{nnz: nnreal | nnz * nnz = nnx}" sqrt
               "reals/")
         (- const-decl "[numfield, numfield -> numfield]" number_fields
            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)
         (<= const-decl "bool" reals nil)
         (numfield nonempty-type-eq-decl nil number_fields nil)
         (- const-decl "[numfield -> numfield]" number_fields nil)
         (AND const-decl "[bool, bool -> bool]" booleans nil)
         (real_abs_le1 nonempty-type-eq-decl nil asin nil)
         (real_times_real_is_real application-judgement "real" reals
          nil))
        shostak))
      (asin_TCC5 0
       (asin_TCC5-1 nil 3262199369
        ("" (expand "abs")
         (("" (skolem!)
           (("" (flatten)
             (("" (typepred "pi") (("" (assertnil nil)) nil)) nil))
           nil))
         nil)
        ((posreal_div_posreal_is_posreal application-judgement
          "posreal" real_types nil)
         (minus_nzreal_is_nzreal application-judgement "nzreal"
          real_types nil)
         (nzreal_div_nzreal_is_nzreal application-judgement "nzreal"
          real_types nil)
         (real_le_is_total_order name-judgement "(total_order?[real])"
          real_props nil)
         (minus_odd_is_odd application-judgement "odd_int" integers
          nil)
         (real_lt_is_strict_total_order name-judgement
          "(strict_total_order?[real])" real_props nil)
         (real_gt_is_strict_total_order name-judgement
          "(strict_total_order?[real])" real_props nil)
         (real_ge_is_total_order name-judgement "(total_order?[real])"
          real_props 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)
         (>= const-decl "bool" reals 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)
         (AND const-decl "[bool, bool -> bool]" booleans nil)
         (pi_lb const-decl "posreal" trig_basic nil)
         (< const-decl "bool" reals nil)
         (pi_ub const-decl "posreal" trig_basic nil)
         (pi const-decl "{r: posreal | r > pi_lb AND r < pi_ub}"
          trig_basic nil))
        shostak))
      (asin_neg_restrict_TCC1 0
       (asin_neg_restrict_TCC1-1 nil 3262231650
        ("" (skolem!)
         (("" (typepred "nx!1")
           (("" (expand "abs")
             (("" (lemma "sq_le_abs" ("a" "-nx!1" "b" "1"))
               (("" (grind) nil nil)) nil))
             nil))
           nil))
         nil)
        ((< const-decl "bool" reals nil)
         (real_abs_le1 nonempty-type-eq-decl nil asin nil)
         (AND const-decl "[bool, bool -> bool]" booleans nil)
         (- const-decl "[numfield -> numfield]" number_fields nil)
         (numfield nonempty-type-eq-decl nil number_fields nil)
         (<= const-decl "bool" reals 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)
         (number nonempty-type-decl nil numbers nil)
         (NOT const-decl "[bool -> bool]" booleans nil)
         (bool nonempty-type-eq-decl nil booleans nil)
         (boolean nonempty-type-decl nil booleans nil)
         (real_le_is_total_order name-judgement "(total_order?[real])"
          real_props nil)
         (real_times_real_is_real application-judgement "real" reals
          nil)
         (sq_nz_pos application-judgement "posreal" sq "reals/")
         (real_lt_is_strict_total_order name-judgement
          "(strict_total_order?[real])" real_props nil)
         (nzint_abs_is_pos application-judgement "{j: posint | j >= i}"
          real_defs nil)
         (int_abs_is_nonneg application-judgement
          "{j: nonneg_int | j >= i}" real_defs nil)
         (nzrat_abs_is_pos application-judgement "{r: posrat | r >= q}"
          real_defs nil)
         (minus_odd_is_odd application-judgement "odd_int" integers
          nil)
         (real_ge_is_total_order name-judgement "(total_order?[real])"
          real_props nil)
         (real_minus_real_is_real application-judgement "real" reals
          nil)
         (abs const-decl "{n: nonneg_real | n >= m AND n >= -m}"
              real_defs nil)
         (sq const-decl "nonneg_real" sq "reals/")
         (sq_le_abs formula-decl nil sq "reals/")
         (minus_real_is_real application-judgement "real" reals nil))
        shostak))
      (asin_neg_restrict_TCC2 0
       (asin_neg_restrict_TCC2-1 nil 3262231879 ("" (grind) nil nil)
        nil shostak))
      (asin_neg_restrict 0
       (asin_neg_restrict-2 nil 3322498655
        ("" (skolem 1 ("nx"))
         (("" (typepred "nx")
           (("" (expand "<=")
             (("" (expand "asin")
               (("" (split -1)
                 (("1" (assert)
                   (("1"
                     (lemma "both_sides_times_neg_lt1"
                      ("nz" "-1" "x" "nx" "y" "-1"))
                     (("1"
                       (lemma "lt_times_lt_neg1"
                        ("x" "-1" "ny" "nx" "z" "-1" "npw" "nx"))
                       (("1" (assert)
                         (("1"
                           (lemma "sqrt_lt"
                            ("nny" "0" "nnz" "1-nx*nx"))
                           (("1" (rewrite "sqrt_0" -1)
                             (("1"
                               (lemma
                                "atan_inv_neg"
                                ("nx" "sqrt(1 - nx * nx) / nx"))
                               (("1"
                                 (rewrite "pi_value" 1)
                                 (("1"
                                   (lemma
                                    "div_div1"
                                    ("x"
                                     "1"
                                     "n0y"
                                     "sqrt(1-nx*nx)"
                                     "n0z"
                                     "nx"))
                                   (("1"
                                     (replace -1 -2)
                                     (("1" (assertnil nil))
                                     nil))
                                   nil))
                                 nil)
                                ("2"
                                 (lemma
                                  "both_sides_div_neg_lt1"
                                  ("y"
                                   "0"
                                   "x"
                                   "sqrt(1-nx*nx)"
                                   "nz"
                                   "nx"))
                                 (("2" (assertnil nil))
                                 nil))
                               nil))
                             nil))
                           nil))
                         nil))
                       nil))
                     nil))
                   nil)
                  ("2" (assert)
                   (("2" (case "nx = -1")
                     (("1" (replace -1)
                       (("1" (rewrite "sqrt_0")
                         (("1" (rewrite "atan_0")
                           (("1" (assertnil nil)) nil))
                         nil))
                       nil)
                      ("2" (assertnil nil))
                     nil))
                   nil))
                 nil))
               nil))
             nil))
           nil))
         nil)
        ((< const-decl "bool" reals nil)
         (real_abs_le1 nonempty-type-eq-decl nil asin nil)
         (AND const-decl "[bool, bool -> bool]" booleans nil)
         (- const-decl "[numfield -> numfield]" number_fields nil)
         (numfield nonempty-type-eq-decl nil number_fields nil)
         (<= const-decl "bool" reals 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)
         (number nonempty-type-decl nil numbers nil)
         (NOT const-decl "[bool -> bool]" booleans nil)
         (bool nonempty-type-eq-decl nil booleans nil)
         (boolean nonempty-type-decl nil booleans nil)
         (minus_nzreal_is_nzreal application-judgement "nzreal"
          real_types nil)
         (asin const-decl "real_abs_le_pi2" asin nil)
         (atan_0 formula-decl nil atan nil)
         (int_times_even_is_even application-judgement "even_int"
          integers nil)
         (mult_divides2 application-judgement "(divides(m))" divides
          nil)
         (nzreal_div_nzreal_is_nzreal application-judgement "nzreal"
          real_types nil)
         (real_minus_real_is_real application-judgement "real" reals
          nil)
         (real_div_nzreal_is_real application-judgement "real" reals
          nil)
         (minus_odd_is_odd application-judgement "odd_int" integers
          nil)
         (real_lt_is_strict_total_order name-judgement
          "(strict_total_order?[real])" real_props nil)
         (lt_times_lt_neg1 formula-decl nil real_props nil)
         (real_le_is_total_order name-judgement "(total_order?[real])"
          real_props nil)
         (sqrt_lt formula-decl nil sqrt "reals/")
         (>= const-decl "bool" reals nil)
         (nonneg_real nonempty-type-eq-decl nil real_types nil)
         (- const-decl "[numfield, numfield -> numfield]" number_fields
            nil)
         (* const-decl "[numfield, numfield -> numfield]" number_fields
            nil)
         (real_ge_is_total_order name-judgement "(total_order?[real])"
          real_props nil)
         (atan_inv_neg formula-decl nil atan nil)
         (/= const-decl "boolean" notequal nil)
         (nznum nonempty-type-eq-decl nil number_fields nil)
         (/ const-decl "[numfield, nznum -> numfield]" number_fields
            nil)
         (nnreal type-eq-decl nil real_types nil)
         (= const-decl "[T, T -> boolean]" equalities nil)
         (sqrt const-decl "{nnz: nnreal | nnz * nnz = nnx}" sqrt
               "reals/")
         (div_div1 formula-decl nil real_props nil)
         (nonzero_real nonempty-type-eq-decl nil reals nil)
         (minus_real_is_real application-judgement "real" reals nil)
         (pi_value formula-decl nil atan nil)
         (both_sides_div_neg_lt1 formula-decl nil real_props nil)
         (sqrt_0 formula-decl nil sqrt "reals/")
         (odd_times_odd_is_odd application-judgement "odd_int" integers
          nil)
         (mult_divides1 application-judgement "(divides(n))" divides
          nil)
         (negreal nonempty-type-eq-decl nil real_types nil)
         (nonpos_real nonempty-type-eq-decl nil real_types nil)
         (both_sides_times_neg_lt1 formula-decl nil real_props nil)
         (real_times_real_is_real application-judgement "real" reals
          nil))
        nil))
      (asin_pos_restrict_TCC1 0
       (asin_pos_restrict_TCC1-1 nil 3262251224
        ("" (skosimp*)
         (("" (typepred "px!1")
           (("" (expand "abs")
             ((""
               (lemma "le_times_le_pos"
                ("nnx" "px!1" "y" "1" "nnz" "px!1" "w" "1"))
               (("" (assertnil nil)) nil))
             nil))
           nil))
         nil)
        ((< const-decl "bool" reals nil)
         (real_abs_le1 nonempty-type-eq-decl nil asin nil)
         (AND const-decl "[bool, bool -> bool]" booleans nil)
         (- const-decl "[numfield -> numfield]" number_fields nil)
         (numfield nonempty-type-eq-decl nil number_fields nil)
         (<= const-decl "bool" reals 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)
         (number nonempty-type-decl nil numbers nil)
         (NOT const-decl "[bool -> bool]" booleans nil)
         (bool nonempty-type-eq-decl nil booleans nil)
         (boolean nonempty-type-decl nil booleans nil)
         (real_times_real_is_real application-judgement "real" reals
          nil)
         (real_minus_real_is_real application-judgement "real" reals
          nil)
         (real_lt_is_strict_total_order name-judgement
          "(strict_total_order?[real])" real_props nil)
         (minus_odd_is_odd application-judgement "odd_int" integers
          nil)
         (real_le_is_total_order name-judgement "(total_order?[real])"
          real_props nil)
         (real_ge_is_total_order name-judgement "(total_order?[real])"
          real_props nil)
         (le_times_le_pos formula-decl nil real_props nil)
         (>= const-decl "bool" reals nil)
         (nonneg_real nonempty-type-eq-decl nil real_types nil))
        shostak))
      (asin_pos_restrict_TCC2 0
       (asin_pos_restrict_TCC2-1 nil 3262251224 ("" (grind) nil nil)
        nil shostak))
      (asin_pos_restrict 0
       (asin_pos_restrict-1 nil 3408901117
        ("" (skolem 1 ("px"))
         (("" (case "abs(px) <= 1")
           (("1" (expand "<=")
             (("1" (split -1)
               (("1" (expand "asin")
                 (("1" (assert)
                   (("1" (lemma "sq_nz_pos" ("nz" "px"))
                     (("1" (expand "sq")
                       (("1"
                         (lemma "lt_times_lt_pos1"
                          ("px" "px" "y" "1" "nnz" "px" "w" "1"))
                         (("1" (assert)
                           (("1"
                             (lemma "sqrt_lt"
                              ("nny" "0" "nnz" "1-px*px"))
                             (("1" (rewrite "sqrt_0")
                               (("1"
                                 (lemma
                                  "atan_inv"
                                  ("px" "sqrt(1 - px * px) / px"))
                                 (("1"
                                   (lemma
                                    "div_div1"
                                    ("x"
                                     "1"
                                     "n0y"
                                     "sqrt(1-px*px)"
                                     "n0z"
                                     "px"))
                                   (("1"
                                     (replace -1 -2)
                                     (("1"
                                       (rewrite "pi_value" 1)
                                       (("1" (assertnil nil))
                                       nil))
                                     nil))
                                   nil)
                                  ("2"
                                   (lemma
                                    "posreal_div_posreal_is_posreal"
                                    ("px" "sqrt(1-px*px)" "py" "px"))
                                   (("2" (assertnil nil))
                                   nil))
                                 nil))
                               nil))
                             nil))
                           nil))
                         nil))
                       nil))
                     nil))
                   nil))
                 nil)
                ("2" (expand "asin")
                 (("2" (assert)
                   (("2" (lift-if)
                     (("2" (expand "abs")
                       (("2" (assert)
                         (("2" (replace -1)
                           (("2" (assert)
                             (("2" (rewrite "atan_0")
                               (("2" (assertnil nil)) nil))
                             nil))
                           nil))
                         nil))
                       nil))
                     nil))
                   nil))
                 nil))
               nil))
             nil)
            ("2" (typepred "px")
             (("2" (hide 2) (("2" (grind) nil nil)) nil)) nil))
           nil))
         nil)
        ((< const-decl "bool" reals nil)
         (real_abs_le1 nonempty-type-eq-decl nil asin nil)
         (abs const-decl "{n: nonneg_real | n >= m AND n >= -m}"
              real_defs nil)
         (- const-decl "[numfield -> numfield]" number_fields nil)
         (numfield nonempty-type-eq-decl nil number_fields nil)
         (AND const-decl "[bool, bool -> bool]" booleans nil)
         (nonneg_real nonempty-type-eq-decl nil real_types nil)
         (>= const-decl "bool" reals nil)
         (<= const-decl "bool" reals nil)
         (bool nonempty-type-eq-decl nil booleans 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)
         (minus_nzreal_is_nzreal application-judgement "nzreal"
          real_types nil)
         (posreal_div_posreal_is_posreal application-judgement
          "posreal" real_types nil)
         (real_minus_real_is_real application-judgement "real" reals
          nil)
         (real_div_nzreal_is_real application-judgement "real" reals
          nil)
         (real_lt_is_strict_total_order name-judgement
          "(strict_total_order?[real])" real_props nil)
         (sq const-decl "nonneg_real" sq "reals/")
         (real_le_is_total_order name-judgement "(total_order?[real])"
          real_props nil)
         (sqrt_0 formula-decl nil sqrt "reals/")
         (posreal_div_posreal_is_posreal judgement-tcc nil real_types
          nil)
         (div_div1 formula-decl nil real_props nil)
         (nonzero_real nonempty-type-eq-decl nil reals nil)
         (pi_value formula-decl nil atan nil)
         (nzreal_div_nzreal_is_nzreal application-judgement "nzreal"
          real_types nil)
         (sqrt const-decl "{nnz: nnreal | nnz * nnz = nnx}" sqrt
               "reals/")
         (= const-decl "[T, T -> boolean]" equalities nil)
         (nnreal type-eq-decl nil real_types nil)
         (/ const-decl "[numfield, nznum -> numfield]" number_fields
            nil)
         (nznum nonempty-type-eq-decl nil number_fields nil)
         (atan_inv formula-decl nil atan nil)
         (* const-decl "[numfield, numfield -> numfield]" number_fields
            nil)
         (- const-decl "[numfield, numfield -> numfield]" number_fields
            nil)
         (sqrt_lt formula-decl nil sqrt "reals/")
         (real_gt_is_strict_total_order name-judgement
          "(strict_total_order?[real])" real_props nil)
         (real_ge_is_total_order name-judgement "(total_order?[real])"
          real_props nil)
         (posreal nonempty-type-eq-decl nil real_types nil)
         (> const-decl "bool" reals nil)
         (lt_times_lt_pos1 formula-decl nil real_props nil)
         (nzreal nonempty-type-eq-decl nil reals nil)
         (/= const-decl "boolean" notequal nil)
         (sq_nz_pos judgement-tcc nil sq "reals/")
         (asin const-decl "real_abs_le_pi2" asin nil)
         (atan_0 formula-decl nil atan nil)
         (int_times_even_is_even application-judgement "even_int"
          integers nil)
         (mult_divides2 application-judgement "(divides(m))" divides
          nil)
         (nnreal_div_posreal_is_nnreal application-judgement "nnreal"
          real_types nil)
         (odd_minus_odd_is_even application-judgement "even_int"
          integers nil)
         (posint_times_posint_is_posint application-judgement "posint"
          integers nil)
         (odd_times_odd_is_odd application-judgement "odd_int" integers
          nil)
         (mult_divides1 application-judgement "(divides(n))" divides
          nil)
         (minus_odd_is_odd application-judgement "odd_int" integers
          nil)
         (NOT const-decl "[bool -> bool]" booleans nil)
         (real_times_real_is_real application-judgement "real" reals
          nil))
        nil)
       (asin_pos_restrict-2 nil 3322498693
        ("" (skolem 1 ("px"))
         (("" (typepred "px")
           (("" (expand "abs" -1)
             (("" (expand "<=" -1)
               (("" (split -1)
                 (("1" (expand "asin")
                   (("1" (assert)
                     (("1" (lemma "sq_nz_pos" ("nz" "px"))
                       (("1" (expand "sq")
                         (("1"
                           (lemma "lt_times_lt_pos1"
                            ("px" "px" "y" "1" "nnz" "px" "w" "1"))
                           (("1" (assert)
                             (("1"
                               (lemma
                                "sqrt_lt"
                                ("nny" "0" "nnz" "1-px*px"))
                               (("1"
                                 (rewrite "sqrt_0")
                                 (("1"
                                   (lemma
                                    "atan_inv_value"
                                    ("px" "sqrt(1 - px * px) / px"))
                                   (("1"
                                     (lemma
                                      "div_div1"
                                      ("x"
                                       "1"
                                       "n0y"
                                       "sqrt(1-px*px)"
                                       "n0z"
                                       "px"))
                                     (("1"
                                       (replace -1 -2)
                                       (("1"
                                         (rewrite "pi_value" 1)
                                         (("1"
                                           (expand "atan" 1)
                                           (("1" (assertnil nil))
                                           nil))
                                         nil))
                                       nil))
                                     nil)
                                    ("2"
                                     (lemma
                                      "posreal_div_posreal_is_posreal"
                                      ("px" "sqrt(1-px*px)" "py" "px"))
                                     (("2" (assertnil nil))
                                     nil))
                                   nil))
                                 nil))
                               nil))
                             nil))
                           nil))
                         nil))
                       nil))
                     nil))
                   nil)
                  ("2" (expand "asin")
                   (("2" (replace -1)
                     (("2" (hide -1 -2)
                       (("2" (rewrite "sqrt_0")
                         (("2" (rewrite "atan_0")
                           (("2" (assertnil nil)) nil))
                         nil))
                       nil))
                     nil))
                   nil))
                 nil))
               nil))
             nil))
           nil))
         nil)
        ((sq const-decl "nonneg_real" sq "reals/")
         (sqrt_0 formula-decl nil sqrt "reals/")
         (pi_value formula-decl nil atan nil)
         (atan const-decl "real_abs_lt_pi2" atan nil)
         (sqrt const-decl "{nnz: nnreal | nnz * nnz = nnx}" sqrt
               "reals/")
         (sqrt_lt formula-decl nil sqrt "reals/")
         (sq_nz_pos judgement-tcc nil sq "reals/")
         (atan_0 formula-decl nil atan nil))
        nil))
      (asin_0 0
       (asin_0-1 nil 3262232045
        ("" (expand "asin")
         (("" (rewrite "sqrt_1") (("" (rewrite "atan_0"nil nil))
           nil))
         nil)
        ((sqrt_1 formula-decl nil sqrt "reals/")
         (sqrt_pos application-judgement "posreal" sqrt "reals/")
         (atan_0 formula-decl nil atan nil)
         (asin const-decl "real_abs_le_pi2" asin nil))
        shostak))
      (asin_sqrt_half_TCC1 0
       (asin_sqrt_half_TCC1-1 nil 3263820156
        ("" (expand "abs")
         (("" (typepred "sqrt(1/2)")
           (("" (assert)
             (("" (lemma "sqrt_le" ("nny" "1/2" "nnz" "1"))
               (("" (rewrite "sqrt_1") (("" (assertnil nil)) nil))
               nil))
             nil))
           nil))
         nil)
        ((minus_odd_is_odd application-judgement "odd_int" integers
          nil)
         (real_le_is_total_order name-judgement "(total_order?[real])"
          real_props nil)
         (real_gt_is_strict_total_order name-judgement
          "(strict_total_order?[real])" real_props nil)
         (posreal_times_posreal_is_posreal application-judgement
          "posreal" real_types nil)
         (real_ge_is_total_order name-judgement "(total_order?[real])"
          real_props nil)
         (sqrt_1 formula-decl nil sqrt "reals/")
         (sqrt_le formula-decl nil sqrt "reals/")
         (posrat_div_posrat_is_posrat application-judgement "posrat"
          rationals nil)
         (sqrt_pos application-judgement "posreal" sqrt "reals/")
         (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)
         (>= const-decl "bool" reals nil)
         (nonneg_real nonempty-type-eq-decl nil real_types nil)
         (nnreal type-eq-decl nil real_types 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)
         (sqrt const-decl "{nnz: nnreal | nnz * nnz = nnx}" sqrt
               "reals/")
         (/= const-decl "boolean" notequal nil)
         (nznum nonempty-type-eq-decl nil number_fields nil)
         (/ const-decl "[numfield, nznum -> numfield]" number_fields
            nil)
         (> const-decl "bool" reals nil))
        shostak))
      (asin_sqrt_half 0
       (asin_sqrt_half-2 nil 3322498751
        ("" (expand "asin")
         (("" (typepred "sqrt(1/2)")
           (("" (lemma "sqrt_lt" ("nny" "1/2" "nnz" "1"))
             (("" (rewrite "sqrt_1" -1)
               (("" (assert)
                 (("" (rewrite "sq_rew" 1)
                   (("" (rewrite "div_simp" 1)
                     (("" (rewrite "pi_value") (("" (assertnil nil))
                       nil))
                     nil))
                   nil))
                 nil))
               nil))
             nil))
           nil))
         nil)
        ((> const-decl "bool" reals nil)
         (/ const-decl "[numfield, nznum -> numfield]" number_fields
            nil)
         (nznum nonempty-type-eq-decl nil number_fields nil)
         (/= const-decl "boolean" notequal nil)
         (sqrt const-decl "{nnz: nnreal | nnz * nnz = nnx}" sqrt
               "reals/")
         (* const-decl "[numfield, numfield -> numfield]" number_fields
            nil)
         (numfield nonempty-type-eq-decl nil number_fields nil)
         (= const-decl "[T, T -> boolean]" equalities nil)
         (nnreal type-eq-decl nil real_types nil)
         (nonneg_real nonempty-type-eq-decl nil real_types nil)
         (>= const-decl "bool" reals 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)
         (number nonempty-type-decl nil numbers nil)
         (NOT const-decl "[bool -> bool]" booleans nil)
         (bool nonempty-type-eq-decl nil booleans nil)
         (boolean nonempty-type-decl nil booleans nil)
         (posrat_div_posrat_is_posrat application-judgement "posrat"
          rationals nil)
         (sqrt_1 formula-decl nil sqrt "reals/")
         (minus_nzreal_is_nzreal application-judgement "nzreal"
          real_types nil)
         (minus_odd_is_odd application-judgement "odd_int" integers
          nil)
         (sq_rew formula-decl nil sq "reals/")
         (sq_nz_pos application-judgement "posreal" sq "reals/")
         (sq_sqrt formula-decl nil sqrt "reals/")
         (pi_value formula-decl nil atan nil)
         (real_times_real_is_real application-judgement "real" reals
          nil)
         (real_div_nzreal_is_real application-judgement "real" reals
          nil)
         (div_simp formula-decl nil real_props nil)
         (nonzero_real nonempty-type-eq-decl nil reals nil)
         (real_ge_is_total_order name-judgement "(total_order?[real])"
          real_props nil)
         (real_gt_is_strict_total_order name-judgement
          "(strict_total_order?[real])" real_props nil)
         (real_lt_is_strict_total_order name-judgement
          "(strict_total_order?[real])" real_props nil)
         (nzreal_div_nzreal_is_nzreal application-judgement "nzreal"
          real_types nil)
         (real_minus_real_is_real application-judgement "real" reals
          nil)
         (posreal_div_posreal_is_posreal application-judgement
          "posreal" real_types nil)
         (sqrt_lt formula-decl nil sqrt "reals/")
         (asin const-decl "real_abs_le_pi2" asin nil)
         (posreal_times_posreal_is_posreal application-judgement
          "posreal" real_types nil)
         (sqrt_pos application-judgement "posreal" sqrt "reals/"))
        nil))
      (asin_1 0
       (asin_1-1 nil 3262276037
        ("" (expand "asin") (("" (propax) nil nil)) nil)
        ((asin const-decl "real_abs_le_pi2" asin nil)) shostak))
      (asin_neg_TCC1 0
       (asin_neg_TCC1-1 nil 3262231915 ("" (grind) nil nilnil
        shostak))
      (asin_neg 0
       (asin_neg-1 nil 3262232085
        ("" (skolem 1 ("x"))
         (("" (expand "asin")
           (("" (case "x = -1")
             (("1" (assertnil nil)
              ("2" (case "x = 1")
               (("1" (assertnil nil)
                ("2" (case "-1 < x & x < 1")
                 (("1" (flatten -1)
                   (("1" (assert)
                     (("1"
                       (lemma "atan_neg" ("x" "x / sqrt(1 - -x * -x)"))
                       (("1" (assertnil nil)
                        ("2" (hide 4)
                         (("2" (lemma "asin_TCC3" ("x" "x"))
                           (("2" (assertnil nil)) nil))
                         nil))
                       nil))
                     nil))
                   nil)
                  ("2" (hide 4)
                   (("2" (assert)
                     (("2" (typepred "x") (("2" (grind) nil nil)) nil))
                     nil))
                   nil))
                 nil))
               nil))
             nil))
           nil))
         nil)
        ((minus_real_is_real application-judgement "real" reals nil)
         (real_times_real_is_real application-judgement "real" reals
          nil)
         (asin const-decl "real_abs_le_pi2" asin nil)
         (- const-decl "[numfield, numfield -> numfield]" number_fields
            nil)
         (sqrt const-decl "{nnz: nnreal | nnz * nnz = nnx}" sqrt
               "reals/")
         (* const-decl "[numfield, numfield -> numfield]" number_fields
            nil)
         (nnreal type-eq-decl nil real_types nil)
         (nonneg_real nonempty-type-eq-decl nil real_types nil)
         (>= const-decl "bool" reals nil)
         (/ const-decl "[numfield, nznum -> numfield]" number_fields
            nil)
         (nznum nonempty-type-eq-decl nil number_fields nil)
         (/= const-decl "boolean" notequal nil)
         (atan_neg formula-decl nil atan nil)
         (real_ge_is_total_order name-judgement "(total_order?[real])"
          real_props nil)
         (real_div_nzreal_is_real application-judgement "real" reals
          nil)
         (real_minus_real_is_real application-judgement "real" reals
          nil)
         (< const-decl "bool" reals nil)
         (nzreal_div_nzreal_is_nzreal application-judgement "nzreal"
          real_types nil)
         (minus_nzreal_is_nzreal application-judgement "nzreal"
          real_types nil)
         (posreal_div_posreal_is_posreal application-judgement
          "posreal" real_types nil)
         (real_lt_is_strict_total_order name-judgement
          "(strict_total_order?[real])" real_props nil)
         (minus_odd_is_odd application-judgement "odd_int" integers
          nil)
         (number nonempty-type-decl nil numbers nil)
         (boolean nonempty-type-decl nil booleans nil)
         (= const-decl "[T, T -> boolean]" equalities 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)
         (bool nonempty-type-eq-decl nil booleans 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 nil))
        shostak))
      (asin_minus1 0
       (asin_minus1-1 nil 3262276084
        ("" (expand "asin") (("" (propax) nil nil)) nil)
        ((asin const-decl "real_abs_le_pi2" asin nil)) shostak))
      (asin_minus_sqrt_half_TCC1 0
       (asin_minus_sqrt_half_TCC1-1 nil 3263821369
        ("" (expand "abs")
         (("" (typepred "sqrt(1/2)")
           (("" (assert)
             (("" (lemma "sqrt_le" ("nny" "1/2" "nnz" "1"))
               (("" (rewrite "sqrt_1") (("" (assertnil nil)) nil))
               nil))
             nil))
           nil))
         nil)
        ((minus_nzreal_is_nzreal application-judgement "nzreal"
          real_types nil)
         (minus_odd_is_odd application-judgement "odd_int" integers
          nil)
         (real_le_is_total_order name-judgement "(total_order?[real])"
          real_props nil)
         (real_gt_is_strict_total_order name-judgement
          "(strict_total_order?[real])" real_props nil)
         (posreal_times_posreal_is_posreal application-judgement
          "posreal" real_types nil)
         (real_ge_is_total_order name-judgement "(total_order?[real])"
          real_props nil)
         (sqrt_1 formula-decl nil sqrt "reals/")
         (sqrt_le formula-decl nil sqrt "reals/")
         (posrat_div_posrat_is_posrat application-judgement "posrat"
          rationals nil)
         (sqrt_pos application-judgement "posreal" sqrt "reals/")
         (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)
         (>= const-decl "bool" reals nil)
         (nonneg_real nonempty-type-eq-decl nil real_types nil)
         (nnreal type-eq-decl nil real_types 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)
         (sqrt const-decl "{nnz: nnreal | nnz * nnz = nnx}" sqrt
               "reals/")
         (/= const-decl "boolean" notequal nil)
         (nznum nonempty-type-eq-decl nil number_fields nil)
         (/ const-decl "[numfield, nznum -> numfield]" number_fields
            nil)
         (> const-decl "bool" reals nil))
        shostak))
      (asin_minus_sqrt_half 0
       (asin_minus_sqrt_half-1 nil 3263819795
        ("" (lemma "asin_sqrt_half")
         (("" (rewrite "asin_neg" 1)
           (("1" (assertnil nil)
            ("2" (hide-all-but 1)
             (("2" (expand "abs")
               (("2" (lemma "sqrt_le" ("nny" "1/2" "nnz" "1"))
                 (("2" (rewrite "sqrt_1") (("2" (assertnil nil))
                   nil))
                 nil))
               nil))
             nil))
           nil))
         nil)
        ((posrat_div_posrat_is_posrat application-judgement "posrat"
          rationals nil)
         (sqrt_pos application-judgement "posreal" sqrt "reals/")
         (asin_neg formula-decl nil asin 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)
         (bool nonempty-type-eq-decl nil booleans 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 nil)
         (>= const-decl "bool" reals nil)
         (nonneg_real nonempty-type-eq-decl nil real_types nil)
         (nnreal type-eq-decl nil real_types nil)
         (= const-decl "[T, T -> boolean]" equalities nil)
         (* const-decl "[numfield, numfield -> numfield]" number_fields
            nil)
         (sqrt const-decl "{nnz: nnreal | nnz * nnz = nnx}" sqrt
               "reals/")
         (/= const-decl "boolean" notequal nil)
         (nznum nonempty-type-eq-decl nil number_fields nil)
         (/ const-decl "[numfield, nznum -> numfield]" number_fields
            nil)
         (minus_nzreal_is_nzreal application-judgement "nzreal"
          real_types nil)
         (minus_real_is_real application-judgement "real" reals nil)
         (posreal_div_posreal_is_posreal application-judgement
          "posreal" real_types nil)
         (nzreal_div_nzreal_is_nzreal application-judgement "nzreal"
          real_types nil)
         (asin_sqrt_half formula-decl nil asin nil))
        shostak))
      (asin_strict_increasing 0
       (asin_strict_increasing-3 nil 3322498826
        ("" (lemma "atan_strict_increasing")
         (("" (expand "strict_increasing?")
           (("" (skolem 1 ("x" "y"))
             (("" (flatten)
               (("" (expand "asin")
                 (("" (case "abs(x) <= 1")
                   (("1" (case "abs(y) <= 1")
                     (("1"
                       (case "FORALL (z:real): abs(z) < 1 => 0 < sqrt(1-z*z)")
                       (("1" (expand "<=" (-2 -3))
                         (("1" (split -3)
                           (("1" (inst-cp -2 "x")
                             (("1" (assert)
                               (("1"
                                 (case "y = -1")
                                 (("1"
                                   (hide 1)
                                   (("1"
                                     (lemma "trichotomy" ("x" "x"))
                                     (("1"
                                       (split -1)
                                       (("1" (assertnil nil)
                                        ("2" (assertnil nil)
                                        ("3"
                                         (expand "abs" -3)
                                         (("3" (assertnil nil))
                                         nil))
                                       nil))
                                     nil))
                                   nil)
                                  ("2"
                                   (case "y < 1")
                                   (("1"
                                     (assert)
                                     (("1"
                                       (case "x= -1")
                                       (("1" (assertnil nil)
                                        ("2"
                                         (expand "abs" -3)
                                         (("2"
                                           (assert)
                                           (("2"
                                             (inst -3 "y")
                                             (("2"
                                               (split -5)
                                               (("1"
                                                 (assert)
                                                 (("1"
                                                   (inst
                                                    -
                                                    "x / sqrt(1 - x * x)"
                                                    "y / sqrt(1 - y * y)")
                                                   (("1"
                                                     (split -6)
                                                     (("1"
                                                       (propax)
                                                       nil
                                                       nil)
                                                      ("2"
                                                       (hide 4)
                                                       (("2"
                                                         (lemma
                                                          "div_mult_pos_lt1"
                                                          ("z"
                                                           "x"
                                                           "py"
                                                           "sqrt(1-x*x)"
                                                           "x"
                                                           "y / sqrt(1 - y * y)"))
                                                         (("2"
                                                           (replace
                                                            -1
                                                            1)
                                                           (("2"
                                                             (lemma
                                                              "div_mult_pos_lt2"
                                                              ("x"
                                                               "x"
                                                               "z"
                                                               "y*sqrt(1-x*x)"
                                                               "py"
                                                               "sqrt(1-y*y)"))
                                                             (("1"
                                                               (replace
                                                                -1
                                                                1)
                                                               (("1"
                                                                 (hide
                                                                  -1
                                                                  -2)
                                                                 (("1"
                                                                   (lemma
                                                                    "trichotomy"
                                                                    ("x"
                                                                     "x"))
                                                                   (("1"
                                                                     (split
                                                                      -1)
                                                                     (("1"
                                                                       (lemma
                                                                        "sq_lt"
                                                                        ("nna"
                                                                         "x * sqrt(1 - y * y)"
                                                                         "nnb"
                                                                         "y * sqrt(1 - x * x)"))
                                                                       (("1"
                                                                         (replace
                                                                          -1
                                                                          1
                                                                          rl)
                                                                         (("1"
                                                                           (rewrite
                                                                            "sq_times"
                                                                            1)
                                                                           (("1"
                                                                             (rewrite
                                                                              "sq_times"
                                                                              1)
                                                                             (("1"
                                                                               (expand
                                                                                "sq"
                                                                                1)
                                                                               (("1"
                                                                                 (lemma
                                                                                  "sq_lt"
                                                                                  ("nna"
                                                                                   "x"
                                                                                   "nnb"
                                                                                   "y"))
                                                                                 (("1"
                                                                                   (expand
                                                                                    "sq"
                                                                                    -1)
                                                                                   (("1"
                                                                                     (assert)
                                                                                     nil
                                                                                     nil))
                                                                                   nil)
                                                                                  ("2"
                                                                                   (assert)
                                                                                   nil
                                                                                   nil)
                                                                                  ("3"
                                                                                   (assert)
                                                                                   nil
                                                                                   nil))
                                                                                 nil))
                                                                               nil))
                                                                             nil))
                                                                           nil))
                                                                         nil)
                                                                        ("2"
                                                                         (lemma
                                                                          "posreal_times_posreal_is_posreal"
                                                                          ("px"
                                                                           "y"
                                                                           "py"
                                                                           "sqrt(1-x*x)"))
                                                                         (("1"
                                                                           (assert)
                                                                           nil
                                                                           nil)
                                                                          ("2"
                                                                           (assert)
                                                                           nil
                                                                           nil))
                                                                         nil)
                                                                        ("3"
                                                                         (lemma
                                                                          "posreal_times_posreal_is_posreal"
                                                                          ("px"
                                                                           "x"
                                                                           "py"
                                                                           "sqrt(1-y*y)"))
                                                                         (("1"
                                                                           (assert)
                                                                           nil
                                                                           nil)
                                                                          ("2"
                                                                           (assert)
                                                                           nil
                                                                           nil))
                                                                         nil))
                                                                       nil)
                                                                      ("2"
                                                                       (replace
                                                                        -1)
                                                                       (("2"
                                                                         (rewrite
                                                                          "sqrt_1"
                                                                          1)
                                                                         (("2"
                                                                           (assert)
                                                                           nil
                                                                           nil))
                                                                         nil))
                                                                       nil)
                                                                      ("3"
                                                                       (case
                                                                        "y < 0")
                                                                       (("1"
                                                                         (lemma
                                                                          "both_sides_times_neg_lt1"
                                                                          ("nz"
                                                                           "-1"
                                                                           "y"
                                                                           "x * sqrt(1 - y * y)"
--> --------------------

--> maximum size reached

--> --------------------

¤ Dauer der Verarbeitung: 0.70 Sekunden  (vorverarbeitet)  ¤





Download des
Quellennavigators
Download des
sprechenden Kalenders

in der Quellcodebibliothek suchen




Haftungshinweis

Die Informationen auf dieser Webseite wurden nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit, noch Qualität der bereit gestellten Informationen zugesichert.


Bemerkung:

Die farbliche Syntaxdarstellung ist noch experimentell.


Bot Zugriff