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Quellcode-Bibliothek
© Kompilation durch diese Firma
[Weder Korrektheit noch Funktionsfähigkeit der Software werden zugesichert.]
Datei:
direct_sos.pvs
Sprache: Lisp
Untersuchung PVS©
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(trig_approx
(sin_term_TCC1 0
(sin_term_TCC1-1 nil 3320763259
("" (skosimp) (("" (assert) nil nil)) 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)
(even_plus_odd_is_odd application-judgement "odd_int" integers nil)
(nnint_plus_posint_is_posint application-judgement "posint"
integers nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil))
shostak))
(sin_term_next 0
(sin_term_next-1 nil 3320769270
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(("" (expand "sin_term")
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(("" (expand "expt" 1 2)
(("" (expand "expt" 1 2)
(("" (expand "expt" 1 1)
((""
(name-replace "X"
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(("" (rewrite "cross_mult")
(("" (expand "factorial" 1 1)
(("" (expand "factorial" 1 1)
(("" (expand "factorial" 1 5)
(("" (typepred "factorial(1+2*n!1)")
((""
(name-replace "F" "factorial(1 + 2 * n!1)")
(("" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((nnint_times_nnint_is_nnint application-judgement "nonneg_int"
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(even_times_int_is_even application-judgement "even_int" integers
nil)
(mult_divides1 application-judgement "(divides(n))" divides nil)
(mult_divides2 application-judgement "(divides(m))" divides nil)
(int_exp application-judgement "int" exponentiation nil)
(nzreal_exp application-judgement "nzreal" exponentiation nil)
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(/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
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nil)
(nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(- const-decl "[numfield -> numfield]" number_fields nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
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(rational_pred const-decl "[real -> boolean]" rationals nil)
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(real_pred const-decl "[number_field -> boolean]" reals nil)
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(* const-decl "[numfield, numfield -> numfield]" number_fields nil)
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(number_field_pred const-decl "[number -> boolean]" number_fields
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(posint_plus_nnint_is_posint application-judgement "posint"
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(minus_odd_is_odd application-judgement "odd_int" integers nil)
(^ const-decl "real" exponentiation nil)
(nzreal_expt application-judgement "nzreal" exponentiation nil)
(int_expt application-judgement "int" exponentiation nil))
shostak))
(sin_term_neg 0
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(("" (expand "sin_term")
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nil)
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(("2" (inst-cp - "a!1")
(("1" (inst - "-a!1")
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((sin_term const-decl "real" trig_approx nil)
(* const-decl "[numfield, numfield -> numfield]" number_fields nil)
(expt_plus formula-decl nil exponentiation nil)
(minus_real_is_real application-judgement "real" reals nil)
(OR const-decl "[bool, bool -> bool]" booleans nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(expt_times formula-decl nil exponentiation nil)
(expt_x1 formula-decl nil exponentiation nil)
(nzreal nonempty-type-eq-decl nil reals nil)
(a!1 skolem-const-decl "real" trig_approx nil)
(/= const-decl "boolean" notequal nil)
(^ const-decl "real" exponentiation nil)
(int_times_even_is_even application-judgement "even_int" integers
nil)
(minus_even_is_even application-judgement "even_int" integers nil)
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integers nil)
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(minus_rat_is_rat application-judgement "rat" rationals nil)
(nnrat_div_posrat_is_nnrat application-judgement "nonneg_rat"
rationals nil)
(nat_expt application-judgement "nat" exponentiation nil)
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(minus_odd_is_odd application-judgement "odd_int" integers nil)
(int_expt application-judgement "int" exponentiation nil)
(nzreal_expt application-judgement "nzreal" exponentiation 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)
(bool nonempty-type-eq-decl nil booleans nil)
(>= const-decl "bool" reals nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(expt def-decl "real" exponentiation nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(- const-decl "[numfield -> numfield]" number_fields nil)
(nnint_times_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(even_times_int_is_even application-judgement "even_int" integers
nil)
(mult_divides1 application-judgement "(divides(n))" divides nil)
(mult_divides2 application-judgement "(divides(m))" divides nil)
(int_exp application-judgement "int" exponentiation nil)
(nzreal_exp application-judgement "nzreal" exponentiation nil)
(real_times_real_is_real application-judgement "real" reals nil)
(real_div_nzreal_is_real application-judgement "real" 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)
(= const-decl "[T, T -> boolean]" equalities nil)
(boolean nonempty-type-decl nil booleans nil)
(number nonempty-type-decl nil numbers nil))
shostak))
(sin_terms_alternate 0
(sin_terms_alternate-1 nil 3320772448
("" (skosimp)
(("" (expand "sin_term")
(("" (rewrite "div_mult_pos_gt1" 2)
(("" (rewrite "div_mult_pos_lt1" 2)
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(("" (rewrite "expt_plus" 2)
(("" (rewrite "expt_x1")
(("" (name-replace "S" "(-1)^n!1")
((""
(lemma "both_sides_times_neg_lt1"
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(("" (replace -1 2)
(("" (hide -1)
(("" (expand ">")
(("" (lemma "trichotomy" ("x" "S"))
(("" (split -1)
(("1"
(lemma
"both_sides_times_pos_lt1"
("pz" "S" "x" "0"))
(("1"
(rewrite "zero_times1" -1)
(("1"
(inst-cp - "a!1 ^ (1 + 2 * n!1)")
(("1"
(assert)
(("1"
(replace -2 2)
(("1"
(inst
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"a!1 ^ (3 + 2 * n!1)")
(("1"
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(("1"
(hide -1)
(("1"
(expand "^")
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(expand "expt" 2 1)
(("1"
(expand
"expt"
2
1)
(("1"
(case-replace
"0 < expt(a!1, (1 + 2 * n!1))")
(("1"
(assert)
(("1"
(lemma
"posreal_times_posreal_is_posreal"
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"a!1*a!1"
"py"
"expt(a!1, 1 + 2 * n!1)"))
(("1"
(assert)
nil
nil)
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(hide
-1
3)
(("2"
(lemma
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("x"
"a!1"))
(("2"
(split
-1)
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("pz"
"a!1"
"x"
"0"
"y"
"a!1"))
(("1"
(assert)
nil
nil)
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(assert)
nil
nil))
nil)
("2"
(assert)
nil
nil)
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(lemma
"both_sides_times_neg_lt1"
("nz"
"a!1"
"x"
"0"
"y"
"a!1"))
(("1"
(assert)
nil
nil)
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nil
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(assert)
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(case
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(lemma
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("pz"
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"x"
"0"
"y"
"expt(a!1, 1 + 2 * n!1)"))
(("1"
(assert)
nil
nil))
nil)
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-1
2)
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(lemma
"trichotomy"
("x"
"a!1"))
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("pz"
"a!1"
"x"
"0"
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"a!1"))
(("1"
(assert)
nil
nil)
("2"
(assert)
nil
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nil)
("2"
(assert)
nil
nil)
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(lemma
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("nz"
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"x"
"0"
"y"
"a!1"))
(("1"
(assert)
nil
nil)
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(assert)
nil
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nil))
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nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (assert) nil nil))
nil)
("2"
(expand "S" -1)
(("2"
(lemma
"expt_nonzero"
("n0x" "-1" "i" "n!1"))
(("2" (assert) nil nil))
nil))
nil)
("3"
(lemma
"both_sides_times_neg_lt1"
("nz" "S" "x" "0"))
(("1"
(inst-cp - "a!1 ^ (1 + 2 * n!1)")
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(case "0)
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(("1"
(expand "expt" 2 1)
(("1"
(lemma
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("pz"
"a!1*a!1"
"x"
"expt(a!1, 1 + 2 * n!1)"
"y"
"0"))
(("1"
(assert)
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(replace
-1
2
rl)
(("1"
(rewrite
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(case-replace
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(assert)
nil
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nil))
nil)
("2"
(assert)
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nil))
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nil))
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("2"
(hide 3)
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(lemma
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(split -1)
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(lemma
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("pz"
"a!1"
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"a!1"))
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(assert)
nil
nil)
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(assert)
nil
nil))
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(assert)
nil
nil)
("3"
(lemma
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("nz"
"a!1"
"x"
"0"
"y"
"a!1"))
(("1"
(assert)
nil
nil)
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(assert)
nil
nil))
nil))
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nil))
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nil))
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nil))
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nil))
nil))
nil)
("2" (assert) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((nnint_times_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(even_times_int_is_even application-judgement "even_int" integers
nil)
(mult_divides1 application-judgement "(divides(n))" divides nil)
(mult_divides2 application-judgement "(divides(m))" divides nil)
(int_exp application-judgement "int" exponentiation nil)
(nzreal_exp application-judgement "nzreal" exponentiation nil)
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(div_mult_pos_lt1 formula-decl nil real_props nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
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(int_minus_int_is_int application-judgement "int" integers nil)
(nzint_times_nzint_is_nzint application-judgement "nzint" integers
nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
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(AND const-decl "[bool, bool -> bool]" booleans nil)
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real_props nil)
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(< const-decl "bool" reals nil)
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(<= const-decl "bool" reals nil)
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(real_gt_is_strict_total_order name-judgement
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(- const-decl "[numfield -> numfield]" number_fields nil)
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(/= const-decl "boolean" notequal nil)
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(* const-decl "[numfield, numfield -> numfield]" number_fields nil)
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(factorial def-decl "posnat" factorial "ints/")
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(int nonempty-type-eq-decl nil integers nil)
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(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)
(div_mult_pos_gt1 formula-decl nil extra_real_props nil)
(minus_odd_is_odd application-judgement "odd_int" integers nil)
(odd_plus_even_is_odd application-judgement "odd_int" integers nil)
(posint_plus_nnint_is_posint application-judgement "posint"
integers nil))
shostak))
(sin_term_nonzero 0
(sin_term_nonzero-1 nil 3320769218
("" (expand "sin_term")
(("" (skosimp*)
(("" (rewrite "div_cancel3")
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(("" (split)
(("1" (flatten)
(("1" (replace -1)
(("1" (expand "^" 1 2)
(("1" (expand "expt") (("1" (assert) nil nil)) nil))
nil))
nil))
nil)
("2" (flatten)
(("2" (rewrite "zero_times1")
(("2" (rewrite "zero_times3")
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(lemma "expt_nonzero" ("n0x" "a!1" "i" "1+2*n!1"))
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nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
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(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(boolean nonempty-type-decl nil booleans nil)
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(posint_plus_nnint_is_posint application-judgement "posint"
integers nil)
(sin_term const-decl "real" trig_approx nil)
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(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))
shostak))
(sin_term_zero 0
(sin_term_zero-1 nil 3320924247
("" (skosimp)
(("" (lemma "sin_term_nonzero" ("a" "a!1" "n" "n!1"))
(("" (assert)
(("" (split)
(("1" (flatten) (("1" (assert) nil nil)) nil)
("2" (flatten) (("2" (assert) nil nil)) nil))
nil))
nil))
nil))
nil)
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(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(boolean nonempty-type-decl nil booleans nil)
(number nonempty-type-decl nil numbers nil)
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shostak))
(sin_term_gt0 0
(sin_term_gt0-1 nil 3320931387
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(("" (skosimp)
(("" (case-replace "a!1=0")
(("1" (expand "^" 1 2)
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(("2" (rewrite "expt_x1")
(("2" (rewrite "expt_times")
(("2" (lemma "expt_pos" ("px" "a!1^2" "i" "n!1"))
(("1"
(lemma "posreal_div_posreal_is_posreal"
("px" "(a!1 ^ 2) ^ n!1" "py"
"factorial(1 + 2 * n!1)"))
(("1"
(lemma "both_sides_times_pos_gt1"
("pz" "(a!1 ^ 2) ^ n!1 / factorial(1 + 2 * n!1)"
"x" "(-1)^n!1*a!1" "y" "0"))
(("1" (rewrite "zero_times1")
(("1" (replace -1 2)
(("1" (hide-all-but (1 2))
(("1" (case "forall (n:nat): (-1)^(2*n) =1")
(("1" (lemma "trichotomy" ("x" "a!1"))
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(split -1)
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(assert)
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(split 2)
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(flatten)
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(lemma "even_or_odd")
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(inst - "n!1")
(("1"
(assert)
(("1"
(hide 1 2)
(("1"
(expand "odd?")
(("1"
(skosimp)
(("1"
(replace -1)
(("1"
(rewrite
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(rewrite
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(inst
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"j!1")
(("1"
(assert)
nil
nil)
("2"
(assert)
nil
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2"
(flatten)
(("2"
(expand "even?")
(("2"
(skosimp)
(("2"
(inst - "j!1")
(("1" (assert) nil nil)
("2" (assert) nil nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (propax) nil nil)
("3"
(assert)
(("3"
(split 2)
(("1"
(flatten)
(("1"
(lemma
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("x" "n!1"))
(("1"
(assert)
(("1"
(hide 1)
(("1"
(expand "even?")
(("1"
(skosimp)
(("1"
(inst - "j!1")
(("1"
(assert)
nil
nil)
("2"
(assert)
nil
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2"
(flatten)
(("2"
(expand "odd?")
(("2"
(skosimp)
(("2"
(replace -1)
(("2"
(rewrite "expt_plus")
(("2"
(rewrite "expt_x1")
(("2"
(inst - "j!1")
(("1"
(assert)
nil
nil)
("2"
(assert)
nil
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (hide-all-but 1)
(("2"
(skosimp)
(("2"
(rewrite "expt_times")
(("2"
(expand "^" 1 1)
(("2"
(expand "expt")
(("2"
(expand "expt")
(("2"
(expand "expt")
(("2"
(rewrite "expt_1i")
nil
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (assert) nil nil))
nil)
("2" (assert) nil nil))
nil)
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(("2" (lemma "pos_times_lt" ("x" "a!1" "y" "a!1"))
(("2" (grind) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((expt_plus formula-decl nil exponentiation 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)
(numfield nonempty-type-eq-decl nil number_fields nil)
(* const-decl "[numfield, numfield -> numfield]" number_fields nil)
(bool nonempty-type-eq-decl nil booleans nil)
(>= const-decl "bool" reals nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(/= const-decl "boolean" notequal nil)
(nzreal nonempty-type-eq-decl nil reals nil)
(expt_times formula-decl nil exponentiation nil)
(pos_times_lt formula-decl nil real_props nil)
(posreal_div_posreal_is_posreal judgement-tcc nil real_types nil)
(nonneg_int nonempty-type-eq-decl nil integers nil)
(posnat nonempty-type-eq-decl nil integers nil)
(factorial def-decl "posnat" factorial "ints/")
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(zero_times1 formula-decl nil real_props nil)
(expt_1i formula-decl nil exponentiation nil)
(trichotomy formula-decl nil real_axioms nil)
(j!1 skolem-const-decl "int" trig_approx nil)
(j!1 skolem-const-decl "int" trig_approx nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(j!1 skolem-const-decl "int" trig_approx nil)
(even? const-decl "bool" integers nil)
(rat_exp application-judgement "rat" exponentiation nil)
(nzrat_times_nzrat_is_nzrat application-judgement "nzrat" rationals
nil)
(j!1 skolem-const-decl "int" trig_approx nil)
(odd? const-decl "bool" integers nil)
(even_or_odd formula-decl nil naturalnumbers nil)
(- const-decl "[numfield -> numfield]" number_fields nil)
(/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
(nznum nonempty-type-eq-decl nil number_fields nil)
(both_sides_times_pos_gt1 formula-decl nil real_props nil)
(minus_odd_is_odd application-judgement "odd_int" integers nil)
(real_div_nzreal_is_real application-judgement "real" reals nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(OR const-decl "[bool, bool -> bool]" booleans nil)
(posreal nonempty-type-eq-decl nil real_types nil)
(> const-decl "bool" reals nil)
(nonneg_real nonempty-type-eq-decl nil real_types nil)
(expt_pos formula-decl nil exponentiation nil)
(expt_x1 formula-decl nil exponentiation nil)
(nat_expt application-judgement "nat" exponentiation nil)
(^ const-decl "real" exponentiation nil)
(odd_plus_even_is_odd application-judgement "odd_int" integers nil)
(posint_plus_nnint_is_posint application-judgement "posint"
integers nil)
(nnrat_div_posrat_is_nnrat application-judgement "nonneg_rat"
rationals nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(expt def-decl "real" exponentiation 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)
(sin_term const-decl "real" trig_approx nil)
(real_times_real_is_real application-judgement "real" reals nil)
(nzreal_exp application-judgement "nzreal" exponentiation nil)
(int_exp application-judgement "int" exponentiation 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))
shostak))
(sin_term_lt0 0
(sin_term_lt0-1 nil 3320932130
("" (skosimp)
(("" (lemma "trichotomy" ("x" "a!1"))
(("" (split -1)
(("1" (assert)
(("1" (lemma "sin_term_gt0" ("a" "a!1" "n" "n!1"))
(("1" (assert)
(("1" (rewrite "even_or_odd")
(("1" (split 1)
(("1" (flatten) (("1" (assert) nil nil)) nil)
("2" (flatten)
(("2" (assert)
(("2"
(lemma "sin_term_nonzero"
("a" "a!1" "n" "n!1"))
(("2" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (replace -1)
(("2" (assert)
(("2" (lemma "sin_term_zero" ("a" "0" "n" "n!1"))
(("2" (assert) nil nil)) nil))
nil))
nil)
("3" (assert)
(("3" (lemma "sin_term_gt0" ("a" "a!1" "n" "n!1"))
(("3" (assert)
(("3" (rewrite "even_or_odd")
(("3" (split 1)
(("1" (flatten) (("1" (assert) nil nil)) nil)
("2" (flatten)
(("2" (assert)
(("2"
(lemma "sin_term_nonzero"
("a" "a!1" "n" "n!1"))
(("2" (assert) nil nil)) nil))
nil))
nil))
nil))
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)
(trichotomy formula-decl nil real_axioms nil)
(sin_term_zero formula-decl nil trig_approx 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)
(sin_term_nonzero formula-decl nil trig_approx nil)
(even_or_odd formula-decl nil naturalnumbers nil)
(sin_term_gt0 formula-decl nil trig_approx 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)
(bool nonempty-type-eq-decl nil booleans nil)
(>= const-decl "bool" reals nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil))
shostak))
(sin_tends_to_0 0
(sin_tends_to_0-1 nil 3320988819
("" (skosimp)
(("" (case-replace "a!1=0")
(("1" (hide -1)
(("1" (expand "tends_to_0?")
(("1" (skosimp)
(("1" (inst + "0")
(("1" (skosimp)
(("1" (expand "sin_term")
(("1" (expand "^" 1 2)
(("1" (assert)
(("1" (expand "expt" 1)
(("1" (rewrite "abs_div")
(("1" (expand "abs") (("1" (assert) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (lemma "exp_tends_to_0" ("n0a" "a!1"))
(("1" (expand "exp_term")
(("1" (expand "sin_term")
(("1" (expand "tends_to_0?")
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(rewrite "abs_div")
(("1"
(rewrite "abs_mult")
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(case-replace
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(case "even?(i!1)")
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(skosimp)
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(replace -2)
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(rewrite
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(expand "abs")
(("1"
(propax)
nil
nil))
nil))
nil))
nil))
nil))
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nil)
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(rewrite "even_or_odd")
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(expand "odd?")
(("2"
(skosimp)
(("2"
(replace -1)
(("2"
(rewrite
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(rewrite
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(replace -2)
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(rewrite
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(expand
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nil))
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("2" (assert) nil nil))
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(number_field_pred const-decl "[number -> boolean]" number_fields
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(rational_pred const-decl "[real -> boolean]" rationals nil)
(rational nonempty-type-from-decl nil rationals nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
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(>= const-decl "bool" reals nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(even_times_int_is_even application-judgement "even_int" integers
nil)
(mult_divides1 application-judgement "(divides(n))" divides nil)
(mult_divides2 application-judgement "(divides(m))" divides nil)
(rat_exp application-judgement "rat" exponentiation nil)
(nzreal_exp application-judgement "nzreal" exponentiation nil)
(nnrat_exp application-judgement "nnrat" exponentiation nil)
(rat_times_rat_is_rat application-judgement "rat" rationals nil)
(rat_div_nzrat_is_rat application-judgement "rat" rationals nil)
(sin_term const-decl "real" trig_approx nil)
(odd_plus_even_is_odd application-judgement "odd_int" integers nil)
--> --------------------
--> maximum size reached
--> --------------------
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Lebenszyklus
Die hierunter aufgelisteten Ziele sind für diese Firma wichtig
Ziele
Entwicklung einer Software für die statische Quellcodeanalyse
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