| products/sources/formale sprachen/PVS/trig_fnd/ |
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Quellcode-Bibliothek© Kompilation durch diese Firma[Weder Korrektheit noch Funktionsfähigkeit der Software werden zugesichert.]Datei: players_set.pvs Sprache: LispOriginal von: PVS© |
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(trig_approx
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(skosimp) (("" (expand "sin_term") (("" (case-replace "a!1=0") (("1" (expand "^") (("1" (name-replace "S" "expt((-1), n!1)") (("1" (expand "expt") (("1" (assert) nil nil)) nil)) nil)) nil) ("2" (lemma "expt_plus" ("i" "1" "j" "2*n!1")) (("2" (inst-cp - "a!1") (("1" (inst - "-a!1") (("1" (replace -1) (("1" (replace -2) (("1" (rewrite "expt_x1") (("1" (rewrite "expt_x1") (("1" (lemma "expt_times" ("i" "2" "j" "n!1")) (("1" (inst-cp - "a!1") (("1" (inst - "-a!1") (("1" (case-replace "(-a!1) ^ 2 = a!1 ^ 2") (("1" (assert) nil nil) ("2" (hide-all-but (1 2)) (("2" (grind) nil nil)) nil)) nil) ("2" (assert) nil nil)) nil) ("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil) ("2" (assert) nil nil)) nil) ("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil) ((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 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(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) (sin_term const-decl "real" trig_approx nil) (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) (nzreal nonempty-type-eq-decl nil reals nil) (expt_plus formula-decl nil exponentiation nil) (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) (posreal_times_posreal_is_posreal judgement-tcc nil real_types nil) (expt def-decl "real" exponentiation nil) (AND const-decl "[bool, bool -> bool]" booleans nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (both_sides_times_pos_lt1 formula-decl nil real_props nil) (expt_nonzero formula-decl nil exponentiation nil) (S skolem-const-decl "int" trig_approx nil) (trichotomy formula-decl nil real_axioms nil) (negreal nonempty-type-eq-decl nil real_types nil) (< const-decl "bool" reals nil) (nonpos_real nonempty-type-eq-decl nil real_types nil) (<= const-decl "bool" reals nil) (both_sides_times_neg_lt1 formula-decl nil real_props nil) (expt_x1 formula-decl nil exponentiation nil) (zero_times1 formula-decl nil real_props nil) (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (- const-decl "[numfield -> numfield]" number_fields nil) (^ const-decl "real" exponentiation nil) (/= const-decl "boolean" notequal nil) (OR const-decl "[bool, bool -> bool]" booleans nil) (* const-decl "[numfield, numfield -> numfield]" number_fields nil) (+ const-decl "[numfield, numfield -> numfield]" number_fields nil) (numfield nonempty-type-eq-decl nil number_fields nil) (factorial def-decl "posnat" factorial "ints/") (posnat nonempty-type-eq-decl nil integers nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (posreal nonempty-type-eq-decl nil real_types nil) (> const-decl "bool" reals nil) (nonneg_real nonempty-type-eq-decl nil real_types 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) (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") (("" (lemma "expt_nonzero" ("n0x" "-1" "i" "n!1")) (("" (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") (("2" (lemma "expt_nonzero" ("n0x" "a!1" "i" "1+2*n!1")) (("1" (assert) nil nil) ("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((expt_nonzero formula-decl nil exponentiation nil) (nzreal nonempty-type-eq-decl nil reals nil) (zero_times3 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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) ((nat nonempty-type-eq-decl nil naturalnumbers nil) (>= const-decl "bool" reals nil) (bool nonempty-type-eq-decl nil booleans nil) (int nonempty-type-eq-decl nil integers nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (rational nonempty-type-from-decl nil rationals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (real nonempty-type-from-decl nil reals nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (number_field nonempty-type-from-decl nil number_fields nil) 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