| Quellcodebibliothek Statistik Leitseite products/Sources/formale Sprachen/PVS/reals/ (Beweissystem der NASA Version 6.0.9©) Datei vom 28.9.2014 mit Größe 140 kB |
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Quelle harmonic_polynomials.prfSprache: Lisp |
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(harmonic_polynomials (harmonic_poly_real_TCC1 0 (harmonic_poly_real_TCC1-1 nil 3261618989 ("" (skosimp*) (("" (inst + "1") (("" (assert) nil nil)) nil)) nil) ((number nonempty-type-decl nil numbers nil) (boolean nonempty-type-decl nil booleans nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (number_field nonempty-type-from-decl nil number_fields nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (real nonempty-type-from-decl nil reals nil) (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) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil)) shostak)) (harmonic_poly_real_TCC2 0 (harmonic_poly_real_TCC2-1 nil 3261619116 ("" (skosimp*) (("" (lemma "even_div2") (("" (inst?) 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"harmonic_polynomial_imag_rec" 1) (("2" (name-replace "U" "harmonic_poly_real(i, x, y)") (("2" (name-replace "V" "harmonic_poly_imag(i, x, y)") (("2" (expand "sq") (("2" (case "x=0") (("1" (replace -1) (("1" (case "y=0") (("1" (replace -1) (("1" (expand "^" 1) (("1" (expand "expt") (("1" (assert) nil nil)) nil)) nil)) nil) ("2" (lemma "sq_nz_pos" ("nz" "y")) (("1" (expand "sq") (("1" (lemma "expt_plus" ("n0x" "y*y" "i" "1" "j" "i")) (("1" (rewrite "expt_x1" -1) (("1" (replace -1 2) (("1" (assert) nil nil)) nil)) nil) ("2" (assert) nil nil)) nil)) nil) ("2" (assert) nil nil)) nil)) nil)) nil) ("2" (lemma "sq_pos" ("a" "y")) (("2" (lemma "sq_nz_pos" ("nz" "x")) (("1" (expand "sq") (("1" (lemma "expt_plus" ("n0x" "x*x+y*y" "i" "1" "j" "i")) (("1" (rewrite "expt_x1" -1) (("1" (replace -1 2) (("1" (replace -4 2 rl) (("1" (assert) nil nil)) nil)) nil)) nil) ("2" (assert) nil nil)) nil)) nil) ("2" (assert) nil nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil)) nil) ((nnreal_plus_nnreal_is_nnreal application-judgement "nnreal" real_types nil) (number nonempty-type-decl nil numbers nil) (boolean nonempty-type-decl nil booleans nil) (number_field_pred const-decl "[number -> boolean]" number_fields nil) (number_field nonempty-type-from-decl nil number_fields nil) (real_pred const-decl "[number_field -> boolean]" reals nil) (real nonempty-type-from-decl nil reals nil) (rational_pred const-decl "[real -> boolean]" rationals nil) (rational nonempty-type-from-decl nil rationals nil) (integer_pred const-decl "[rational -> boolean]" integers nil) (int nonempty-type-eq-decl nil integers nil) (bool nonempty-type-eq-decl nil booleans nil) (>= const-decl "bool" reals nil) (nat nonempty-type-eq-decl nil naturalnumbers nil) (pred type-eq-decl nil defined_types nil) (IMPLIES const-decl "[bool, bool -> bool]" booleans nil) (> const-decl "bool" reals 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) (nonneg_real nonempty-type-eq-decl nil real_types nil) (sq const-decl "nonneg_real" sq nil) (nonneg_int nonempty-type-eq-decl nil integers nil) (posnat nonempty-type-eq-decl nil integers nil) (harmonic_poly_real const-decl "real" harmonic_polynomials nil) (harmonic_poly_imag const-decl "real" harmonic_polynomials nil) (OR const-decl "[bool, bool -> bool]" booleans nil) (/= const-decl "boolean" notequal nil) (^ const-decl "real" exponentiation nil) (nat_induction formula-decl nil naturalnumbers nil) (real_gt_is_strict_total_order name-judgement "(strict_total_order?[real])" real_props nil) (nnreal_exp application-judgement "nnreal" exponentiation nil) (nnint_plus_posint_is_posint application-judgement "posint" integers nil) (AND const-decl "[bool, bool -> bool]" booleans nil) (real_ge_is_total_order name-judgement "(total_order?[real])" real_props nil) (- const-decl "[numfield, numfield -> numfield]" number_fields nil) (harmonic_polynomial_real_rec formula-decl nil harmonic_polynomials nil) (posint_plus_nnint_is_posint application-judgement "posint" integers nil) (int_minus_int_is_int application-judgement "int" integers nil) (int_plus_int_is_int application-judgement "int" integers nil) (odd_minus_odd_is_even application-judgement "even_int" integers nil) (odd_plus_odd_is_even application-judgement "even_int" integers nil) (even_minus_odd_is_odd application-judgement "odd_int" integers nil) (real_times_real_is_real application-judgement "real" reals nil) (real_minus_real_is_real application-judgement "real" reals nil) (sq_pos formula-decl nil sq nil) (sq_nz_pos judgement-tcc nil sq nil) (nzreal nonempty-type-eq-decl nil reals nil) (expt_plus formula-decl nil exponentiation nil) (* const-decl "[numfield, 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) (expt def-decl "real" exponentiation nil) (nat_exp application-judgement "nat" exponentiation nil) (nnint_plus_nnint_is_nnint application-judgement "nonneg_int" integers nil) (even_plus_even_is_even application-judgement "even_int" integers nil) (mult_divides2 application-judgement "(divides(m))" divides nil) (nat_expt application-judgement "nat" exponentiation nil) (real_plus_real_is_real application-judgement "real" reals nil) (harmonic_polynomial_imag_rec formula-decl nil harmonic_polynomials nil) (harmonic_polynomial_real_n1 formula-decl nil harmonic_polynomials nil) (expt_x1 formula-decl nil exponentiation nil) (harmonic_polynomial_imag_n1 formula-decl nil harmonic_polynomials nil)) shostak)))
¤ Dauer der Verarbeitung: 0.95 Sekunden (vorverarbeitet am 2026-05-05) ¤*© Formatika GbR, Deutschland |
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2026-05-26