Ziele Untersuchung
mit Columbo Integrität von
Datenbanken Interaktion und
Portierbarkeit Ergonomie der
Schnittstellen

Angebot Produkte Projekt Beratung

Mittel Analytik Modellierung Sprachen Algebra Logik Hardware Denken Kreativität

Zusammenhänge Gesellschaft Wirtschaft Branche Firma


products/sources/formale Sprachen/PVS/complex_integration/ (Beweissystem der NASA Version 6.0.9^©) Datei vom 28.9.2014 mit Größe 4 kB

Quelle cal_L_real.pvs Sprache: PVS

cal_L_real[(IMPORTING measure_integration@subset_algebra_def)
           T:TYPE, S:sigma_algebra[T]]: THEORY

BEGIN

  IMPORTING cal_L_complex[T,S]

  mu:  VAR measure_type[T,S]
  nu:  VAR finite_measure[T,S]
  h,h1,h2:   VAR [T->real]
  x:   VAR T
  c:   VAR real
  p,q: VAR {a:real | a >= 1}

  cal_L_real_infty?(mu,h):bool
    = cal_L_complex_infty?(mu,lambda x: complex_(h(x),0))

  cal_L_real_infty(mu): TYPE+ = (lambda h: cal_L_real_infty?(mu,h))
                                           CONTAINING (lambda x: 0)

  cal_L_real_infty?(nu,h): bool = cal_L_real_infty?(to_measure(nu),h)

  cal_L_real_infty(nu): TYPE+ = cal_L_real_infty(to_measure(nu))
                                           CONTAINING (lambda x: 0)

  cal_L_real?(mu,p,h):bool
    = cal_L_complex?(mu,p,lambda x: complex_(h(x),0))

  cal_L_real(mu,p): TYPE+ = (lambda h: cal_L_real?(mu,p,h))
                                           CONTAINING (lambda x: 0)

  cal_L_real?(nu,p,h):bool = cal_L_real?(to_measure(nu),p,h)

  cal_L_real(nu,p): TYPE+ = cal_L_real(to_measure(nu),p)
                                           CONTAINING (lambda x: 0)

  cal_L_real_1_def: LEMMA cal_L_real?(mu,1,h) <=> integrable?[T,S,mu](h)

  scal_cal_LR: LEMMA cal_L_real?(mu,p,h) => cal_L_real?(mu,p,c*h)
  sum_cal_LR:  LEMMA cal_L_real?(mu,p,h1) AND cal_L_real?(mu,p,h2) =>
                    cal_L_real?(mu,p,h1+h2)
  opp_cal_LR:  LEMMA cal_L_real?(mu,p,h) => cal_L_real?(mu,p,-h)
  diff_cal_LR: LEMMA cal_L_real?(mu,p,h1) AND cal_L_real?(mu,p,h2) =>
                    cal_L_real?(mu,p,h1-h2)

  prod_cal_LR: LEMMA p > 1 AND 1/p + 1/q = 1  AND
                    cal_L_real?(mu,p,h1) AND
                    cal_L_real?(mu,q,h2) =>
                    cal_L_real?(mu,1,h1*h2)

  scal_cal_L_inftyR: LEMMA cal_L_real_infty?(mu,h) =>
                          cal_L_real_infty?(mu,c*h)
  sum_cal_L_inftyR:  LEMMA cal_L_real_infty?(mu,h1) AND
                          cal_L_real_infty?(mu,h2) =>
                          cal_L_real_infty?(mu,h1+h2)
  opp_cal_L_inftyR:  LEMMA cal_L_real_infty?(mu,h) =>
                          cal_L_real_infty?(mu,-h)
  diff_cal_L_inftyR: LEMMA cal_L_real_infty?(mu,h1) AND
                          cal_L_real_infty?(mu,h2) =>
                          cal_L_real_infty?(mu,h1-h2)
  prod_cal_L_inftyR: LEMMA cal_L_real_infty?(mu,h1) AND
                          cal_L_real_infty?(mu,h2) =>
                          cal_L_real_infty?(mu,h1*h2)

  prod_cal_L_1_inftyR: LEMMA cal_L_real?(mu,1,h1)     AND
                            cal_L_real_infty?(mu,h2) =>
                            cal_L_real?(mu,1,h1*h2)

  prod_cal_L_infty_1R: LEMMA cal_L_real_infty?(mu,h1) AND
                            cal_L_real?(mu,1,h2)     =>
                            cal_L_real?(mu,1,h1*h2)

  scal_cal_L_fmR: LEMMA cal_L_real?(nu,p,h) => cal_L_real?(nu,p,c*h)
  sum_cal_L_fmR:  LEMMA cal_L_real?(nu,p,h1) AND cal_L_real?(nu,p,h2) =>
                       cal_L_real?(nu,p,h1+h2)
  opp_cal_L_fmR:  LEMMA cal_L_real?(nu,p,h) => cal_L_real?(nu,p,-h)
  diff_cal_L_fmR: LEMMA cal_L_real?(nu,p,h1) AND cal_L_real?(nu,p,h2) =>
                       cal_L_real?(nu,p,h1-h2)

  prod_cal_L_fmR: LEMMA p > 1 AND 1/p + 1/q = 1  AND
                       cal_L_real?(nu,p,h1) AND
                       cal_L_real?(nu,q,h2) =>
                       cal_L_real?(nu,1,h1*h2)

  scal_cal_L_infty_fmR: LEMMA cal_L_real_infty?(nu,h) =>
                             cal_L_real_infty?(nu,c*h)
  sum_cal_L_infty_fmR:  LEMMA cal_L_real_infty?(nu,h1) AND
                             cal_L_real_infty?(nu,h2) =>
                             cal_L_real_infty?(nu,h1+h2)
  opp_cal_L_infty_fmR:  LEMMA cal_L_real_infty?(nu,h) =>
                             cal_L_real_infty?(nu,-h)
  diff_cal_L_infty_fmR: LEMMA cal_L_real_infty?(nu,h1) AND
                             cal_L_real_infty?(nu,h2) =>
                             cal_L_real_infty?(nu,h1-h2)
  prod_cal_L_infty_fmR: LEMMA cal_L_real_infty?(nu,h1) AND
                             cal_L_real_infty?(nu,h2) =>
                             cal_L_real_infty?(nu,h1*h2)

  prod_cal_L_1_infty_fmR: LEMMA cal_L_real?(nu,1,h1)     AND
                               cal_L_real_infty?(nu,h2) =>
                               cal_L_real?(nu,1,h1*h2)

  prod_cal_L_infty_1_fmR: LEMMA cal_L_real_infty?(nu,h1) AND
                               cal_L_real?(nu,1,h2)     =>
                               cal_L_real?(nu,1,h1*h2)

END cal_L_real

quality88%

¤ Dauer der Verarbeitung: 0.13 Sekunden (vorverarbeitet) ¤

Wurzel

Suchen

Beweissystem der NASA

Beweissystem Isabelle

NIST Cobol Testsuite

Cephes Mathematical Library

Wiener Entwicklungsmethode

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.