| Quellcodebibliothek Statistik Leitseite products/sources/formale Sprachen/PVS/vect_analysis/ (Beweissystem der NASA Version 6.0.9©) Datei vom 28.9.2014 mit Größe 1017 B |
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Quelle deriv_sincos_ax.pvs Sprache: PVS |
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deriv_sincos_ax[ T : TYPE FROM real ] : THEORY
BEGIN ASSUMING IMPORTING analysis@deriv_domain connected_domain: ASSUMPTION connected?[T] not_one_element : ASSUMPTION not_one_element?[T] ENDASSUMING AUTO_REWRITE+ connected_domain AUTO_REWRITE+ not_one_element IMPORTING trig@trig_basic, analysis@derivatives a,b,t: VAR T k,alpha: VAR real sin_continuous: AXIOM continuous?[T](LAMBDA (x: T): k * sin(alpha * x)) cos_continuous: AXIOM continuous?[T](LAMBDA (x: T): k * cos(alpha * x)) sin_derivable: AXIOM derivable?[T](LAMBDA (x: T): k * sin(alpha * x)) cos_derivable: AXIOM derivable?[T](LAMBDA (x: T): k * cos(alpha * x)) deriv_sin: AXIOM alpha /= 0 IMPLIES deriv[T](LAMBDA (x:T): k*sin(alpha*x)) = (LAMBDA (t: T): k*alpha*cos(alpha*t)) deriv_cos: AXIOM alpha /= 0 IMPLIES deriv[T](LAMBDA (x:T): k*cos(alpha*x)) = (LAMBDA (t: T): -k*alpha*sin(alpha*t)) END deriv_sincos_ax ¤ Dauer der Verarbeitung: 0.1 Sekunden (vorverarbeitet) ¤*© Formatika GbR, Deutschland |
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2026-03-28