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Datei: gs_bands_2D.pvs Sprache: PVS

Original von: PVS^©

%------------------------------------------------------------------------------
% gs_bands_2D.pvs
% ACCoRD v.1.0
%------------------------------------------------------------------------------

gs_bands_2D[D:posreal,B:nnreal,T: {AB: posreal|AB>B}] : THEORY
BEGIN

  IMPORTING analysis@interm_value_thm,
       vect_analysis@vect2_cont_dot[real],
            omega_v2[D,B,T],
            gs_line[D],
     line_solutions[D],
            bands_util

  s     : VAR Vect2
  vo,vi,
  nvo : VAR Nz_vect2
  sp    : VAR Sp_vect2
  ss    : VAR Ss_vect2
  band  : VAR ConnectedGt(0)
  gsp   : VAR posreal
  k     : VAR real
  pm,
  eps   : VAR Sign

  gs_band_pos : JUDGEMENT
    (band) SUBTYPE_OF posreal

  gs2v2_continuous : JUDGEMENT
    gs2v2(vo) HAS_TYPE continuous_rv_fun

  %-----------------------------------------------%
  % 2-D Ground Speed Critical Points              %
  %-----------------------------------------------%

  gs_critical?(s,vo,vi)(gsp) : bool =
    LET gso = gs2v2(vo)(gsp) IN
    (sqv(s)>=sq(D) AND gs_line?(s,vo,vi)(gso)) OR
    gs_only_circle?(s,vo,vi,T,Entry)(gso) OR
    (B>0 AND gs_only_circle?(s,vo,vi,B,Exit)(gso))

  Vgs(vo,vi)(gsp:real) : Vect2 =
    gs2v2(vo)(gsp)-vi

  Vgs_continuous : JUDGEMENT
    Vgs(vo,vi) HAS_TYPE continuous_rv_fun

  Omega_gs(s,vo,vi) : (continuous_rr?) =
    omega_v2(s) o Vgs(vo,vi)

  Omega_gs_critical : LEMMA
    Omega_gs(s,vo,vi)(gsp) = 0 AND
    NOT (sqv(s)>=sq(D) AND two_parallel?(s,vo,vi)) IMPLIES
      gs_critical?(s,vo,vi)(gsp)

  % Bands do not contain critical points
  gs_band?(s,vo,vi)(band) : bool =
    FORALL (gso:(band)) :
      NOT gs_critical?(s,vo,vi)(gso)

  gs_green?(s,vo,vi)(band) : bool =
    FORALL (gso:(band)) :
      NOT conflict_2D?(s,Vgs(vo,vi)(gso))

  gs_green_two_parallel : LEMMA
    two_parallel?(sp,vo,vi) IMPLIES
    gs_green?(sp,vo,vi)(band)

  gs_red?(s,vo,vi)(band) : bool =
    FORALL (gso:(band)) :
      conflict_2D?(s,Vgs(vo,vi)(gso))

  gs_line_color : LEMMA
    pm*(Q(ss,eps)*vo) > 0 IFF
    IF pm*(eps*det(ss,vo)) > 0 THEN pm*(ss*vo) > 0 AND sq(D)*sqv(vo) > sq(det(ss,vo))
    ELSE pm*(ss*vo) > 0 OR pm*(ss*vo) <= 0 AND sq(D)*sqv(vo) < sq(det(ss,vo))
    ENDIF

  %------------------------------------------------%
  % THEOREM: Ground Speed Green Bands Correctness  %
  %------------------------------------------------%

  gs_green_band : THEOREM
    FORALL (gso:(band)) :
       gs_band?(s,vo,vi)(band) IMPLIES
       (NOT cd2d?(s,Vgs(vo,vi)(gso)) IFF
        gs_green?(s,vo,vi)(band))

  %-----------------------------------------------%
  % THEOREM: Ground Speed Red Bands Correctness   %
  %-----------------------------------------------%

  gs_red_band : THEOREM
    FORALL (gso:(band)) :
      gs_band?(s,vo,vi)(band) IMPLIES
      (cd2d?(s,Vgs(vo,vi)(gso)) IFF
        gs_red?(s,vo,vi)(band))

END gs_bands_2D

¤ Dauer der Verarbeitung: 0.15 Sekunden (vorverarbeitet) ¤

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