reserve m,n for Nat,
  a,b for Int_position,
  i,j for Instruction of SCMPDS,
  s,s1,s2 for State of SCMPDS,
  I,J for Program of SCMPDS;

theorem Th6:
  (I ';' i). card I =i &  card I in dom (I ';' i)
proof
A1:  0 in dom Load i by COMPOS_1:50;
  thus (I ';' i). (card I) =(I ';' i).(0+card I)
    .=(I ';' i).( 0 + card I)
    .=(I ';' Load i).( 0 + card I) by SCMPDS_4:def 3
    .=(Load i). 0 by A1,AFINSQ_1:def 3
    .=i;
  card (I ';' i) = card I+1 by Th4;
  then card I < card (I ';' i) by XREAL_1:29;
  hence thesis by AFINSQ_1:66;
end;
