reserve
  i, j, k for Element of NAT,
  I,I2,I3,I4 for Element of Segm 15,
  i1 for Element of NAT,
  d1,d2,d3,d4,d5 for Element of SCM-Data-Loc,
  k1,k2 for Integer;

theorem
  [14,{},<*0*>] in SCMPDS-Instr
proof
  set S1=the set of all  [14,{},<*k1*>] where k1 is Element of INT;
  set S2=the set of all  [1,{},<*d1*>];
  set S3={ [I2,{},<*d2,k2*>] where I2 is Element of Segm
  15, d2 is Element of SCM-Data-Loc, k2 is Element of INT : I2 in {2,3} };
  0 is Element of INT by INT_1:def 2;
  then [14,{},<*0*>] in S1;
  then [14,{},<*0*>] in {[0,{},{}]} \/ S1 by XBOOLE_0:def 3;
  then [14,{},<*0*>] in {[0,{},{}]} \/ S1 \/ S2 by XBOOLE_0:def 3;
  then [14,{},<*0*>] in {[0,{},{}]} \/ S1 \/ S2 \/ S3 by XBOOLE_0:def 3;
  then [14,{},<*0*>] in {[0,{},{}]} \/ S1 \/ S2 \/ S3 \/ { [I3,{},<*d3,k3,k4*>]
  where I3 is Element
of Segm 15, d3 is Element of SCM-Data-Loc, k3,k4 is Element of INT: I3 in {4,5,
  6,7,8} } by XBOOLE_0:def 3;
  hence thesis by XBOOLE_0:def 3;
end;
