set S1 = { [0 ,<*k1*>] where k1 is Element of INT : verum } ;
set S2 = { [1,<*d1*>] where d1 is Element of SCM-Data-Loc : verum } ;
set S3 = { [I2,<*d2,k2*>] where I2 is Element of Segm 14, 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 [0 ,<*0 *>] in { [0 ,<*k1*>] where k1 is Element of INT : verum } ;
then [0 ,<*0 *>] in { [0 ,<*k1*>] where k1 is Element of INT : verum } \/ { [1,<*d1*>] where d1 is Element of SCM-Data-Loc : verum } by XBOOLE_0:def 3;
then [0 ,<*0 *>] in ({ [0 ,<*k1*>] where k1 is Element of INT : verum } \/ { [1,<*d1*>] where d1 is Element of SCM-Data-Loc : verum } ) \/ { [I2,<*d2,k2*>] where I2 is Element of Segm 14, d2 is Element of SCM-Data-Loc , k2 is Element of INT : I2 in {2,3} } by XBOOLE_0:def 3;
then [0 ,<*0 *>] in (({ [0 ,<*k1*>] where k1 is Element of INT : verum } \/ { [1,<*d1*>] where d1 is Element of SCM-Data-Loc : verum } ) \/ { [I2,<*d2,k2*>] where I2 is Element of Segm 14, d2 is Element of SCM-Data-Loc , k2 is Element of INT : I2 in {2,3} } ) \/ { [I3,<*d3,k3,k4*>] where I3 is Element of Segm 14, 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 [0 ,<*0 *>] in SCMPDS-Instr by XBOOLE_0:def 3; :: thesis: verum