reserve x,y,z for set,
  k for Element of NAT;
reserve J,J1,K for Element of Segm 13,
  a for Element of NAT,
  b,b1,b2,c,c1,c2 for Element of SCM-Data-Loc,
  f,f1,f2 for Element of SCM+FSA-Data*-Loc;

theorem Th5:
  x in {11,12} implies [x,{},<*c,f*>] in SCM+FSA-Instr
proof
  assume
A1: x in {11,12};
  then x = 11 or x = 12 by TARSKI:def 2;
  then reconsider x as Element of Segm 13 by NAT_1:44;
  [x,{},<*c,f*>] in { [K,{},<*c1,f1*>] : K in {11,12}} by A1;
  then [x,{},<*c,f*>] in SCM-Instr \/ { [J,{},<*c2,f2,b*>] : J in {9,10} }
    \/ { [K,{},<*c1,f1*>] : K in {11,12} }
    by XBOOLE_0:def 3;
  then [x,{},<*c,f*>] in SCM-Instr \/ { [J,{},<*c2,f2,b*>] : J in {9,10} }
   \/ { [K,{},<*c1,f1*>] : K in {11,12} };
  hence thesis;
end;
