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 Th1:
  SCM-Instr c= SCM+FSA-Instr
proof
A1: SCM-Instr c= SCM-Instr \/ { [J,{},<*c,f,b*>] : J in {9,10} }
      by XBOOLE_1:7;
   SCM-Instr \/ { [J,{},<*c,f,b*>] : J in {9,10} }
     c= SCM-Instr \/ { [J1,{},<*c2,f2,b2*>] : J1 in {9,10} }
   \/ { [K,{},<*c1,f1*>] : K in {11,12} } by XBOOLE_1:7;
   then
A2: SCM-Instr
     c= SCM-Instr \/ { [J,{},<*c,f,b*>] : J in {9,10} }
   \/ { [K,{},<*c1,f1*>] : K in {11,12} } by A1;
  thus thesis by A2;
end;
