reserve x for set,
  k for Element of NAT;
reserve s for State of SCMPDS;
reserve d1,d2,d3,d4,d5 for Element of SCM-Data-Loc,
  k1,k2,k3,k4,k5,k6 for Integer;
reserve I for Instruction of SCMPDS;

theorem Th6:
  x in { 2,3 } implies [x,{},<*d2,k2*>] in SCMPDS-Instr
proof
  assume
A1: x in { 2,3 };
  then x = 2 or x = 3 by TARSKI:def 2;
  then reconsider x as Element of Segm 15 by NAT_1:44;
  k2 is Element of INT by INT_1:def 2;
  then [x,{},<*d2,k2*>] in S3 by A1;
  then [x,{},<*d2,k2*>] in {[0,{},{}]} \/ S1 \/ S2 \/ S3 by XBOOLE_0:def 3;
  then [x,{},<*d2,k2*>] in {[0,{},{}]} \/ S1 \/ S2 \/ S3 \/ S4
     by XBOOLE_0:def 3;
  hence thesis by XBOOLE_0:def 3;
end;
