reserve x,y,z for set;
reserve I,J,K for Element of Segm 9,
  i,a,a1,a2 for Nat,
  b,b1,b2,c,c1 for Element of SCM-Data-Loc;

theorem Th3:
  x in { 7, 8 } implies [x,<*a2*>,<*b2*>] in SCM-Instr
proof
  assume
A1: x in { 7, 8 };
  then x = 7 or x = 8 by TARSKI:def 2;
  then reconsider x as Element of Segm 9 by NAT_1:44;
  [x,<*a2*>,<*b2*>] in { [K,<*a1*>,<*b1*>] : K in { 7,8 } } by A1;
  then
  [x,<*a2*>,<*b2*>] in { [SCM-Halt,{},{}] } \/ { [J,<*a*>,{}] : J = 6 }
   \/ { [K,<*a1*>,<*b1*>] : K in { 7,8 } } by XBOOLE_0:def 3;
  hence thesis by XBOOLE_0:def 3;
end;
