reserve x,y for set;
reserve i, j, k for Nat;
reserve I,J,K for Element of Segm 9,
  a,a1 for Nat,
  b,b1,c for Element of Data-Locations SCM;

theorem
  for l being Instruction of SCM holds InsCode(l) <= 8
proof
  let l be Instruction of SCM;
  l in { [SCM-Halt,{},{}] } \/ { [J,<*a*>,{}] : J = 6 }
   \/ { [K,<*a1*>,<*b1*>] : K in { 7,8 } }
    or l in { [I,{},<*b,c*>] : I in { 1,2,3,4,5} }
       by AMI_3:27,XBOOLE_0:def 3;
  then
A1: l in { [SCM-Halt,{},{}] } \/ { [J,<*a*>,{}] : J = 6 }
 or l in { [K,<*a1*>,<*b1*>]
  : K in { 7,8 } } or l in { [I,{},<*b,c*>] : I in { 1,2,3,4,5} } by
XBOOLE_0:def 3;
  per cases by A1,XBOOLE_0:def 3;
  suppose
    l in { [SCM-Halt,{},{}] };
    then l = [SCM-Halt,{},{}] by TARSKI:def 1;
    then l`1_3 = 0;
    hence thesis;
  end;
  suppose
    l in { [J,<*a*>,{}] : J = 6 };
    then ex J,a st l = [J,<*a*>,{}] & J = 6;
    then l`1_3 = 6;
    hence thesis;
  end;
  suppose
    l in { [K,<*a1*>,<*b1*>] : K in { 7,8 } };
    then ex K,a1,b1 st l = [K,<*a1*>,<*b1*>] & K in { 7,8 };
    then l`1_3 in { 7,8 };
    then l`1_3 = 7 or l`1_3 = 8 by TARSKI:def 2;
    hence thesis;
  end;
  suppose
    l in { [I,{},<*b,c*>] : I in { 1,2,3,4,5} };
    then ex I,b,c st l = [I,{},<*b,c*>] & I in { 1,2,3,4,5};
    then l`1_3 in { 1,2,3,4,5};
    then l`1_3 = 1 or l`1_3 = 2 or l`1_3 = 3 or l`1_3 = 4 or l`1_3 = 5
     by ENUMSET1:def 3;
    hence thesis;
  end;
end;
