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;
reserve a, b for Data-Location,
  loc for Nat;
reserve I,J,K for Element of Segm 9,
  a,a1 for Nat,
  b,b1,c for Element of Data-Locations SCM,
  da,db for Data-Location;

theorem
  for ins being Instruction of SCM st InsCode ins = 6 holds ex loc
  st ins = SCM-goto loc
proof
  let ins be Instruction of SCM such that
A1: InsCode ins = 6;
  now
    assume ins in { [I,{},<*b,c*>] : I in { 1,2,3,4,5} };
    then consider I,b,c such that
A2: ins = [I,{},<*b,c*>] and
A3: I in { 1,2,3,4,5};
    InsCode ins = I by A2;
    hence contradiction by A1,A3,ENUMSET1:def 3;
  end;
  then
A4: ins in { [SCM-Halt,{},{}] } \/ { [J,<*a*>,{}] : J = 6 }
 \/ { [K,<*a1*>,<*b1*>] :
  K in { 7,8 } } by AMI_3:27,XBOOLE_0:def 3;
  now
    assume ins in { [K,<*a1*>,<*b1*>] : K in { 7,8 } };
    then consider K,a1,b1 such that
A5: ins = [K,<*a1*>,<*b1*>] and
A6: K in { 7,8 };
    InsCode ins = K by A5;
    hence contradiction by A1,A6,TARSKI:def 2;
  end;
  then
A7: ins in { [SCM-Halt,{},{}] } \/ { [J,<*a*>,{}] : J = 6 }
 by A4,XBOOLE_0:def 3;
  InsCode halt SCM = 0 by COMPOS_1:70;
  then not ins in { [SCM-Halt,{},{}] } by A1,AMI_3:26,TARSKI:def 1;
  then ins in { [J,<*a*>,{}] : J = 6 } by A7,XBOOLE_0:def 3;
  then consider J,a such that
A8: ins = [J,<*a*>,{}] & J = 6;
  reconsider loc = a as Nat;
  take loc;
  thus thesis by A8;
end;
