reserve F for total
  NAT-defined (the InstructionsF of SCM)-valued Function;

theorem Th9:
  for k, n being Element of NAT, s being State of SCM, il being
  Element of NAT st IC Comput(F,s,k) = n &
   F.n = SCM-goto il
holds IC Comput(F,s,k+1) = il & for d being Data-Location holds
   Comput(F,s,k+1).d = Comput(F,s,k).d
proof
  let k, n be Element of NAT, s be State of SCM, il be Element of NAT;
  assume
A1: IC Comput(F,s,k) = n & F.n = SCM-goto il;
  set csk1 = Comput(F,s,k+1);
  set csk = Comput(F,s,k);
A2:  dom F = NAT by PARTFUN1:def 2;
A3: csk1 = Exec(CurInstr(F,csk), csk) by Lm1
    .= Exec(SCM-goto il, csk) by A1,A2,PARTFUN1:def 6;
  hence IC csk1 = il by AMI_3:7;
  thus thesis by A3,AMI_3:7;
end;
