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

theorem Th11:
  for k, n being Element of NAT, s being State of SCM, a being
  Data-Location, il being Element of NAT st IC Comput(F,s,k) =
  n & F.n = a >0_goto il holds ( Comput(F,s,k).a > 0 implies IC
Comput(F,s,k+1) = il) & ( Comput(F,s,k).a <= 0
implies IC Comput(F,s,k
  +1) = (n+1)) & 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, a be Data-Location, il be
  Element of NAT;
  assume that
A1: IC Comput(F,s,k) = n and
A2: F.n = a >0_goto il;
  set csk1 = Comput(F,s,k+1);
  set csk = Comput(F,s,k);
A3:  dom F = NAT by PARTFUN1:def 2;
  csk1 = Exec(CurInstr(F,csk), csk) by Lm1
    .= Exec(a >0_goto il, csk) by A1,A2,A3,PARTFUN1:def 6;
 hence thesis by A1,AMI_3:9;
end;
