reserve N for with_zero set;
reserve N for with_zero set;
reserve x,y,z,A,B for set,
  f,g,h for Function,
  i,j,k for Nat;
reserve S for IC-Ins-separated non empty
     with_non-empty_values AMI-Struct over N,
  s for State of S;
reserve N for non empty with_zero set,
 S for IC-Ins-separated non empty with_non-empty_values AMI-Struct over N,
  s for State of S;
reserve n for Nat;
reserve N for with_zero non empty set;
reserve N for with_zero non empty set,
  S for IC-Ins-separated non empty AMI-Struct over N;
reserve m,n for Nat;

theorem
 for N be non empty with_zero set
 for S being halting IC-Ins-separated
  non empty with_non-empty_values AMI-Struct over N
  for p being NAT-defined (the InstructionsF of S)-valued Function
 for s being State of S st LifeSpan(p,s) <= j & p halts_on s
   holds Comput(p,s,j) = Comput(p,s,LifeSpan(p,s))
proof
  let N;
  let S be halting IC-Ins-separated
   non empty with_non-empty_values AMI-Struct over N,
  p being NAT-defined (the InstructionsF of S)-valued Function,
  s be State of S;
  assume that
A1: LifeSpan(p,s) <= j and
A2: p halts_on s;
  CurInstr(p,Comput(p,s,LifeSpan(p,s))) = halt S by A2,Def15;
  hence thesis by A1,Th5;
end;
