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;
reserve S for IC-Ins-separated halting
  non empty with_non-empty_values AMI-Struct over N;

theorem
  for F being Instruction-Sequence of S
  for s being State of S, k being Nat
   st F halts_on Comput(F,s,k)
   holds Result(F,Comput(F,s,k)) = Result(F,s)
proof
  let F be Instruction-Sequence of S;
  let s be State of S, k be Nat;
  set s2 = Comput(F,s,k);
  assume
A1: F halts_on s2;
  then consider l being Nat such that
A2: Result(F,s2) = Comput(F,s2,l) &
    CurInstr(F,Result(F,s2)) = halt S by Def9;
A3: F halts_on s by A1,Th22;
  Comput(F,Comput(F,s,k),l) = Comput(F,s,k+l) by Th4;
  hence thesis by A3,A2,Def9;
end;
