reserve i,j,k for Nat;

theorem Th6:
  for s being State of SCM
  for P being Instruction-Sequence of SCM
  st Euclid-Algorithm c= P
  for k,i st IC
  Comput(P,s,k) = 4 holds Comput(P,s,k+i) = Comput(P,s,k)
proof
  let s be State of SCM;
  let P be Instruction-Sequence of SCM such that
A1: Euclid-Algorithm c= P;
  let k,i;
  assume IC Comput(P,s,k) = 4;
  then P halts_at IC Comput(P,s,k) by A1,Lm3;
  hence thesis by EXTPRO_1:20,NAT_1:11;
end;
