theorem Th49:
  for b being Element of X for g being Euclidean ExecutionFunction
  of A,Funcs(X,INT), Funcs(X,INT)\(b,0) for x being Variable of g holds g.(s, x
  is_odd).b = s.x mod 2 & g.(s, x is_even).b = (s.x+1) mod 2 & for z st z <> b
  holds g.(s, x is_odd).z = s.z
proof
  let b be Element of X;
  let f be Euclidean ExecutionFunction of A,Funcs(X,INT), Funcs(X,INT)\(b,0);
  let x be Variable of f;
  (.x).s = s.x by Th22;
  hence thesis by Th48;
end;
