reserve A for preIfWhileAlgebra;
reserve A for Euclidean preIfWhileAlgebra;
reserve X for non empty countable set;
reserve T for Subset of Funcs(X, INT);
reserve f for Euclidean ExecutionFunction of A, Funcs(X, INT), T;
reserve A for Euclidean preIfWhileAlgebra,
  X for non empty countable set,
   z for (Element of X),
  s,s9 for (Element of Funcs(X, INT)),
  T for Subset of Funcs(X, INT),
  f for Euclidean ExecutionFunction of A, Funcs(X, INT), T,
  v for INT-Variable of A,f,
  t for INT-Expression of A,f;
reserve i for Integer;

theorem
  for x,y being Variable of f holds f.(s, x/=y).x = s.x div s.y & for z
  st z <> x holds f.(s, x/=y).z = s.z
proof
  let x,y be Variable of f;
A1: x/=y = x/=.y;
  (.y).s = s.y by Th22;
  hence thesis by A1,Th46;
end;
