theorem Th25:
  for x being Variable of f for i being Integer holds f.(s,
  x:=i).x = i & for z st z <> x holds f.(s, x:=i).z = s.z
proof
  let x be Variable of f;
  let i be Integer;
A1: .(i,A,f).s = i;
  (^x).s = x;
  hence thesis by A1,Th24;
end;
