theorem
  for x being Variable of f holds f.(s, x%=i).x = s.x mod i & for z st z
  <> x holds f.(s, x%=i).z = s.z
proof
  let x be Variable of f;
A3: .(^(x qua Element of X)).s = s.((^(x qua Element of X)).s) by Def19;
  (.x mod .(i,A,f)).s = (.x).s mod (.(i,A,f).s) by Def30;
  hence thesis by A3,Th24;
end;
