theorem Th45:
  for x being Variable of f holds f.(s, x/=i).x = s.x div 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 div .(i,A,f)).s = (.x).s div (.(i,A,f).s) by Def29;
  hence thesis by A3,Th24;
end;
