theorem Th31:
  for x being Variable of f holds f.(s, x*=i).x = s.x*i & for z st
  z <> x holds f.(s, x*=i).z = s.z
proof
  let x be Variable of f;
A2: .(^(x qua Element of X)).s = s.((^(x qua Element of X)).s) by Def19;
  (.x*i).s = ((.x).s*i) by Def10;
  hence thesis by A2,Th24;
end;
