theorem Th15:
  for Q being Subset of SA holds w in left-Lang(Q) iff Q meets w
  -succ_of (the InitS of SA, SA)
proof
  let Q be Subset of SA;
  thus w in left-Lang(Q) implies Q meets w-succ_of (the InitS of SA, SA)
  proof
    assume w in left-Lang(Q);
    then ex w9 st w9 = w & Q meets w9-succ_of (the InitS of SA, SA);
    hence thesis;
  end;
  thus thesis;
end;
