theorem Th103:
  s in x-succ_of (X, TS) iff ex t st t in X & t, x ==>* s, TS
proof
  thus s in x-succ_of (X, TS) implies ex t st t in X & t, x ==>* s, TS
  proof
    assume s in x-succ_of (X, TS);
    then ex s9 st s9 = s & ex t st t in X & t, x ==>* s9, TS;
    hence thesis;
  end;
  thus thesis;
end;
