theorem Th19:
  S c= T & s ==>. t, S implies s ==>.t, T
proof
  assume that
A1: S c= T and
A2: s ==>. t, S;
  consider v, w, s1, t1 such that
A3: s = v^s1^w & t = v^t1^w and
A4: s1 -->. t1, S by A2;
  s1 -->. t1, T by A1,A4;
  hence thesis by A3;
end;
