theorem Th25:
  for TS being transition-system over F holds x, u ==>. y, v, TS
  implies x, u^w ==>. y, v^w, TS
proof
  let TS be transition-system over F;
  assume x, u ==>. y, v, TS;
  then consider u1 such that
A1: x, u1 -->. y, TS and
A2: u = u1^v;
  u^w = u1^(v^w) by A2,AFINSQ_1:27;
  hence thesis by A1;
end;
