theorem Th21:
  for TS1 being transition-system over F1, TS2 being
transition-system over F2 st the Tran of TS1 = the Tran of TS2 & x1, x2 ==>. y1
  , y2, TS1 holds x1, x2 ==>. y1, y2, TS2
proof
  let TS1 be transition-system over F1, TS2 be transition-system over F2 such
  that
A1: the Tran of TS1 = the Tran of TS2 and
A2: x1, x2 ==>. y1, y2, TS1;
  consider v, w such that
A3: v = y2 & x1, w -->. y1, TS1 & x2 = w^v by A2;
  take v, w;
  thus thesis by A1,A3;
end;
