theorem
  x, u ==>* y, TS & y, v ==>* z, TS implies x, u^v ==>* z, TS
proof
  assume that
A1: x, u ==>* y, TS and
A2: y, v ==>* z, TS;
  x, u^v^{} ==>* y, v, TS by A1,Th96;
  then
A3: x, u^v^<%>E ==>* y, v^{}, TS;
  y, v ==>* z, <%>E, TS by A2;
  then x, u^v^{} ==>* z, <%>E, TS by A3,Th83;
  hence thesis;
end;
