theorem Th63:
  not <%>E in rng dom (the Tran of TS) implies for P being
  RedSequence of ==>.-relation(TS) st P.1 = [x, <%e%>] & P.len P = [y, <%>E]
  holds len P = 2
proof
  assume
A1: not <%>E in rng dom (the Tran of TS);
  let P be RedSequence of ==>.-relation(TS) such that
A2: P.1 = [x, <%e%>] & P.len P = [y, <%>E];
  len P <= len <%e%> + 1 by A1,A2,Th62;
  then
 len P <= 1 + 1 by AFINSQ_1:34;
  then
A3: len P = 0 or ... or len P = 2;
  len P <> 1 by A2,XTUPLE_0:1;
  hence thesis by A3;
end;
