theorem Th79:
  not <%>E in rng dom (the Tran of TS) implies (==>.-relation(TS)
reduces [x, <%e%>], [y, <%>E] implies [[x, <%e%>], [y, <%>E]] in ==>.-relation(
  TS))
proof
  assume
A1: not <%>E in rng dom (the Tran of TS);
  assume ==>.-relation(TS) reduces [x, <%e%>], [y, <%>E];
  then consider P being RedSequence of ==>.-relation(TS) such that
A2: P.1 = [x, <%e%>] & P.len P = [y, <%>E] by REWRITE1:def 3;
A3: len P = 1 + 1 by A1,A2,Th63;
  then 1 in dom P & 1 + 1 in dom P by FINSEQ_3:25;
  hence thesis by A2,A3,REWRITE1:def 2;
end;
