reserve x, y, X for set;
reserve E for non empty set;
reserve e for Element of E;
reserve u, u1, v, v1, v2, w, w9, w1, w2 for Element of E^omega;
reserve F for Subset of E^omega;
reserve i, k, l for Nat;
reserve TS for non empty transition-system over F;
reserve S, T for Subset of TS;
reserve SA for non empty semiautomaton over F;
reserve A for non empty automaton over F;
reserve p, q for Element of A;
reserve TS for non empty transition-system over Lex(E) \/ {<%>E};

theorem Th26:
  ==>.-relation(TS) reduces [x, u^w], [y, v^w] implies
  ==>.-relation(TS) reduces [x, u], [y, v]
proof
  assume ==>.-relation(TS) reduces [x, u^w], [y, v^w];
  then
  ex p being RedSequence of ==>.-relation(TS) st p.1 = [x, u ^w] & p.len p
  = [y, v^w] by REWRITE1:def 3;
  then
  ex q being RedSequence of ==>.-relation(TS) st q.1 = [x, u ] & q.len q =
  [y, v] by Th25;
  hence thesis by REWRITE1:def 3;
end;
