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;

theorem Th7:
  len u > 0 implies ex e, u1 st u = <%e%>^u1
proof
  assume len u > 0;
  then consider k such that
A1: len u = k + 1 by NAT_1:6;
  ex u1, e st len u1 = k & u = <%e%>^u1 by A1,FLANG_1:9;
  hence thesis;
end;
