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 Th12:
  x, <%e%> ==>* y, <%>E, _bool TS implies x, <%e%> ==>. y, <%>E, _bool TS
proof
  not <%>E in rng dom (the Tran of _bool TS) by REWRITE3:def 1;
  hence thesis by REWRITE3:92;
end;
