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 Th1:
  i >= k + l implies i >= k
proof
  assume i >= k + l;
  then i + l >= k + l + 0 by XREAL_1:7;
  hence thesis by XREAL_1:6;
end;
