reserve S for non empty non void ManySortedSign,
  V for non-empty ManySortedSet of the carrier of S,
  A for non-empty MSAlgebra over S,
  X for non empty Subset of S-Terms V,
  t for Element of X;

theorem
  X-CircuitStr is void iff for t being Element of X holds t is root &
  not t.{} in [:the carrier' of S, {the carrier of S}:] by TREES_9:25;
