reserve i for Nat,
  j for Element of NAT,
  X,Y,x,y,z for set;
reserve C for initialized ConstructorSignature,
  s for SortSymbol of C,
  o for OperSymbol of C,
  c for constructor OperSymbol of C;
reserve a,b for expression of C, an_Adj C;
reserve t, t1,t2 for expression of C, a_Type C;
reserve p for FinSequence of QuasiTerms C;
reserve e for expression of C;
reserve a,a9 for expression of C, an_Adj C;
reserve q for pure expression of C, a_Type C,
  A for finite Subset of QuasiAdjs C;
reserve T for quasi-type of C;

theorem
  len p = len the_arity_of c implies
  vars (c-trm p) = union {vars t where t is quasi-term of C: t in rng p}
proof
  assume len p = len the_arity_of c;
  then c-trm p = [c, the carrier of C]-tree p by Def35;
  hence thesis by Th89;
end;
