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 Th75:
  for m being constructor OperSymbol of C
  st the_result_sort_of m = a_Type C & len p = len the_arity_of m
  holds m-trm p is pure expression of C, a_Type C
proof
  let v be constructor OperSymbol of C such that
A1: the_result_sort_of v = a_Type C;
  assume
A2: len p = len the_arity_of v;
  then reconsider a = v-trm p as expression of C, a_Type C by A1,Th52;
  a is pure
  by A2,Th55;
  hence thesis;
end;
