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;

theorem Th73:
  [x,y] is quasi-type of C iff
  x is finite Subset of QuasiAdjs C & y is pure expression of C, a_Type C
proof
  thus
  now
    assume [x,y] is quasi-type of C;
    then ex A,q st ( [x,y] = [A,q]) by Th72;
    hence x is finite Subset of QuasiAdjs C &
    y is pure expression of C, a_Type C by XTUPLE_0:1;
  end;
  thus thesis by Th72;
end;
