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;
reserve f for valuation of C;
reserve x for variable;

theorem
  for A,B being Subset of QuasiAdjs C st A c= B holds A at f c= B at f
proof
  let A,B be Subset of QuasiAdjs C;
  assume A c= B;
  then A\/B = B by XBOOLE_1:12;
  then B at f = (A at f)\/(B at f) by Th145;
  hence thesis by XBOOLE_1:7;
end;
