reserve x,y,X,Y for set;
reserve C,D,E for non empty set;
reserve SC for Subset of C;
reserve SD for Subset of D;
reserve SE for Subset of E;
reserve c,c1,c2 for Element of C;
reserve d,d1,d2 for Element of D;
reserve e for Element of E;
reserve f,f1,g for PartFunc of C,D;
reserve t for PartFunc of D,C;
reserve s for PartFunc of D,E;
reserve h for PartFunc of C,E;
reserve F for PartFunc of D,D;

theorem
  (SC --> d)|SC is constant
proof
  take d;
  let c;
  assume
A1: c in dom((SC --> d)|SC);
  then
A2: c in SC /\ dom (SC --> d) by RELAT_1:61;
  then c in SC by XBOOLE_0:def 4;
  then (SC --> d)/.c = d by Th29;
  then ((SC --> d)|SC)/.c = d by A2,Th16;
  hence thesis by A1,PARTFUN1:def 6;
end;
