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 Th39:
  X misses dom f implies f|X is constant
proof
  assume
A1: X /\ dom f = {};
  now
    set d = the Element of D;
    take d;
    let c;
    thus c in X /\ dom f implies f/.c = d by A1;
  end;
  hence thesis by Th35;
end;
