
theorem Th19:
  for X,Y being set, f being Function holds X-indexing f tolerates Y-indexing f
proof
  let X,Y be set, f be Function;
  Y-indexing f = ((X \/ Y)-indexing f)|Y by Th17,XBOOLE_1:7;
  then
A1: Y-indexing f c= (X \/ Y) -indexing f by RELAT_1:59;
  X-indexing f = ((X \/ Y)-indexing f)|X by Th17,XBOOLE_1:7;
  then X-indexing f c= (X \/ Y)-indexing f by RELAT_1:59;
  hence thesis by A1,PARTFUN1:52;
end;
