theorem
for R,S being Relation st R,S are_isomorphic & R is finite
 holds S is finite
proof
 let R,S be Relation;
  given F being Function such that
A1: F is_isomorphism_of R,S;
  assume R is finite;
  then field R is finite;
  then dom F is finite by A1;
  then rng F is finite by FINSET_1:8;
  then field S is finite by A1;
  hence thesis;
end;
