reserve A,B,C for Ordinal,
  K,L,M,N for Cardinal,
  x,y,y1,y2,z,u for object,X,Y,Z,Z1,Z2 for set,
  n for Nat,
  f,f1,g,h for Function,
  Q,R for Relation;
reserve ff for Cardinal-Function;
reserve F,G for Cardinal-Function;
reserve A,B for set;
reserve A,B for Ordinal;
reserve n,k for Nat;

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;
