reserve X,Y for set,
  x,x1,x2,y,y1,y2,z for set,
  f,g,h for Function;
reserve M for non empty set;
reserve D for non empty set;
reserve P for Relation;
reserve O for Order of X;
reserve R,P for Relation,
  X,X1,X2,Y,Z,x,y,z,u for set,
  g,h for Function,
  O for Order of X,
  D for non empty set,
  d,d1,d2 for Element of D,
  A1,A2,B for Ordinal,
  L,L1,L2 for Sequence;
reserve A,C for Ordinal;

theorem
  dom R is finite & rng R is finite implies R is finite
proof
  assume that
A1: dom R is finite and
A2: rng R is finite;
  field R is finite by A1,A2;
  hence thesis by Th86;
end;
