reserve X,Y,Z for set,
  a,b,c,d,x,y,z,u for object,
  R for Relation,
  A,B,C for Ordinal;
reserve H for Function;
reserve f,g for Function;

theorem
  X,Y are_equipotent & Y,Z are_equipotent implies X,Z are_equipotent
proof
  given f such that
A1: f is one-to-one & dom f = X & rng f = Y;
  given g such that
A2: g is one-to-one & dom g = Y & rng g = Z;
  take g*f;
  thus thesis by A1,A2,RELAT_1:27,28;
end;
