theorem Th37:
  X,Y are_equipotent & X is finite implies Y is finite
proof
  assume X,Y are_equipotent;
  then consider f such that
  f is one-to-one and
A1: dom f = X and
A2: rng f = Y;
  given p being Function such that
A3: rng p = X and
A4: dom p in omega;
  take f*p;
  thus rng(f*p) = Y by A1,A2,A3,RELAT_1:28;
  thus thesis by A1,A3,A4,RELAT_1:27;
end;
