theorem Th27:
  for f being Function st rng p c= dom f & q = f*p holds len q = len p
proof
  let f be Function;
  assume rng p c= dom f;
  then dom(f*p) = dom p by RELAT_1:27;
  then dom(f*p) = Seg len p by FINSEQ_1:def 3;
  hence thesis by FINSEQ_1:def 3;
end;
